INTERNATIONAL TELECOMMUNICATION UNION

CCITTTHE INTERNATIONALTELEGRAPH AND TELEPHONECONSULTATIVE COMMITTEETERMINAL EQUIPMENT AND PROTOCOLSFOR TELEMATIC SERVICESINFORMATION TECHNOLOGY –DIGITAL COMPRESSION AND CODING
OF CONTINUOUS-TONE STILL IMAGES –REQUIREMENTS AND GUIDELINES

Recommendation T.81

T.81
(09/92)Foreword
ITU (International Telecommunication Union) is the United Nations Specialized Agency in the field of
telecommunications. The CCITT (the International Telegraph and Telephone Consultative Committee) is a permanentorgan of the ITU. Some 166 member countries, 68 telecom operating entities, 163 scientific and industrial organizations
and 39 international organizations participate in CCITT which is the body which sets world telecommunications
standards (Recommendations).
The approval of Recommendations by the members of CCITT is covered by the procedure laid down in CCITT Resolution
No. 2 (Melbourne, 1988). In addition, the Plenary Assembly of CCITT, which meets every four years, approves
Recommendations submitted to it and establishes the study programme for the following period.
In some areas of information technology, which fall within CCITT’s purview, the necessary standards are prepared on acollaborative basis with ISO and IEC. The text of CCITT Recommendation T.81 was approved on 18th September 1992.
The identical text is also published as ISO/IEC International Standard 10918-1.

___________________CCITT NOTE

In this Recommendation, the expression “Administration” is used for conciseness to indicate both a telecommunication
administration and a recognized private operating agency.

 ITU 1993
All rights reserved. No part of this publication may be reproduced or utilized in any form or by any means, electronic ormechanical, including photocopying and microfilm, without permission in writing from the ITU.

Contents
Page
Introduction..............................................................................................................................................................

iii

1

Scope ............................................................................................................................................................

1

2

Normative references.....................................................................................................................................

1

3

Definitions, abbreviations and symbols .........................................................................................................

1

4

General .........................................................................................................................................................

12

5

Interchange format requirements ...................................................................................................................

23

6

Encoder requirements ...................................................................................................................................

23

7

Decoder requirements ...................................................................................................................................

23

Annex A – Mathematical definitions........................................................................................................................

24

Annex B – Compressed data formats........................................................................................................................

31

Annex C – Huffman table specification....................................................................................................................

50

Annex D – Arithmetic coding ..................................................................................................................................

54

Annex E – Encoder and decoder control procedures ................................................................................................

77

Annex F – Sequential DCT-based mode of operation...............................................................................................

87

Annex G – Progressive DCT-based mode of operation.............................................................................................

119

Annex H – Lossless mode of operation ....................................................................................................................

132

Annex J – Hierarchical mode of operation................................................................................................................

137

Annex K – Examples and guidelines........................................................................................................................

143

Annex L – Patents....................................................................................................................................................

179

Annex M – Bibliography..........................................................................................................................................

181

CCITT Rec. T.81 (1992 E)iIntroduction
This CCITT Recommendation | ISO/IEC International Standard was prepared by CCITT Study Group VIII and the Joint
Photographic Experts Group (JPEG) of ISO/IEC JTC 1/SC 29/WG 10. This Experts Group was formed in 1986 toestablish a standard for the sequential progressive encoding of continuous tone grayscale and colour images.
Digital Compression and Coding of Continuous-tone Still images, is published in two parts:–

Requirements and guidelines;–

Compliance testing.

This part, Part 1, sets out requirements and implementation guidelines for continuous-tone still image encoding anddecoding processes, and for the coded representation of compressed image data for interchange between applications.
These processes and representations are intended to be generic, that is, to be applicable to a broad range of applications forcolour and grayscale still images within communications and computer systems. Part 2, sets out tests for determining
whether implementations comply with the requirments for the various encoding and decoding processes specified in Part1.
The user’s attention is called to the possibility that – for some of the coding processes specified herein – compliance withthis Recommendation | International Standard may require use of an invention covered by patent rights. See Annex L for
further information.
The requirements which these processes must satisfy to be useful for specific image communications applications such as
facsimile, Videotex and audiographic conferencing are defined in CCITT Recommendation T.80. The intent is that thegeneric processes of Recommendation T.80 will be incorporated into the various CCITT Recommendations for terminal
equipment for these applications.
In addition to the applications addressed by the CCITT and ISO/IEC, the JPEG committee has developped a compression
standard to meet the needs of other applications as well, including desktop publishing, graphic arts, medical imaging andscientific imaging.
Annexes A, B, C, D, E, F, G, H and J are normative, and thus form an integral part of this Specification. Annexes K, L
and M are informative and thus do not form an integral part of this Specification.
This Specification aims to follow the guidelines of CCITT and ISO/IEC JTC 1 on Rules for presentation of CCITT |ISO/IEC common text.

ISO/IEC 10918-1 : 1993(E)INTERNATIONAL STANDARD
ISO/IEC 10918-1 : 1993(E)
CCITT Rec. T.81 (1992 E)

CCITT RECOMMENDATIONINFORMATION TECHNOLOGY – DIGITAL COMPRESSION
AND CODING OF CONTINUOUS-TONE STILL IMAGES –REQUIREMENTS AND GUIDELINES
1

Scope

This CCITT Recommendation | International Standard is applicable to continuous-tone – grayscale or colour – digital still
image data. It is applicable to a wide range of applications which require use of compressed images. It is not applicable tobi-level image data.
This Specification–

specifies processes for converting source image data to compressed image data;–

specifies processes for converting compressed image data to reconstructed image data;–

gives guidance on how to implement these processes in practice;–specifies coded representations for compressed image data.

NOTE – This Specification does not specify a complete coded image representation. Such representations may include
certain parameters, such as aspect ratio, component sample registration, and colour space designation, which are applicationdependent.

2

Normative references

The following CCITT Recommendations and International Standards contain provisions which, through reference in thistext, constitute provisions of this CCITT Recommendation | International Standard. At the time of publication, theeditions indicated were valid. All Recommendations and Standards are subject to revision, and parties to agreements
based on this CCITT Recommendation | International Standard are encouraged to investigate the possibility of applying
the most recent edition of the Recommendations and Standards listed below. Members of IEC and ISO maintain registersof currently valid International Standards. The CCITT Secretariat maintains a list of currently valid CCITT
Recommendations.
–

CCITT Recommendation T.80 (1992), Common components for image compression and communication –Basic principles.

3

Definitions, abbreviations and symbols

3.1

Definitions and abbreviations

For the purposes of this Specification, the following definitions apply.
3.1.1
abbreviated format: A representation of compressed image data which is missing some or all of the tablespecifications required for decoding, or a representation of table-specification data without frame headers, scan headers,and entropy-coded segments.
3.1.2

AC coefficient: Any DCT coefficient for which the frequency is not zero in at least one dimension.

3.1.3(adaptive) (binary) arithmetic decoding: An entropy decoding procedure which recovers the sequence ofsymbols from the sequence of bits produced by the arithmetic encoder.
3.1.4(adaptive) (binary) arithmetic encoding: An entropy encoding procedure which codes by means of a recursive
subdivision of the probability of the sequence of symbols coded up to that point.
3.1.5
application environment: The standards for data representation, communication, or storage which have been
established for a particular application.
CCITT Rec. T.81 (1992 E)

1

ISO/IEC 10918-1 : 1993(E)3.1.6

arithmetic decoder: An embodiment of arithmetic decoding procedure.

3.1.7

arithmetic encoder: An embodiment of arithmetic encoding procedure.

3.1.8
baseline (sequential): A particular sequential DCT-based encoding and decoding process specified in thisSpecification, and which is required for all DCT-based decoding processes.
3.1.9

binary decision: Choice between two alternatives.

3.1.10bit stream: Partially encoded or decoded sequence of bits comprising an entropy-coded segment.

3.1.11

block: An 8 × 8 array of samples or an 8 × 8 array of DCT coefficient values of one component.

3.1.12

block-row: A sequence of eight contiguous component lines which are partitioned into 8 × 8 blocks.

3.1.13byte: A group of 8 bits.

3.1.14 byte stuffing: A procedure in which either the Huffman coder or the arithmetic coder inserts a zero byte into
the entropy-coded segment following the generation of an encoded hexadecimal X’FF’ byte.
3.1.15 carry bit: A bit in the arithmetic encoder code register which is set if a carry-over in the code register overflows
the eight bits reserved for the output byte.
3.1.16 ceiling function: The mathematical procedure in which the greatest integer value of a real number is obtainedby selecting the smallest integer value which is greater than or equal to the real number.
3.1.17class (of coding process): Lossy or lossless coding processes.

3.1.18 code register: The arithmetic encoder register containing the least significant bits of the partially completed
entropy-coded segment. Alternatively, the arithmetic decoder register containing the most significant bits of a partiallydecoded entropy-coded segment.
3.1.19coder: An embodiment of a coding process.

3.1.20coding: Encoding or decoding.

3.1.21

coding model: A procedure used to convert input data into symbols to be coded.

3.1.22(coding) process: A general term for referring to an encoding process, a decoding process, or both.

3.1.23colour image: A continuous-tone image that has more than one component.

3.1.24columns: Samples per line in a component.

3.1.25component: One of the two-dimensional arrays which comprise an image.

3.1.26compressed data: Either compressed image data or table specification data or both.

3.1.27compressed image data: A coded representation of an image, as specified in this Specification.

3.1.28compression: Reduction in the number of bits used to represent source image data.

3.1.29 conditional exchange: The interchange of MPS and LPS probability intervals whenever the size of the LPS
interval is greater than the size of the MPS interval (in arithmetic coding).
3.1.30 (conditional) probability estimate: The probability value assigned to the LPS by the probability estimation
state machine (in arithmetic coding).
3.1.31 conditioning table: The set of parameters which select one of the defined relationships between prior coding
decisions and the conditional probability estimates used in arithmetic coding.
3.1.32 context: The set of previously coded binary decisions which is used to create the index to the probability
estimation state machine (in arithmetic coding).
3.1.33

continuous-tone image: An image whose components have more than one bit per sample.

3.1.34

data unit: An 8 × 8 block of samples of one component in DCT-based processes; a sample in lossless processes.

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ISO/IEC 10918-1 : 1993(E)3.1.35

DC coefficient: The DCT coefficient for which the frequency is zero in both dimensions.

3.1.36 DC prediction: The procedure used by DCT-based encoders whereby the quantized DC coefficient from thepreviously encoded 8 × 8 block of the same component is subtracted from the current quantized DC coefficient.
3.1.37 (DCT) coefficient: The amplitude of a specific cosine basis function – may refer to an original DCT coefficient,
to a quantized DCT coefficient, or to a dequantized DCT coefficient.
3.1.38decoder: An embodiment of a decoding process.

3.1.39image.

decoding process: A process which takes as its input compressed image data and outputs a continuous-tone

3.1.40 default conditioning: The values defined for the arithmetic coding conditioning tables at the beginning ofcoding of an image.
3.1.41 dequantization: The inverse procedure to quantization by which the decoder recovers a representation of the
DCT coefficients.
3.1.42 differential component: The difference between an input component derived from the source image and thecorresponding reference component derived from the preceding frame for that component (in hierarchical mode coding).
3.1.43 differential frame: A frame in a hierarchical process in which differential components are either encoded or
decoded.
3.1.44 (digital) reconstructed image (data): A continuous-tone image which is the output of any decoder defined inthis Specification.
3.1.45 (digital) source image (data): A continuous-tone image used as input to any encoder defined in thisSpecification.
3.1.46(digital) (still) image: A set of two-dimensional arrays of integer data.

3.1.47 discrete cosine transform; DCT: Either the forward discrete cosine transform or the inverse discrete cosine
transform.
3.1.48 downsampling (filter): A procedure by which the spatial resolution of an image is reduced (in hierarchicalmode coding).
3.1.49encoder: An embodiment of an encoding process.

3.1.50data.

encoding process: A process which takes as its input a continuous-tone image and outputs compressed image

3.1.51 entropy-coded (data) segment: An independently decodable sequence of entropy encoded bytes of compressed
image data.
3.1.52 (entropy-coded segment) pointer: The variable which points to the most recently placed (or fetched) byte in
the entropy encoded segment.
3.1.53

entropy decoder: An embodiment of an entropy decoding procedure.

3.1.54 entropy decoding: A lossless procedure which recovers the sequence of symbols from the sequence of bits
produced by the entropy encoder.
3.1.55entropy encoder: An embodiment of an entropy encoding procedure.

3.1.56 entropy encoding: A lossless procedure which converts a sequence of input symbols into a sequence of bits
such that the average number of bits per symbol approaches the entropy of the input symbols.
3.1.57 extended (DCT-based) process: A descriptive term for DCT-based encoding and decoding processes in which
additional capabilities are added to the baseline sequential process.
3.1.58 forward discrete cosine transform; FDCT: A mathematical transformation using cosine basis functions whichconverts a block of samples into a corresponding block of original DCT coefficients.
CCITT Rec. T.81 (1992 E)

3

ISO/IEC 10918-1 : 1993(E)3.1.59 frame: A group of one or more scans (all using the same DCT-based or lossless process) through the data of one
or more of the components in an image.
3.1.60 frame header: A marker segment that contains a start-of-frame marker and associated frame parameters that arecoded at the beginning of a frame.
3.1.61

frequency: A two-dimensional index into the two-dimensional array of DCT coefficients.

3.1.62(frequency) band: A contiguous group of coefficients from the zig-zag sequence (in progressive mode coding).

3.1.63 full progression: A process which uses both spectral selection and successive approximation (in progressivemode coding).
3.1.64grayscale image: A continuous-tone image that has only one component.

3.1.65 hierarchical: A mode of operation for coding an image in which the first frame for a given component isfollowed by frames which code the differences between the source data and the reconstructed data from the previous
frame for that component. Resolution changes are allowed between frames.
3.1.66 hierarchical decoder: A sequence of decoder processes in which the first frame for each component is followed
by frames which decode an array of differences for each component and adds it to the reconstructed data from thepreceding frame for that component.
3.1.67 hierarchical encoder: The mode of operation in which the first frame for each component is followed by frames
which encode the array of differences between the source data and the reconstructed data from the preceding frame forthat component.
3.1.68 horizontal sampling factor: The relative number of horizontal data units of a particular component with respect
to the number of horizontal data units in the other components.
3.1.69Huffman decoder: An embodiment of a Huffman decoding procedure.

3.1.70 Huffman decoding: An entropy decoding procedure which recovers the symbol from each variable length code
produced by the Huffman encoder.
3.1.71

Huffman encoder: An embodiment of a Huffman encoding procedure.

3.1.72

Huffman encoding: An entropy encoding procedure which assigns a variable length code to each input symbol.

3.1.73

Huffman table: The set of variable length codes required in a Huffman encoder and Huffman decoder.

3.1.74

image data: Either source image data or reconstructed image data.

3.1.75 interchange format: The representation of compressed image data for exchange between application
environments.
3.1.76 interleaved: The descriptive term applied to the repetitive multiplexing of small groups of data units from eachcomponent in a scan in a specific order.
3.1.77 inverse discrete cosine transform; IDCT: A mathematical transformation using cosine basis functions whichconverts a block of dequantized DCT coefficients into a corresponding block of samples.
3.1.78 Joint Photographic Experts Group; JPEG: The informal name of the committee which created thisSpecification. The “joint” comes from the CCITT and ISO/IEC collaboration.
3.1.79 latent output: Output of the arithmetic encoder which is held, pending resolution of carry-over (in arithmeticcoding).
3.1.80less probable symbol; LPS: For a binary decision, the decision value which has the smaller probability.

3.1.81 level shift: A procedure used by DCT-based encoders and decoders whereby each input sample is either
converted from an unsigned representation to a two’s complement representation or from a two’s complement
representation to an unsigned representation.

4

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)3.1.82 lossless: A descriptive term for encoding and decoding processes and procedures in which the output of thedecoding procedure(s) is identical to the input to the encoding procedure(s).
3.1.83 lossless coding: The mode of operation which refers to any one of the coding processes defined in thisSpecification in which all of the procedures are lossless (see Annex H).
3.1.84lossy: A descriptive term for encoding and decoding processes which are not lossless.

3.1.85 marker: A two-byte code in which the first byte is hexadecimal FF (X’FF’) and the second byte is a value
between 1 and hexadecimal FE (X’FE’).
3.1.86

marker segment: A marker and associated set of parameters.

3.1.87 MCU-row: The smallest sequence of MCU which contains at least one line of samples or one block-row fromevery component in the scan.
3.1.88minimum coded unit; MCU: The smallest group of data units that is coded.

3.1.89modes (of operation): The four main categories of image coding processes defined in this Specification.

3.1.90more probable symbol; MPS: For a binary decision, the decision value which has the larger probability.

3.1.91 non-differential frame: The first frame for any components in a hierarchical encoder or decoder. The
components are encoded or decoded without subtraction from reference components. The term refers also to any frame inmodes other than the hierarchical mode.
3.1.92 non-interleaved: The descriptive term applied to the data unit processing sequence when the scan has only one
component.
3.1.93parameters: Fixed length integers 4, 8 or 16 bits in length, used in the compressed data formats.

3.1.94point transform: Scaling of a sample or DCT coefficient.

3.1.95precision: Number of bits allocated to a particular sample or DCT coefficient.

3.1.96predictor: A linear combination of previously reconstructed values (in lossless mode coding).

3.1.97 probability estimation state machine: An interlinked table of probability values and indices which is used toestimate the probability of the LPS (in arithmetic coding).
3.1.98 probability interval: The probability of a particular sequence of binary decisions within the ordered set of all
possible sequences (in arithmetic coding).
3.1.99 (probability) sub-interval: A portion of a probability interval allocated to either of the two possible binary
decision values (in arithmetic coding).
3.1.100 procedure: A set of steps which accomplishes one of the tasks which comprise an encoding or decoding
process.
3.1.101 process: See coding process.
3.1.102 progressive (coding): One of the DCT-based processes defined in this Specification in which each scan
typically improves the quality of the reconstructed image.
3.1.103 progressive DCT-based: The mode of operation which refers to any one of the processes defined in Annex G.
3.1.104 quantization table: The set of 64 quantization values used to quantize the DCT coefficients.
3.1.105 quantization value: An integer value used in the quantization procedure.
3.1.106 quantize: The act of performing the quantization procedure for a DCT coefficient.
3.1.107 reference (reconstructed) component: Reconstructed component data which is used in a subsequent frame of ahierarchical encoder or decoder process (in hierarchical mode coding).

CCITT Rec. T.81 (1992 E)

5

ISO/IEC 10918-1 : 1993(E)3.1.108 renormalization: The doubling of the probability interval and the code register value until the probability
interval exceeds a fixed minimum value (in arithmetic coding).
3.1.109 restart interval: The integer number of MCUs processed as an independent sequence within a scan.
3.1.110 restart marker: The marker that separates two restart intervals in a scan.
3.1.111 run (length): Number of consecutive symbols of the same value.
3.1.112 sample: One element in the two-dimensional array which comprises a component.
3.1.113 sample-interleaved: The descriptive term applied to the repetitive multiplexing of small groups of samples fromeach component in a scan in a specific order.
3.1.114 scan: A single pass through the data for one or more of the components in an image.
3.1.115 scan header: A marker segment that contains a start-of-scan marker and associated scan parameters that arecoded at the beginning of a scan.
3.1.116 sequential (coding): One of the lossless or DCT-based coding processes defined in this Specification in which
each component of the image is encoded within a single scan.
3.1.117 sequential DCT-based: The mode of operation which refers to any one of the processes defined in Annex F.
3.1.118 spectral selection: A progressive coding process in which the zig-zag sequence is divided into bands of one ormore contiguous coefficients, and each band is coded in one scan.
3.1.119 stack counter: The count of X’FF’ bytes which are held, pending resolution of carry-over in the arithmetic
encoder.
3.1.120 statistical conditioning: The selection, based on prior coding decisions, of one estimate out of a set of
conditional probability estimates (in arithmetic coding).
3.1.121 statistical model: The assignment of a particular conditional probability estimate to each of the binaryarithmetic coding decisions.
3.1.122 statistics area: The array of statistics bins required for a coding process which uses arithmetic coding.
3.1.123 statistics bin: The storage location where an index is stored which identifies the value of the conditional
probability estimate used for a particular arithmetic coding binary decision.
3.1.124 successive approximation: A progressive coding process in which the coefficients are coded with reduced
precision in the first scan, and precision is increased by one bit with each succeeding scan.
3.1.125 table specification data: The coded representation from which the tables used in the encoder and decoder are
generated and their destinations specified.
3.1.126 transcoder: A procedure for converting compressed image data of one encoder process to compressed image
data of another encoder process.
3.1.127 (uniform) quantization: The procedure by which DCT coefficients are linearly scaled in order to achievecompression.
3.1.128 upsampling (filter): A procedure by which the spatial resolution of an image is increased (in hierarchical mode
coding).
3.1.129 vertical sampling factor: The relative number of vertical data units of a particular component with respect tothe number of vertical data units in the other components in the frame.
3.1.130 zero byte: The X’00’ byte.
3.1.131 zig-zag sequence: A specific sequential ordering of the DCT coefficients from (approximately) lowest spatial
frequency to highest.
3.1.132 3-sample predictor: A linear combination of the three nearest neighbor reconstructed samples to the left andabove (in lossless mode coding).
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ISO/IEC 10918-1 : 1993(E)
3.2

Symbols

The symbols used in this Specification are listed below.
A

probability interval

AC

AC DCT coefficientACji

AC coefficient predicted from DC values

Ahsuccessive approximation bit position, highAl

successive approximation bit position, lowApiith 8-bit parameter in APPn segment

APPn

marker reserved for application segmentsBcurrent byte in compressed data

B2

next byte in compressed data when B = X’FF’

BE

counter for buffered correction bits for Huffman coding in the successive approximation
process

BITS

16-byte list containing number of Huffman codes of each lengthBPpointer to compressed data

BPST

pointer to byte before start of entropy-coded segment

BRcounter for buffered correction bits for Huffman coding in the successive approximation
processBxbyte modified by a carry-overCvalue of bit stream in code registerCicomponent identifier for frameCuhorizontal frequency dependent scaling factor in DCT

Cv

vertical frequency dependent scaling factor in DCT

CE

conditional exchange

C-low

low order 16 bits of the arithmetic decoder code registerCmi

ith 8-bit parameter in COM segment

CNT

bit counter in NEXTBYTE procedure

CODE

Huffman code value

CODESIZE(V)code size for symbol V

COM

comment marker

Csconditioning table value

Csi

component identifier for scanCT

renormalization shift counterCxhigh order 16 bits of arithmetic decoder code register

CX

conditional exchangedjidata unit from horizontal position i, vertical position j

djik

dji for component k

Ddecision decoded
CCITT Rec. T.81 (1992 E)

7

ISO/IEC 10918-1 : 1993(E)Da

in DC coding, the DC difference coded for the previous block from the same component;in lossless coding, the difference coded for the sample immediately to the left

DAC

define-arithmetic-coding-conditioning marker

Db

the difference coded for the sample immediately above

DC

DC DCT coefficientDCi

DC coefficient for ith block in componentDCk

kth DC value used in prediction of AC coefficients

DHP

define hierarchical progression marker

DHT

define-Huffman-tables marker

DIFF

difference between quantized DC and prediction

DNL

define-number-of-lines marker

DQT

define-quantization-tables marker

DRI

define restart interval marker

E

exponent in magnitude category upper boundEC

event counter

ECS

entropy-coded segment

ECSi

ith entropy-coded segment

Ehhorizontal expansion parameter in EXP segment

EHUFCO

Huffman code table for encoder

EHUFSI

encoder table of Huffman code sizes

EOB

end-of-block for sequential; end-of-band for progressive

EOBn

run length category for EOB runs

EOBx

position of EOB in previous successive approximation scan

EOB0, EOB1, ..., EOB14

run length categories for EOB runs

EOI

end-of-image marker

Evvertical expansion parameter in EXP segment

EXP

expand reference components marker

FREQ(V)frequency of occurrence of symbol V

Hihorizontal sampling factor for ith component

Hmaxlargest horizontal sampling factor

HUFFCODE

list of Huffman codes corresponding to lengths in HUFFSIZEHUFFSIZE

list of code lengths

HUFFVAL

list of values assigned to each Huffman codeisubscript index

I

integer variable

Index(S)index to probability estimation state machine table for context index S

jsubscript index

J

integer variable

8

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)JPG

marker reserved for JPEG extensions

JPGnmarker reserved for JPEG extensions

ksubscript index

K

integer variableKmin

index of 1st AC coefficient in band (1 for sequential DCT)

Kx

conditioning parameter for AC arithmetic coding modelL

DC and lossless coding conditioning lower bound parameterLielement in BITS list in DHT segment

Li(t)element in BITS list in the DHT segment for Huffman table tLalength of parameters in APPn segment

LASTK

largest value of K

Lclength of parameters in COM segment

Ld

length of parameters in DNL segment

Lelength of parameters in EXP segment

Lflength of frame header parametersLhlength of parameters in DHT segment

Lp

length of parameters in DAC segment

LPS

less probable symbol (in arithmetic coding)Lqlength of parameters in DQT segment

Lr

length of parameters in DRI segment

Ls

length of scan header parameters

LSB

least significant bitmmodulo 8 counter for RSTm marker

mtnumber of Vi,j parameters for Huffman table t

M

bit mask used in coding magnitude of V

Mn

nth statistics bin for coding magnitude bit pattern category

MAXCODE

table with maximum value of Huffman code for each code length

MCU

minimum coded unit

MCUi

ith MCU

MCUR

number of MCU required to make up one MCU-row

MINCODE

table with minimum value of Huffman code for each code length

MPS

more probable symbol (in arithmetic coding)

MPS(S)

more probable symbol for context-index S

MSB

most significant bit

M2, M3, M4, ... , M15

designation of context-indices for coding of magnitude bits in the arithmetic coding
modelsn

integer variableNdata unit counter for MCU coding

N/A

not applicable
CCITT Rec. T.81 (1992 E)

9ISO/IEC 10918-1 : 1993(E)Nbnumber of data units in MCU

Next_Index_LPS

new value of Index(S) after a LPS renormalization

Next_Index_MPS

new value of Index(S) after a MPS renormalizationNfnumber of components in frame

NL

number of lines defined in DNL segment

Ns

number of components in scan

OTHERS(V)index to next symbol in chainPsample precision

Pqquantizer precision parameter in DQT segment

Pq(t)quantizer precision parameter in DQT segment for quantization table t

PREDquantized DC coefficient from the most recently coded block of the component

Pt

point transform parameterPxcalculated value of sample

Qjiquantizer value for coefficient ACji

Qvu

quantization value for DCT coefficient Svu

Q00

quantizer value for DC coefficient

QACji

quantized AC coefficient predicted from DC values

QDCk

kth quantized DC value used in prediction of AC coefficientsQe

LPS probability estimate

Qe(S)LPS probability estimate for context index S

Qk

kth element of 64 quantization elements in DQT segment

rvu

reconstructed image sample

R

length of run of zero amplitude AC coefficientsRvu

dequantized DCT coefficientRareconstructed sample value

Rbreconstructed sample value

Rc

reconstructed sample value

Rdrounding in prediction calculation

RES

reserved markers

Rirestart interval in DRI segment

RRRR

4-bit value of run length of zero AC coefficientsRScomposite value used in Huffman coding of AC coefficients

RSTm

restart marker number msyx

reconstructed value from IDCT

S

context index

Svu

DCT coefficient at horizontal frequency u, vertical frequency v

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ISO/IEC 10918-1 : 1993(E)SC

context-index for coding of correction bit in successive approximation codingSe

end of spectral selection band in zig-zag sequenceSEcontext-index for coding of end-of-block or end-of-band

SI

Huffman code size

SIGN

1 if decoded sense of sign is negative and 0 if decoded sense of sign is positive

SIZE

length of a Huffman code

SLL

shift left logical operation

SLL α βlogical shift left of α by β bits

SN

context-index for coding of first magnitude category when V is negative

SOF0baseline DCT process frame marker

SOF1

extended sequential DCT frame marker, Huffman coding

SOF2

progressive DCT frame marker, Huffman coding

SOF3

lossless process frame marker, Huffman coding

SOF5

differential sequential DCT frame marker, Huffman coding

SOF6

differential progressive DCT frame marker, Huffman coding

SOF7

differential lossless process frame marker, Huffman coding

SOF9

sequential DCT frame marker, arithmetic coding

SOF10

progressive DCT frame marker, arithmetic coding

SOF11

lossless process frame marker, arithmetic coding

SOF13

differential sequential DCT frame marker, arithmetic coding

SOF14

differential progressive DCT frame marker, arithmetic coding

SOF15

differential lossless process frame marker, arithmetic coding

SOI

start-of-image marker

SOS

start-of-scan marker

SP

context-index for coding of first magnitude category when V is positive

Sqvu

quantized DCT coefficient

SRL

shift right logical operation

SRL α βlogical shift right of α by β bits

Ss

start of spectral selection band in zig-zag sequenceSScontext-index for coding of sign decisionSSSS

4-bit size category of DC difference or AC coefficient amplitude

ST

stack counter

Switch_MPS

parameter controlling inversion of sense of MPS

Sz

parameter used in coding magnitude of V

S0

context-index for coding of V = 0 decisiontsummation index for parameter limits computationT

temporary variable
CCITT Rec. T.81 (1992 E)

11ISO/IEC 10918-1 : 1993(E)Taj

AC entropy table destination selector for jth component in scanTbarithmetic conditioning table destination identifier

Tc

Huffman coding or arithmetic coding table classTdj

DC entropy table destination selector for jth component in scan

TEM

temporary marker

Th

Huffman table destination identifier in DHT segment

Tq

quantization table destination identifier in DQT segment

Tqi

quantization table destination selector for ith component in frameU

DC and lossless coding conditioning upper bound parameterV

symbol or value being either encoded or decodedVivertical sampling factor for ith componentVi,jjth value for length i in HUFFVAL

Vmax

largest vertical sampling factor

Vt

temporary variable

VALPTR

list of indices for first value in HUFFVAL for each code length

V1

symbol value

V2

symbol valuexi

number of columns in ith componentX

number of samples per line in component with largest horizontal dimension

Xi

ith statistics bin for coding magnitude category decision

X1, X2, X3, ... , X15

designation of context-indices for coding of magnitude categories in the arithmetic coding
modelsXHUFCO

extended Huffman code table

XHUFSI

table of sizes of extended Huffman codes

X’values’

values within the quotes are hexadecimalyinumber of lines in ith componentYnumber of lines in component with largest vertical dimension

ZRL

value in HUFFVAL assigned to run of 16 zero coefficientsZZ(K)Kth element in zig-zag sequence of quantized DCT coefficients

ZZ(0)quantized DC coefficient in zig-zag sequence order

4

GeneralThe purpose of this clause is to give an informative overview of the elements specified in this Specification. Anotherpurpose is to introduce many of the terms which are defined in clause 3. These terms are printed in italics upon first usage
in this clause.
12

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)4.1

Elements specified in this Specification

There are three elements specified in this Specification:a)An encoder is an embodiment of an encoding process. As shown in Figure 1, an encoder takes as input
digital source image data and table specifications, and by means of a specified set of procedures generates
as output compressed image data.

b)

A decoder is an embodiment of a decoding process. As shown in Figure 2, a decoder takes as input
compressed image data and table specifications, and by means of a specified set of procedures generates as
output digital reconstructed image data.

c)

The interchange format, shown in Figure 3, is a compressed image data representation which includes alltable specifications used in the encoding process. The interchange format is for exchange between
application environments.

Encoder
TISO0650-93/d001

Sourceimage data

Table
specifications

Compressed
image data

Figure 1 – Encoder
FIGURE 1 [D01] 5 cm = 195%

Decoder
TISO0660-93/d002

Compressed
image data

Table
specifications

Reconstructed
image data

Figure 2 – Decoder
FIGURE 2 [D02] 6 cm 234%
Figures 1 and 2 illustrate the general case for which the continuous-tone source and reconstructed image data consist ofmultiple components. (A colour image consists of multiple components; a grayscale image consists only of a single
component.) A significant portion of this Specification is concerned with how to handle multiple-component images in a
flexible, application-independent way.

CCITT Rec. T.81 (1992 E)

13

ISO/IEC 10918-1 : 1993(E)Application environmentA

Compressed image data, including table specifications

Application environment
B
TISO0670-93/d003

Figure 3 – Interchange format for compressed image data
FIGURE 3 [D03] 9,5cm = 371 %These figures are also meant to show that the same tables specified for an encoder to use to compress a particular image
must be provided to a decoder to reconstruct that image. However, this Specification does not specify how applications
should associate tables with compressed image data, nor how they should represent source image data generally within
their specific environments.
Consequently, this Specification also specifies the interchange format shown in Figure 3, in which table specifications areincluded within compressed image data. An image compressed with a specified encoding process within
one application environment, A, is passed to a different environment, B, by means of the interchange format.
The interchange format does not specify a complete coded image representation. Application-dependent information,e.g. colour space, is outside the scope of this Specification.

4.2

Lossy and lossless compression

This Specification specifies two classes of encoding and decoding processes, lossy and lossless processes. Those based on
the discrete cosine transform (DCT) are lossy, thereby allowing substantial compression to be achieved while producing areconstructed image with high visual fidelity to the encoder’s source image.
The simplest DCT-based coding process is referred to as the baseline sequential process. It provides a capability which is
sufficient for many applications. There are additional DCT-based processes which extend the baseline sequential process
to a broader range of applications. In any decoder using extended DCT-based decoding processes, the baseline decoding
process is required to be present in order to provide a default decoding capability.
The second class of coding processes is not based upon the DCT and is provided to meet the needs of applications
requiring lossless compression. These lossless encoding and decoding processes are used independently of any of the
DCT-based processes.
A table summarizing the relationship among these lossy and lossless coding processes is included in 4.11.
The amount of compression provided by any of the various processes is dependent on the characteristics of the particular
image being compressed, as well as on the picture quality desired by the application and the desired speed of compression
and decompression.

14

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)

4.3

DCT-based coding

Figure 4 shows the main procedures for all encoding processes based on the DCT. It illustrates the special case of a singlecomponent image; this is an appropriate simplification for overview purposes, because all processes specified in thisSpecification operate on each image component independently.

DCT-based encoder

8 × 8 blocks

FDCT

Sourceimage data

Quantizer

Entropy
encoderTable
specifications

Table
specifications

Compressed
image data
TISO0680-93/d004

Figure 4 – DCT-based encoder simplified diagram
FIGURE 4 [D04] 7 cm = 273 %In the encoding process the input component’s samples are grouped into 8 × 8 blocks, and each block is transformed by
the forward DCT (FDCT) into a set of 64 values referred to as DCT coefficients. One of these values is referred to as the
DC coefficient and the other 63 as the AC coefficients.
Each of the 64 coefficients is then quantized using one of 64 corresponding values from a quantization table (determinedby one of the table specifications shown in Figure 4). No default values for quantization tables are specified in thisSpecification; applications may specify values which customize picture quality for their particular image characteristics,
display devices, and viewing conditions.
After quantization, the DC coefficient and the 63 AC coefficients are prepared for entropy encoding, as shown in Figure
5. The previous quantized DC coefficient is used to predict the current quantized DC coefficient, and the difference is
encoded. The 63 quantized AC coefficients undergo no such differential encoding, but are converted into a onedimensional zig-zag sequence, as shown in Figure 5.
The quantized coefficients are then passed to an entropy encoding procedure which compresses the data further. One of
two entropy coding procedures can be used, as described in 4.6. If Huffman encoding is used, Huffman tablespecifications must be provided to the encoder. If arithmetic encoding is used, arithmetic coding conditioning tablespecifications may be provided, otherwise the default conditioning table specifications shall be used.
Figure 6 shows the main procedures for all DCT-based decoding processes. Each step shown performs essentially the
inverse of its corresponding main procedure within the encoder. The entropy decoder decodes the zig-zag sequence ofquantized DCT coefficients. After dequantization the DCT coefficients are transformed to an 8 × 8 block of samples by
the inverse DCT (IDCT).

4.4

Lossless coding

Figure 7 shows the main procedures for the lossless encoding processes. A predictor combines the reconstructed values of
up to three neighbourhood samples at positions a, b, and c to form a prediction of the sample at position x as shown in
Figure 8. This prediction is then subtracted from the actual value of the sample at position x, and the difference islosslessly entropy-coded by either Huffman or arithmetic coding.

CCITT Rec. T.81 (1992 E)

15

ISO/IEC 10918-1 : 1993(E)DC AC 01
DC i - 1

DC i

Block i - 1

Block i

AC 07

DIFF = DC i - DC i - 1
TISO0690-93/d005

AC 70
Differential DC encoding

AC 77
Zig-zag orderFigure 5 – Preparation of quantized coefficients for entropy encoding
FIGURE 5 [D05] 8 cm = 313 %DCT-based decoder

Entropy
decoder

Dequantizer

IDCT

TISO0700-93/d006

Compressed
image data

Table
specifications

Reconstructed
image data

Table
specifications

Figure 6 – DCT-based decoder simplified diagram
FIGURE 6 [D06] 6,5 cm = 254 %Lossless encoder

Predictor

Entropy
encoder
TISO0710-93/d007

Table
specifications

Sourceimage data

Figure 7 – Lossless encoder simplified diagram
FIGURE 7 [D07] 6,5 cm = 254 %16

CCITT Rec. T.81 (1992 E)

Compressed
image data

ISO/IEC 10918-1 : 1993(E)

c

b

a

x

TISO0720-93/d008

Figure 8 – 3-sample prediction neighbourhood
FIGURE 8 [D08] 5 cm = 195 %This encoding process may also be used in a slightly modified way, whereby the precision of the input samples is reduced
by one or more bits prior to the lossless coding. This achieves higher compression than the lossless process (but lower
compression than the DCT-based processes for equivalent visual fidelity), and limits the reconstructed image’s worst-casesample error to the amount of input precision reduction.

4.5

Modes of operation

There are four distinct modes of operation under which the various coding processes are defined: sequential
DCT-based, progressive DCT-based, lossless, and hierarchical. (Implementations are not required to provide all ofthese.) The lossless mode of operation was described in 4.4. The other modes of operation are compared as follows.
For the sequential DCT-based mode, 8 × 8 sample blocks are typically input block by block from left to right, and blockrow by block-row from top to bottom. After a block has been transformed by the forward DCT, quantized and prepared for
entropy encoding, all 64 of its quantized DCT coefficients can be immediately entropy encoded and output as part of thecompressed image data (as was described in 4.3), thereby minimizing coefficient storage requirements.
For the progressive DCT-based mode, 8 × 8 blocks are also typically encoded in the same order, but in multiple scansthrough the image. This is accomplished by adding an image-sized coefficient memory buffer (not shown in Figure 4)
between the quantizer and the entropy encoder. As each block is transformed by the forward DCT and quantized, itscoefficients are stored in the buffer. The DCT coefficients in the buffer are then partially encoded in each of multiple
scans. The typical sequence of image presentation at the output of the decoder for sequential versus progressive modes ofoperation is shown in Figure 9.
There are two procedures by which the quantized coefficients in the buffer may be partially encoded within a scan. First,
only a specified band of coefficients from the zig-zag sequence need be encoded. This procedure is called spectral
selection, because each band typically contains coefficients which occupy a lower or higher part of the frequency spectrum
for that 8 × 8 block. Secondly, the coefficients within the current band need not be encoded to their full (quantized)
accuracy within each scan. Upon a coefficient’s first encoding, a specified number of most significant bits is encoded first.
In subsequent scans, the less significant bits are then encoded. This procedure is called successive approximation. Either
procedure may be used separately, or they may be mixed in flexible combinations.
In hierarchical mode, an image is encoded as a sequence of frames. These frames provide reference reconstructedcomponents which are usually needed for prediction in subsequent frames. Except for the first frame for a given
component, differential frames encode the difference between source components and reference reconstructedcomponents. The coding of the differences may be done using only DCT-based processes, only lossless processes, or
DCT-based processes with a final lossless process for each component. Downsampling and upsampling filters may be
used to provide a pyramid of spatial resolutions as shown in Figure 10. Alternatively, the hierarchical mode can be used to
improve the quality of the reconstructed components at a given spatial resolution.
Hierarchical mode offers a progressive presentation similar to the progressive DCT-based mode but is useful inenvironments which have multi-resolution requirements. Hierarchical mode also offers the capability of progressivecoding to a final lossless stage.

CCITT Rec. T.81 (1992 E)

17

ISO/IEC 10918-1 : 1993(E)
AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAA
AAAA
AAAA
AAAA
AAAA
AAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAA
AAAA
AAAA
AAAA
AAAA
AAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAA
AAAA
AAAA
AAAA
AAAA
AAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAA
AAAA
AAAA
AAAA
AAAA
AAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAA
AAAA
AAAA
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAA
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AAAA
AAAA
AAAA
AAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
Progressive

AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAA
AAAA
AA
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AAAA
AAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAA
AAAA
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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AA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAA
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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
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AA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAATISO0730-93/d009

Sequential

Figure 9 – Progressive versus sequential presentation
FIGURE 9 [D09] 9,5 cm = 371 %TISO0740-93/d010

Figure 10 – Hierarchical multi-resolution encoding
FIGURE 10 [D10] 9.5 cm = 374 %4.6

Entropy coding alternatives

Two alternative entropy coding procedures are specified: Huffman coding and arithmetic coding. Huffman coding
procedures use Huffman tables, determined by one of the table specifications shown in Figures 1 and 2. Arithmetic coding
procedures use arithmetic coding conditioning tables, which may also be determined by a table specification. No default
values for Huffman tables are specified, so that applications may choose tables appropriate for their own environments.
Default tables are defined for the arithmetic coding conditioning.

18

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)The baseline sequential process uses Huffman coding, while the extended DCT-based and lossless processes may use
either Huffman or arithmetic coding.

4.7

Sample precision

For DCT-based processes, two alternative sample precisions are specified: either 8 bits or 12 bits per sample. Applications
which use samples with other precisions can use either 8-bit or 12-bit precision by shifting their source image samples
appropriately. The baseline process uses only 8-bit precision. DCT-based implementations which handle 12-bit source
image samples are likely to need greater computational resources than those which handle only
8-bit source images. Consequently in this Specification separate normative requirements are defined for 8-bit and12-bit DCT-based processes.
For lossless processes the sample precision is specified to be from 2 to 16 bits.

4.8

Multiple-component control

Subclauses 4.3 and 4.4 give an overview of one major part of the encoding and decoding processes – those which operateon the sample values in order to achieve compression. There is another major part as well – the procedures which control
the order in which the image data from multiple components are processed to create the compressed data, and which
ensure that the proper set of table data is applied to the proper data units in the image. (A data unit is a sample for losslessprocesses and an 8 × 8 block of samples for DCT-based processes.)
4.8.1

Interleaving multiple components

Figure 11 shows an example of how an encoding process selects between multiple source image components as well as
multiple sets of table data, when performing its encoding procedures. The source image in this example consists of thethree components A, B and C, and there are two sets of table specifications. (This simplified view does not distinguishbetween the quantization tables and entropy coding tables.)A
B

Encoding
process

C

Sourceimage data

Table specification 1

Table specification 2

Compressed
image data
TISO0750-93/d011

Figure 11 – Component-interleave and table-switching control
FIGURE 11 [D11] 7 cm = 273 %In sequential mode, encoding is non-interleaved if the encoder compresses all image data units in component A before
beginning component B, and then in turn all of B before C. Encoding is interleaved if the encoder compresses a data unit
from A, a data unit from B, a data unit from C, then back to A, etc. These alternatives are illustrated in Figure 12, whichshows a case in which all three image components have identical dimensions: X columns by Y lines, for a total of n data
units each.

CCITT Rec. T.81 (1992 E)

19

ISO/IEC 10918-1 : 1993(E)
X

X

A1 A2

X

B 1 B2

Y

C1 C2

Y

Y

An

Bn

Cn
TISO0760-93/d012

A 1 , A 2, ....A n ,B1 , B 2 , ....Bn ,C1 , C 2 , ....C n

Scan 1

Scan 2

Scan 3

Data unit encoding order, non-interleaved
A 1 , B1 , C1 , A 2, B 2 , C 2 , ....A n, B n , C n
Scan 1
Data unit encoding order, interleaved

Figure 12 – Interleaved versus non-interleaved encoding order

FIGURE 12 [D12] 9,5 cm = 371 %These control procedures are also able to handle cases in which the source image components have different dimensions.
Figure 13 shows a case in which two of the components, B and C, have half the number of horizontal samples relative tocomponent A. In this case, two data units from A are interleaved with one each from B and C. Cases in which components
of an image have more complex relationships, such as different horizontal and vertical dimensions, can be handled aswell. (See Annex A.)

X
A1

A2

Y

X/2

X/2

B1 B2

C1 C2

Y

An

Y

B n/2

C n/2
TISO0770-93/d013

A 1 , A 2 , B 1 , C 1 , A 3, A 4, B 2 , C 2 , ....A n-1, A n, Bn/2, C n/2

Scan 1
Data unit encoding order, interleaved

Figure 13 – Interleaved order for components with different dimensions

FIGURE 13 [D13] 8 cm = 313 %20

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)4.8.2

Minimum coded unit

Related to the concepts of multiple-component interleave is the minimum coded unit (MCU). If the compressed image
data is non-interleaved, the MCU is defined to be one data unit. For example, in Figure 12 the MCU for the noninterleaved case is a single data unit. If the compressed data is interleaved, the MCU contains one or more data units fromeach component. For the interleaved case in Figure 12, the (first) MCU consists of the three interleaved data units A1, B1,
C1. In the example of Figure 13, the (first) MCU consists of the four data units A1, A2 , B1, C1.

4.9

Structure of compressed data

Figures 1, 2, and 3 all illustrate slightly different views of compressed image data. Figure 1 shows this data as the output
of an encoding process, Figure 2 shows it as the input to a decoding process, and Figure 3 shows compressed image datain the interchange format, at the interface between applications.
Compressed image data are described by a uniform structure and set of parameters for both classes of encoding processes(lossy or lossless), and for all modes of operation (sequential, progressive, lossless, and hierarchical). The various parts ofthe compressed image data are identified by special two-byte codes called markers. Some markers are followed byparticular sequences of parameters, as in the case of table specifications, frame header, or scan header. Others are usedwithout parameters for functions such as marking the start-of-image and end-of-image. When a marker is associated with aparticular sequence of parameters, the marker and its parameters comprise a marker segment.
The data created by the entropy encoder are also segmented, and one particular marker – the restart marker – is used toisolate entropy-coded data segments. The encoder outputs the restart markers, intermixed with the entropy-coded data, atregular restart intervals of the source image data. Restart markers can be identified without having to decode thecompressed data to find them. Because they can be independently decoded, they have application-specific uses, such asparallel encoding or decoding, isolation of data corruptions, and semi-random access of entropy-coded segments.
There are three compressed data formats:

4.9.1

a)

the interchange format;b)

the abbreviated format for compressed image data;c)the abbreviated format for table-specification data.

Interchange format

In addition to certain required marker segments and the entropy-coded segments, the interchange format shall include themarker segments for all quantization and entropy-coding table specifications needed by the decoding process. Thisguarantees that a compressed image can cross the boundary between application environments, regardless of how eachenvironment internally associates tables with compressed image data.
4.9.2

Abbreviated format for compressed image data

The abbreviated format for compressed image data is identical to the interchange format, except that it does not include alltables required for decoding. (It may include some of them.) This format is intended for use within applications where
alternative mechanisms are available for supplying some or all of the table-specification data needed for decoding.
4.9.3

Abbreviated format for table-specification data

This format contains only table-specification data. It is a means by which the application may install in the decoder thetables required to subsequently reconstruct one or more images.

4.10

Image, frame, and scanCompressed image data consists of only one image. An image contains only one frame in the cases of sequential andprogressive coding processes; an image contains multiple frames for the hierarchical mode.
A frame contains one or more scans. For sequential processes, a scan contains a complete encoding of one or more image
components. In Figures 12 and 13, the frame consists of three scans when non-interleaved, and one scan if all threecomponents are interleaved together. The frame could also consist of two scans: one with a non-interleaved component,
the other with two components interleaved.

CCITT Rec. T.81 (1992 E)

21

ISO/IEC 10918-1 : 1993(E)For progressive processes, a scan contains a partial encoding of all data units from one or more image components.
Components shall not be interleaved in progressive mode, except for the DC coefficients in the first scan for eachcomponent of a progressive frame.

4.11

Summary of coding processes

Table 1 provides a summary of the essential characteristics of the various coding processes specified in this Specification.
The full specification of these processes is contained in Annexes F, G, H, and J.

Table 1 – Summary: Essential characteristics of coding processes

Baseline process (required for all DCT-based decoders)

•
•
•
•
•
•

DCT-based process
Source image: 8-bit samples within each component
Sequential
Huffman coding: 2 AC and 2 DC tables
Decoders shall process scans with 1, 2, 3, and 4 components
Interleaved and non-interleaved scans

Extended DCT-based processes

•
•
•
•
•
•

DCT-based process
Source image: 8-bit or 12-bit samples
Sequential or progressive
Huffman or arithmetic coding: 4 AC and 4 DC tables
Decoders shall process scans with 1, 2, 3, and 4 components
Interleaved and non-interleaved scans

Lossless processes

•
•
•
•
•
•

Predictive process (not DCT-based)
Source image: P-bit samples (2 ≤ P ≤ 16)
Sequential
Huffman or arithmetic coding: 4 DC tables
Decoders shall process scans with 1, 2, 3, and 4 components
Interleaved and non-interleaved scans

Hierarchical processes

•
•
•
•

22

Multiple frames (non-differential and differential)
Uses extended DCT-based or lossless processes
Decoders shall process scans with 1, 2, 3, and 4 components
Interleaved and non-interleaved scans

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)5Interchange format requirements

The interchange format is the coded representation of compressed image data for exchange between application
environments.
The interchange format requirements are that any compressed image data represented in interchange format shall comply
with the syntax and code assignments appropriate for the decoding process selected, as specified in Annex B.
Tests for whether compressed image data comply with these requirements are specified in Part 2 of this Specification.

6

Encoder requirements

An encoding process converts source image data to compressed image data. Each of Annexes F, G, H, and J specifies a
number of distinct encoding processes for its particular mode of operation.
An encoder is an embodiment of one (or more) of the encoding processes specified in Annexes F, G, H, or J. In order tocomply with this Specification, an encoder shall satisfy at least one of the following two requirements.
An encoder shalla)with appropriate accuracy, convert source image data to compressed image data which comply with theinterchange format syntax specified in Annex B for the encoding process(es) embodied by the encoder;b)with appropriate accuracy, convert source image data to compressed image data which comply with theabbreviated format for compressed image data syntax specified in Annex B for the encoding process(es)embodied by the encoder.

For each of the encoding processes specified in Annexes F, G, H, and J, the compliance tests for the above requirements
are specified in Part 2 of this Specification.
NOTE – There is no requirement in this Specification that any encoder which embodies one of the encoding processes
specified in Annexes F, G, H, or J shall be able to operate for all ranges of the parameters which are allowed for that process. An
encoder is only required to meet the compliance tests specified in Part 2, and to generate the compressed data format according toAnnex B for those parameter values which it does use.

7

Decoder requirements

A decoding process converts compressed image data to reconstructed image data. Each of Annexes F, G, H, and J
specifies a number of distinct decoding processes for its particular mode of operation.
A decoder is an embodiment of one (or more) of the decoding processes specified in Annexes F, G, H, or J. In order tocomply with this Specification, a decoder shall satisfy all three of the following requirements.
A decoder shalla)with appropriate accuracy, convert to reconstructed image data any compressed image data with parameters
within the range supported by the application, and which comply with the interchange format syntax
specified in Annex B for the decoding process(es) embodied by the decoder;b)accept and properly store any table-specification data which comply with the abbreviated format for tablespecification data syntax specified in Annex B for the decoding process(es) embodied by the decoder;c)with appropriate accuracy, convert to reconstructed image data any compressed image data which comply
with the abbreviated format for compressed image data syntax specified in Annex B for the decoding
process(es) embodied by the decoder, provided that the table-specification data required for decoding thecompressed image data has previously been installed into the decoder.

Additionally, any DCT-based decoder, if it embodies any DCT-based decoding process other than baseline sequential,
shall also embody the baseline sequential decoding process.
For each of the decoding processes specified in Annexes F, G, H, and J, the compliance tests for the above requirements
are specified in Part 2 of this Specification.

CCITT Rec. T.81 (1992 E)

23

ISO/IEC 10918-1 : 1993(E)Annex A
Mathematical definitions(This annex forms an integral part of this Recommendation | International Standard)

A.1

Source image

Source images to which the encoding processes specified in this Specification can be applied are defined in this annex.
A.1.1

Dimensions and sampling factors

As shown in Figure A.1, a source image is defined to consist of Nf components. Each component, with unique identifier
Ci, is defined to consist of a rectangular array of samples of xi columns by yi lines. The component dimensions are derived
from two parameters, X and Y, where X is the maximum of the xi values and Y is the maximum of the yi values for allcomponents in the frame. For each component, sampling factors Hi and Vi are defined relating component dimensions xi
and yi to maximum dimensions X and Y, according to the following expressions:Lxi = M X ×
M

Hi Oand y iH max PP

L
MY
M

×

Vi O
,
Vmax PP

where Hmax and V max are the maximum sampling factors for all components in the frame, and   is the ceiling function.
As an example, consider an image having 3 components with maximum dimensions of 512 lines and 512 samples per line,
and with the following sampling factors:
Component 0
Component 1
Component 2

H 0 = 4, V0 = 1
H1 = 2, V1 = 2
H 2 = 1, V2 = 1

Then X = 512, Y = 512, Hmax = 4, Vmax = 2, and xi and yi for each component are
Component 0
Component 1
Component 2

x 0 = 512, y 0 = 256
x1 = 256, y1 = 512
x 2 = 128, y 2 = 256

NOTE – The X, Y, Hi , and Vi parameters are contained in the frame header of the compressed image data (see B.2.2),
whereas the individual component dimensions xi and yi are derived by the decoder. Source images with xi and yi dimensions which do
not satisfy the expressions above cannot be properly reconstructed.

A.1.2

Sample precision

A sample is an integer with precision P bits, with any value in the range 0 through 2P – 1. All samples of all components
within an image shall have the same precision P. Restrictions on the value of P depend on the mode of operation, as
specified in B.2 to B.7.
A.1.3

Data unit

A data unit is a sample in lossless processes and an 8 × 8 block of contiguous samples in DCT-based processes. The leftmost 8 samples of each of the top-most 8 rows in the component shall always be the top-left-most block. With this top-leftmost block as the reference, the component is partitioned into contiguous data units to the right and to the bottom (asshown in Figure A.4).
A.1.4

Orientation

Figure A.1 indicates the orientation of an image component by the terms top, bottom, left, and right. The order by which
the data units of an image component are input to the compression encoding procedures is defined to be left-to-right andtop-to-bottom within the component. (This ordering is precisely defined in A.2.) Applications determine which edges of asource image are defined as top, bottom, left, and right.
24

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)

Ci

Top

Samples

Line

yi

Left
C Nf

Right

xi

C Nf-1
C2
C1

Bottoma) Source image with multiple components

TISO0780-93/d014b) Characteristics of an image component

Figure A.1 – Source image characteristics
FIGURE A-1 [D14] 8 cm = 313 %A.2

Order of source image data encoding

The scan header (see B.2.3) specifies the order by which source image data units shall be encoded and placed within thecompressed image data. For a given scan, if the scan header parameter Ns = 1, then data from only one source component– the component specified by parameter Cs1 – shall be present within the scan. This data is non-interleaved by definition.
If Ns > 1, then data from the Ns components Cs1 through CsNs shall be present within the scan. This data shall always beinterleaved. The order of components in a scan shall be according to the order specified in the frame header.
The ordering of data units and the construction of minimum coded units (MCU) is defined as follows.
A.2.1

Minimum coded unit (MCU)

For non-interleaved data the MCU is one data unit. For interleaved data the MCU is the sequence of data units defined by
the sampling factors of the components in the scan.
A.2.2

Non-interleaved order (Ns = 1)

When Ns = 1 (where Ns is the number of components in a scan), the order of data units within a scan shall be left-to-rightand top-to-bottom, as shown in Figure A.2. This ordering applies whenever Ns = 1, regardless of the values of
H1 and V1.

Top

Left

Right

Bottom

TISO0790-93/d015

Figure A.2 – Non-interleaved data ordering

FIGURE A.2 [D15] 3,5 cm = 136 %CCITT Rec. T.81 (1992 E)

25

ISO/IEC 10918-1 : 1993(E)A.2.3

Interleaved order (Ns > 1)

When Ns > 1, each scan component Csi is partitioned into small rectangular arrays of Hk horizontal data units by Vk
vertical data units. The subscripts k indicate that Hk and Vk are from the position in the frame header componentspecification for which Ck = Csi. Within each Hk by Vk array, data units are ordered from left-to-right and top-to-bottom.
The arrays in turn are ordered from left-to-right and top-to-bottom within each component.
As shown in the example of Figure A.3, Ns = 4, and MCU1 consists of data units taken first from the top-left-most regionof Cs1, followed by data units from the corresponding region of Cs2, then from Cs3 and then from Cs4. MCU2 follows thesame ordering for data taken from the next region to the right for the four components.

Cs 1 : H 1 = 2, V 1 = 2
0

1

2

3

4

Cs 2: H 2 = 2, V 2 = 1
5

0

1

2

3

4

Cs 3 : H 3 = 1, V 3 = 2
501

Cs 4 : H 4 = 1, V4 = 1

2

0

0

0

0

0

1

1

1

1

2

2

3

3

1

2

TISO0800-93/d016

11
1
MCU 1 = d 100 d 01
d10
d11
1
1
1
MCU 2 = d 102 d 03
d12
d13
1
1
1
1
MCU 3 = d 04 d 05 d14 d15
11
1
MCU 4 = d 120 d 21
d30
d31

2
d 200 d 01
2
d 202 d 03
22
d 04 d 05
2
d 210 d 11

3
d 00
d 310
3
d 01
d 311
3
d 02 d 312
3
d 20
d 330

d 400 ,
d 401 ,
d 402 ,4,d 10

Cs1 data units

Cs 2

Cs 3

Cs 4

Figure A.3 – Interleaved data ordering example
FIGURE A.3 [D16] 7,5 cm = 293 %A.2.4

Completion of partial MCU

For DCT-based processes the data unit is a block. If xi is not a multiple of 8, the encoding process shall extend the numberof columns to complete the right-most sample blocks. If the component is to be interleaved, the encoding process shall also
extend the number of samples by one or more additional blocks, if necessary, so that the number of blocks is an integer
multiple of Hi. Similarly, if yi is not a multiple of 8, the encoding process shall extend the number of lines to complete thebottom-most block-row. If the component is to be interleaved, the encoding process shall also extend the number of lines
by one or more additional block-rows, if necessary, so that the number of block-rows is an integer multiple of Vi.
NOTE – It is recommended that any incomplete MCUs be completed by replication of the right-most column and the bottom
line of each component.

For lossless processes the data unit is a sample. If the component is to be interleaved, the encoding process shall extend
the number of samples, if necessary, so that the number is a multiple of Hi. Similarly, the encoding process shall extend
the number of lines, if necessary, so that the number of lines is a multiple of Vi.
Any sample added by an encoding process to complete partial MCUs shall be removed by the decoding process.

A.3

DCT compression

A.3.1

Level shift

Before a non-differential frame encoding process computes the FDCT for a block of source image samples, the samples
shall be level shifted to a signed representation by subtracting 2P – 1, where P is the precision parameter specified in B.2.2.
Thus, when P = 8, the level shift is by 128; when P = 12, the level shift is by 2048.

26

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)After a non-differential frame decoding process computes the IDCT and produces a block of reconstructed image samples,
an inverse level shift shall restore the samples to the unsigned representation by adding 2P – 1 and clamping the results to
the range 0 to 2P – 1.
A.3.2

Orientation of samples for FDCT computation

Figure A.4 shows an image component which has been partitioned into 8 × 8 blocks for the FDCT computations. Figure
A.4 also defines the orientation of the samples within a block by showing the indices used in the FDCT equation of A.3.3.
The definitions of block partitioning and sample orientation also apply to any DCT decoding process and the output
reconstructed image. Any sample added by an encoding process to complete partial MCUs shall be removed by the
decoding process.

Ci

Top

Left

s 00

s 01

s 07

s 10

s 11

s 17

s 70

s 71

Right

s 77
TISO0810-93/d017

BottomFigure A.4 – Partition and orientation of 8 x 8 sample blocks
FIGURE A.4 [D17] 6 cm = 234 %A.3.3

FDCT and IDCT (informative)

The following equations specify the ideal functional definition of the FDCT and the IDCT.
NOTE – These equations contain terms which cannot be represented with perfect accuracy by any real implementation. The
accuracy requirements for the combined FDCT and quantization procedures are specified in Part 2 of this Specification. The accuracy
requirements for the combined dequantization and IDCT procedures are also specified in Part 2 of this Specification.
7s yx cos( 2 x + 1) uπ( 2 y + 1) vπ
cos
16
16

Cu C v S vu cos( 2 x + 1) uπ( 2 y + 1) vπ
cos
16
16

FDCT:

S vu =

1C C ∑4 u v x =0

IDCT:

s yx =

1∑
4 u=0

Cu , Cv = 1

2 for u , v = 0

7

7

∑

y=0

7

∑

v=0

where

Cu , Cv = 1 otherwise
otherwise.
A.3.4

DCT coefficient quantization (informative) and dequantization (normative)

After the FDCT is computed for a block, each of the 64 resulting DCT coefficients is quantized by a uniform quantizer.
The quantizer step size for each coefficient Svu is the value of the corresponding element Qvu from the quantization tablespecified by the frame parameter Tqi (see B.2.2).
CCITT Rec. T.81 (1992 E)

27

ISO/IEC 10918-1 : 1993(E)The uniform quantizer is defined by the following equation. Rounding is to the nearest integer:
F Svu IJ
H Qvu K

Sqvu = round G

Sqvu is the quantized DCT coefficient, normalized by the quantizer step size.
NOTE – This equation contains a term which may not be represented with perfect accuracy by any real implementation. The
accuracy requirements for the combined FDCT and quantization procedures are specified in Part 2 of this Specification.

At the decoder, this normalization is removed by the following equation, which defines dequantization:
Rvu = Sqvu × Qvu

NOTE – Depending on the rounding used in quantization, it is possible that the dequantized coefficient may be outside theexpected range.

The relationship among samples, DCT coefficients, and quantization is illustrated in Figure A.5.
A.3.5

Differential DC encoding

After quantization, and in preparation for entropy encoding, the quantized DC coefficient Sq00 is treated separately fromthe 63 quantized AC coefficients. The value that shall be encoded is the difference (DIFF) between the quantized DC
coefficient of the current block (DCi which is also designated as Sq00) and that of the previous block of the same
component (PRED):
DIFF = DCi − PRED

A.3.6

Zig-zag sequence

After quantization, and in preparation for entropy encoding, the quantized AC coefficients are converted to the zig-zag
sequence. The quantized DC coefficient (coefficient zero in the array) is treated separately, as defined in A.3.5. The zigzag sequence is specified in Figure A.6.

A.4

Point transform

For various procedures data may be optionally divided by a power of 2 by a point transform prior to coding. There arethree processes which require a point transform: lossless coding, lossless differential frame coding in the hierarchicalmode, and successive approximation coding in the progressive DCT mode.
In the lossless mode of operation the point transform is applied to the input samples. In the difference coding of thehierarchical mode of operation the point transform is applied to the difference between the input component samples andthe reference component samples. In both cases the point transform is an integer divide by 2Pt, where Pt is the value of thepoint transform parameter (see B.2.3).
In successive approximation coding the point transform for the AC coefficients is an integer divide by 2Al, where Al is the
successive approximation bit position, low (see B.2.3). The point transform for the DC coefficients is an arithmetic-shiftright by Al bits. This is equivalent to dividing by 2Pt before the level shift (see A.3.1).
The output of the decoder is rescaled by multiplying by 2Pt. An example of the point transform is given in K.10.

28

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Quantize

FDCT

s 00

s 01

s 10

s 11

Top

s 07

S 00

S 01

S 07

Sq 00 Sq 01

Sq 07

s 17

S 10

S 11

S 17

Sq 10 Sq 11

Sq 17

Left

s 70

s71

s77

round

S 70

BottomSvu( )= Sq

Right

Source image samples(after level shift)

S 71

vu

Qvu

Sq 70 Sq 71

S 77

Sq 77

Quantized DCT coefficients

DCT coefficients

Q 00

Q 01

Q 07

Q 10

Q 11

Q 17
Transmission

Q 70

Q 71

Q 77

Quantization table

r 00

r 01

r 10

r 11

Top

r 07

R 00

R 01

R 07

Sq 00 Sq 01

Sq 07

r 17

R 10

R 11

R 17

Sq 10 Sq 11

Sq 17

Left

Rvu = Sqvu × Qvu

Right

r 70

r 71

r 77

R 70

Bottom

R 71

R 77

Sq 70 Sq 71

Sq 77
TISO0820-93/d018

Dequantize

IDCT
Reconstructed image samples(before level shift)

Dequantized DCT coefficients

Received quantized DCT coefficients

Figure A.5 – Relationship between 8 × 8-block samples and DCT coefficients

FIGURE A.5 [D18] 21 cm = 821 %CCITT Rec. T.81 (1992 E)

29

ISO/IEC 10918-1 : 1993(E)

10

11

15

16

14

15

27

28

12

14

17

13

16

26

29

42

13

18

12

17

25

30

41

43

19

11

18

24

31

40

44

53

10

19

23

32

39

45

52

54

20

22

33

38

46

51

55

60

21

34

37

47

50

56

59

61

35

36

48

49

57

58

62

63

Figure A.6 – Zig-zag sequence of quantized DCT coefficients

A.5

Arithmetic procedures in lossless and hierarchical modes of operation

In the lossless mode of operation predictions are calculated with full precision and without clamping of either overflow orunderflow beyond the range of values allowed by the precision of the input. However, the division by two which is part ofsome of the prediction calculations shall be approximated by an arithmetic-shift-right by one bit.
The two’s complement differences which are coded in either the lossless mode of operation or the differential frame
coding in the hierarchical mode of operation are calculated modulo 65 536, thereby restricting the precision of thesedifferences to a maximum of 16 bits. The modulo values are calculated by performing the logical AND operation of the
two’s complement difference with X’FFFF’. For purposes of coding, the result is still interpreted as a 16 bit two’s
complement difference. Modulo 65 536 arithmetic is also used in the decoder in calculating the output from the sum of
the prediction and this two’s complement difference.

30

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1 1993(E)
ISO/IEC 10918-1 : 1 1993(E)
CCITT Rec. T.81 (1992 E)

Annex B
Compressed data formats(This annex forms an integral part of this Recommendation | International Standard)
ISO/IEC 10918-1 : 1993(E)
CCITT Rec. T.81 (1992 E)

This annex specifies three compressed data formats:
a)
b)
c)

the interchange format, specified in B.2 and B.3;
the abbreviated format for compressed image data, specified in B.4;
the abbreviated format for table-specification data, specified in B.5.

B.1 describes the constituent parts of these formats. B.1.3 and B.1.4 give the conventions for symbols and figures used in
the format specifications.

B.1

General aspects of the compressed data format specifications

Structurally, the compressed data formats consist of an ordered collection of parameters, markers, and entropy-coded data
segments. Parameters and markers in turn are often organized into marker segments. Because all of these constituent parts
are represented with byte-aligned codes, each compressed data format consists of an ordered sequence of 8-bit bytes. For
each byte, a most significant bit (MSB) and a least significant bit (LSB) are defined.
B.1.1

Constituent parts

This subclause gives a general description of each of the constituent parts of the compressed data format.
B.1.1.1 Parameters
Parameters are integers, with values specific to the encoding process, source image characteristics, and other features
selectable by the application. Parameters are assigned either 4-bit, 1-byte, or 2-byte codes. Except for certain optionalgroups of parameters, parameters encode critical information without which the decoding process cannot properly
reconstruct the image.
The code assignment for a parameter shall be an unsigned integer of the specified length in bits with the particular valueof the parameter.
For parameters which are 2 bytes (16 bits) in length, the most significant byte shall come first in the compressed data’s
ordered sequence of bytes. Parameters which are 4 bits in length always come in pairs, and the pair shall always be
encoded in a single byte. The first 4-bit parameter of the pair shall occupy the most significant 4 bits of the byte. Within
any 16-, 8-, or 4-bit parameter, the MSB shall come first and LSB shall come last.
B.1.1.2 Markers
Markers serve to identify the various structural parts of the compressed data formats. Most markers start marker segments
containing a related group of parameters; some markers stand alone. All markers are assigned two-byte codes: an X’FF’
byte followed by a byte which is not equal to 0 or X’FF’ (see Table B.1). Any marker may optionally be preceded by any
number of fill bytes, which are bytes assigned code X’FF’.
NOTE – Because of this special code-assignment structure, markers make it possible for a decoder to parse the compresseddata and locate its various parts without having to decode other segments of image data.

B.1.1.3 Marker assignments
All markers shall be assigned two-byte codes: a X’FF’ byte followed by a second byte which is not equal to 0 or X’FF’.
The second byte is specified in Table B.1 for each defined marker. An asterisk (*) indicates a marker which stands alone,that is, which is not the start of a marker segment.

CCITT Rec. T.81 (1992 E)

31

ISO/IEC 10918-1 : 1993(E)Table B.1 – Marker code assignments

Code Assignment

SymbolDescription

Start Of Frame markers, non-differential, Huffman coding
SOF0
SOF1
SOF2
SOF3

X’FFC0’X’FFC1’X’FFC2’X’FFC3’Baseline DCT
Extended sequential DCT
Progressive DCT
Lossless (sequential)

Start Of Frame markers, differential, Huffman coding
SOF5
SOF6
SOF7

X’FFC5’X’FFC6’X’FFC7’

Differential sequential DCT
Differential progressive DCT
Differential lossless (sequential)

Start Of Frame markers, non-differential, arithmetic coding
JPG
SOF9
SOF10
SOF11

X’FFC8’X’FFC9’X’FFCA’X’FFCB’

Reserved for JPEG extensions
Extended sequential DCT
Progressive DCT
Lossless (sequential)

Start Of Frame markers, differential, arithmetic coding
SOF13
SOF14
SOF15

X’FFCD’
X’FFCE’X’FFCF’

Differential sequential DCT
Differential progressive DCT
Differential lossless (sequential)

Huffman table specification
X’FFC4’

DHT

Define Huffman table(s)Arithmetic coding conditioning specification
X’FFCC’

DAC

Define arithmetic coding conditioning(s)Restart interval termination
X’FFD0’ through X’FFD7’

RSTm*

Restart with modulo 8 count “m”
Other markers

X’FFD8’X’FFD9’X’FFDA’X’FFDB’X’FFDC’X’FFDD’
X’FFDE’X’FFDF’X’FFE0’ through X’FFEF’
X’FFF0’ through X’FFFD’
X’FFFE’

SOI*
EOI*
SOS
DQT
DNL
DRI
DHP
EXP
APPn
JPGn
COM

Start of image
End of image
Start of scan
Define quantization table(s)Define number of lines
Define restart interval
Define hierarchical progression
Expand reference component(s)Reserved for application segments
Reserved for JPEG extensions
Comment
Reserved markers

X’FF01’
X’FF02’ through X’FFBF’32

CCITT Rec. T.81 (1992 E)

TEM*
RES

For temporary private use in arithmetic coding
Reserved

ISO/IEC 10918-1 : 1993(E)B.1.1.4 Marker segments
A marker segment consists of a marker followed by a sequence of related parameters. The first parameter in a marker
segment is the two-byte length parameter. This length parameter encodes the number of bytes in the marker segment,
including the length parameter and excluding the two-byte marker. The marker segments identified by the SOF and SOS
marker codes are referred to as headers: the frame header and the scan header respectively.
B.1.1.5 Entropy-coded data segments
An entropy-coded data segment contains the output of an entropy-coding procedure. It consists of an integer number ofbytes, whether the entropy-coding procedure used is Huffman or arithmetic.
NOTES
1Making entropy-coded segments an integer number of bytes is performed as follows: for Huffman coding, 1-bits areused, if necessary, to pad the end of the compressed data to complete the final byte of a segment. For arithmetic coding, byte alignment
is performed in the procedure which terminates the entropy-coded segment (see D.1.8).
2
In order to ensure that a marker does not occur within an entropy-coded segment, any X’FF’ byte generated by either aHuffman or arithmetic encoder, or an X’FF’ byte that was generated by the padding of 1-bits described in NOTE 1 above, is followed
by a “stuffed” zero byte (see D.1.6 and F.1.2.3).

B.1.2

SyntaxIn B.2 and B.3 the interchange format syntax is specified. For the purposes of this Specification, the syntax specificationconsists of:
–
–
–
–
–

the required ordering of markers, parameters, and entropy-coded segments;
identification of optional or conditional constituent parts;
the name, symbol, and definition of each marker and parameter;
the allowed values of each parameter;
any restrictions on the above which are specific to the various coding processes.

The ordering of constituent parts and the identification of which are optional or conditional is specified by the syntax
figures in B.2 and B.3. Names, symbols, definitions, allowed values, conditions, and restrictions are specified immediately
below each syntax figure.
B.1.3

Conventions for syntax figures

The syntax figures in B.2 and B.3 are a part of the interchange format specification. The following conventions, illustrated
in Figure B.1, apply to these figures:–parameter/marker indicator: A thin-lined box encloses either a marker or a single parameter;–

segment indicator: A thick-lined box encloses either a marker segment, an entropy-coded data segment,
or combinations of these;–parameter length indicator: The width of a thin-lined box is proportional to the parameter length (4, 8,
or 16 bits, shown as E, B, and D respectively in Figure B.1) of the marker or parameter it encloses; thewidth of thick-lined boxes is not meaningful;–optional/conditional indicator: Square brackets indicate that a marker or marker segment is only
optionally or conditionally present in the compressed image data;–

ordering: In the interchange format a parameter or marker shown in a figure precedes all of those shown
to its right, and follows all of those shown to its left;–entropy-coded data indicator: Angled brackets indicate that the entity enclosed has been entropy
encoded.
[Optional
segment[

Segment

[B]

D

E

F

TISO0830-93/d019

Figure B.1 – Syntax notation conventions

Figure B.1 [D19], = 3 cm = 118%
CCITT Rec. T.81 (1992 E)

33

ISO/IEC 10918-1 : 1993(E)B.1.4

Conventions for symbols, code lengths, and values

Following each syntax figure in B.2 and B.3, the symbol, name, and definition for each marker and parameter shown in
the figure are specified. For each parameter, the length and allowed values are also specified in tabular form.
The following conventions apply to symbols for markers and parameters:

B.2–

all marker symbols have three upper-case letters, and some also have a subscript. Examples: SOI, SOFn;–

all parameter symbols have one upper-case letter; some also have one lower-case letter and some havesubscripts. Examples: Y, Nf, Hi, Tqi.

General sequential and progressive syntax

This clause specifies the interchange format syntax which applies to all coding processes for sequential DCT-based,
progressive DCT-based, and lossless modes of operation.
B.2.1

High-level syntax

Figure B.2 specifies the order of the high-level constituent parts of the interchange format for all non-hierarchicalencoding processes specified in this Specification.
Compressed image data
SOI

Frame

EOI

Frame
DNL
[ segment[

Scan 1[Scan 2

[Scan last[

Frame header[[[ Tables/
misc.

Scan

[

[ Tables/misc.

Scan header[ECS 0

Entropy-coded segment<MCU 1>, <MCU 2>,

···

RST0

0

<MCU >Ri

ECS last-1

RST last-1 ]Entropy-coded segment<MCU n >, <MCU n + 1 >,···ECS last

last

<MCU

>
last

TISO0840-93/d020

Figure B.2 – Syntax for sequential DCT-based, progressive DCT-based,
and lossless modes of operation
Figure B.2 [D20], = 10 cm = 391.%
The three markers shown in Figure B.2 are defined as follows:
SOI: Start of image marker – Marks the start of a compressed image represented in the interchange format or
abbreviated format.
EOI: End of image marker – Marks the end of a compressed image represented in the interchange format or
abbreviated format.
RSTm: Restart marker – A conditional marker which is placed between entropy-coded segments only if restartis enabled. There are 8 unique restart markers (m = 0 - 7) which repeat in sequence from 0 to 7, starting withzero for each scan, to provide a modulo 8 restart interval count.
The top level of Figure B.2 specifies that the non-hierarchical interchange format shall begin with an SOI marker, shallcontain one frame, and shall end with an EOI marker.
34

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)The second level of Figure B.2 specifies that a frame shall begin with a frame header and shall contain one or more scans.
A frame header may be preceded by one or more table-specification or miscellaneous marker segments as specified in
B.2.4. If a DNL segment (see B.2.5) is present, it shall immediately follow the first scan.
For sequential DCT-based and lossless processes each scan shall contain from one to four image components. If two tofour components are contained within a scan, they shall be interleaved within the scan. For progressive DCT-based
processes each image component is only partially contained within any one scan. Only the first scan(s) for the components(which contain only DC coefficient data) may be interleaved.
The third level of Figure B.2 specifies that a scan shall begin with a scan header and shall contain one or more entropycoded data segments. Each scan header may be preceded by one or more table-specification or miscellaneous marker
segments. If restart is not enabled, there shall be only one entropy-coded segment (the one labeled “last”), and no restartmarkers shall be present. If restart is enabled, the number of entropy-coded segments is defined by the size of the image
and the defined restart interval. In this case, a restart marker shall follow each entropy-coded segment except the last one.
The fourth level of Figure B.2 specifies that each entropy-coded segment is comprised of a sequence of entropycoded MCUs. If restart is enabled and the restart interval is defined to be Ri, each entropy-coded segment except the last
one shall contain Ri MCUs. The last one shall contain whatever number of MCUs completes the scan.
Figure B.2 specifies the locations where table-specification segments may be present. However, this Specification hereby
specifies that the interchange format shall contain all table-specification data necessary for decoding the compressed
image. Consequently, the required table-specification data shall be present at one or more of the allowed locations.
B.2.2

Frame header syntax

Figure B.3 specifies the frame header which shall be present at the start of a frame. This header specifies the source image
characteristics (see A.1), the components in the frame, and the sampling factors for each component, and specifies thedestinations from which the quantized tables to be used with each component are retrieved.
Frame header
SOF n

Lf

P

Y

X

Nf

Component-specification
parameters

Frame component-specification parameters
C1

H 1 V1Tq 1

C2

H 2 V2Tq 2

C Nf

H Nf V Nf

Tq Nf
TISO0850-93/d021

Figure B.3 – Frame header syntax
Figure B.3 [D21], = 5.5 cm = 215.%
The markers and parameters shown in Figure B.3 are defined below. The size and allowed values of each parameter are
given in Table B.2. In Table B.2 (and similar tables which follow), value choices are separated by commas (e.g. 8, 12) andinclusive bounds are separated by dashes (e.g. 0 - 3).
SOFn: Start of frame marker – Marks the beginning of the frame parameters. The subscript n identifies whether
the encoding process is baseline sequential, extended sequential, progressive, or lossless, as well as which
entropy encoding procedure is used.
SOF0:

Baseline DCT

SOF1:Extended sequential DCT, Huffman coding

SOF2:

Progressive DCT, Huffman coding

CCITT Rec. T.81 (1992 E)

35

ISO/IEC 10918-1 : 1993(E)
SOF3:

Lossless (sequential), Huffman coding

SOF9:

Extended sequential DCT, arithmetic coding

SOF10: Progressive DCT, arithmetic coding
SOF11: Lossless (sequential), arithmetic coding
Lf: Frame header length – Specifies the length of the frame header shown in Figure B.3 (see B.1.1.4).
P: Sample precision – Specifies the precision in bits for the samples of the components in the frame.
Y: Number of lines – Specifies the maximum number of lines in the source image. This shall be equal to thenumber of lines in the component with the maximum number of vertical samples (see A.1.1). Value 0 indicatesthat the number of lines shall be defined by the DNL marker and parameters at the end of the first scan (seeB.2.5).
X: Number of samples per line – Specifies the maximum number of samples per line in the source image. This
shall be equal to the number of samples per line in the component with the maximum number of horizontal
samples (see A.1.1).
Nf: Number of image components in frame – Specifies the number of source image components in the frame.
The value of Nf shall be equal to the number of sets of frame component specification parameters (Ci, Hi, Vi,
and Tqi) present in the frame header.
Ci: Component identifier – Assigns a unique label to the ith component in the sequence of frame component
specification parameters. These values shall be used in the scan headers to identify the components in the scan.
The value of Ci shall be different from the values of C1 through Ci − 1.
Hi: Horizontal sampling factor – Specifies the relationship between the component horizontal dimension
and maximum image dimension X (see A.1.1); also specifies the number of horizontal data units of component
Ci in each MCU, when more than one component is encoded in a scan.
Vi: Vertical sampling factor – Specifies the relationship between the component vertical dimension andmaximum image dimension Y (see A.1.1); also specifies the number of vertical data units of component Ci ineach MCU, when more than one component is encoded in a scan.
Tqi: Quantization table destination selector – Specifies one of four possible quantization table destinations
from which the quantization table to use for dequantization of DCT coefficients of component Ci is retrieved. If
the decoding process uses the dequantization procedure, this table shall have been installed in this destinationby the time the decoder is ready to decode the scan(s) containing component Ci. The destination shall not be respecified, or its contents changed, until all scans containing Ci have been completed.
Table B.2 – Frame header parameter sizes and values
ValuesParameter

Size (bits)

Sequential DCT
Baseline

36

Progressive DCT

Extended
8 + 3 × Nf

Lf

16

P

18

Y

16

0-65 535

X

16

1-65 535

Nf

18

Ci

18

0-25535Hi

14

1-43550Vi

141-43550

Tqi

18

CCITT Rec. T.81 (1992 E)

Lossless

8-255

1-255

0-312

8, 12

1-255

0-355

8, 12

2-165

1-4

1-255

0-3

0-125

ISO/IEC 10918-1 : 1993(E)B.2.3

Scan header syntax

Figure B.4 specifies the scan header which shall be present at the start of a scan. This header specifies which
component(s) are contained in the scan, specifies the destinations from which the entropy tables to be used with eachcomponent are retrieved, and (for the progressive DCT) which part of the DCT quantized coefficient data is contained in
the scan. For lossless processes the scan parameters specify the predictor and the point transform.
NOTE – If there is only one image component present in a scan, that component is, by definition, non-interleaved. If there ismore than one image component present in a scan, the components present are, by definition, interleaved.
Scan header
SOS

Ls

Ns

Component-specification
parameters

Ss

Se

Ah

Al

Scan component-specification parameters
Cs 1

Td 1 Ta 1

Cs 2

Td 2 Ta 2

Cs Ns
TISO0860-93/d022

Td Ns Ta Ns

Figure B.4 – Scan header syntax
Figure B.4 [D22], = 5.5 cm = 215.%
The marker and parameters shown in Figure B.4 are defined below. The size and allowed values of each parameter are
given in Table B.3.
SOS: Start of scan marker – Marks the beginning of the scan parameters.
Ls: Scan header length – Specifies the length of the scan header shown in Figure B.4 (see B.1.1.4).
Ns: Number of image components in scan – Specifies the number of source image components in the scan. The
value of Ns shall be equal to the number of sets of scan component specification parameters (Csj, Tdj, and Taj)
present in the scan header.
Csj: Scan component selector – Selects which of the Nf image components specified in the frame parameters
shall be the jth component in the scan. Each Csj shall match one of the Ci values specified in the frame header,
and the ordering in the scan header shall follow the ordering in the frame header. If Ns > 1, the order ofinterleaved components in the MCU is Cs1 first, Cs2 second, etc. If Ns > 1, the following restriction shall beplaced on the image components contained in the scan:
Ns

∑

j =1

H j × V j ≤ 10,

where Hj and Vj are the horizontal and vertical sampling factors for scan component j. These sampling factors
are specified in the frame header for component i, where i is the frame component specification index for whichframe component identifier Ci matches scan component selector Csj.
As an example, consider an image having 3 components with maximum dimensions of 512 lines and512 samples per line, and with the following sampling factors:
Component 0

H 0 = 4,

V0 = 1

Component 1

H1 = 1,V1 = 2Component 2

H2 = 2V2 = 2

Then the summation of Hj × Vj is (4 × 1) + (1 × 2) + (2 × 2) = 10.
The value of Csj shall be different from the values of Cs1 to Csj – 1.
CCITT Rec. T.81 (1992 E)

37

ISO/IEC 10918-1 : 1993(E)Tdj: DC entropy coding table destination selector – Specifies one of four possible DC entropy coding table
destinations from which the entropy table needed for decoding of the DC coefficients of component Csj isretrieved. The DC entropy table shall have been installed in this destination (see B.2.4.2 and B.2.4.3) by thetime the decoder is ready to decode the current scan. This parameter specifies the entropy coding table
destination for the lossless processes.
Taj: AC entropy coding table destination selector – Specifies one of four possible AC entropy coding table
destinations from which the entropy table needed for decoding of the AC coefficients of component Csj isretrieved. The AC entropy table selected shall have been installed in this destination (see B.2.4.2 and B.2.4.3)
by the time the decoder is ready to decode the current scan. This parameter is zero for the lossless processes.
Ss: Start of spectral or predictor selection – In the DCT modes of operation, this parameter specifies the first
DCT coefficient in each block in zig-zag order which shall be coded in the scan. This parameter shall be set tozero for the sequential DCT processes. In the lossless mode of operations this parameter is used to select thepredictor.
Se: End of spectral selection – Specifies the last DCT coefficient in each block in zig-zag order which shall be
coded in the scan. This parameter shall be set to 63 for the sequential DCT processes. In the lossless mode ofoperations this parameter has no meaning. It shall be set to zero.
Ah: Successive approximation bit position high – This parameter specifies the point transform used in thepreceding scan (i.e. successive approximation bit position low in the preceding scan) for the band of coefficients
specified by Ss and Se. This parameter shall be set to zero for the first scan of each band of coefficients. In thelossless mode of operations this parameter has no meaning. It shall be set to zero.
Al: Successive approximation bit position low or point transform – In the DCT modes of operation thisparameter specifies the point transform, i.e. bit position low, used before coding the band of coefficients
specified by Ss and Se. This parameter shall be set to zero for the sequential DCT processes. In the losslessmode of operations, this parameter specifies the point transform, Pt.
The entropy coding table destination selectors, Td j and Taj, specify either Huffman tables (in frames using Huffman
coding) or arithmetic coding tables (in frames using arithmetic coding). In the latter case the entropy coding table
destination selector specifies both an arithmetic coding conditioning table destination and an associated statistics area.
Table B.3 – Scan header parameter size and values
ValuesParameter

Size (bits)

Sequential DCT
Baseline

38

Progressive DCT

Lossless

ExtendedLs

16

6 + 2 × Ns

Ns

18

1-4

Csj

18

0-255a)

Tdj

14

0-1

0-3

0-3

0-3

Taj

14

0-1

0-3

0-3

0

Ss

18

0-1

0-1

0-63

1-7b)

Se

18

63-

63-

Ss-63c)

0

Ah

14

0-1

0-1

0-13

0

Al

14

0-1

0-1

0-13

0-15

a)

Csj shall be a member of the set of Ci specified in the frame header.

b)0

for lossless differential frames in the hierarchical mode (see B.3).

c)0

if Ss equals zero.

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)B.2.4

Table-specification and miscellaneous marker segment syntax

Figure B.5 specifies that, at the places indicated in Figure B.2, any of the table-specification segments or miscellaneous
marker segments specified in B.2.4.1 through B.2.4.6 may be present in any order and with no limit on the number ofsegments.
If any table specification for a particular destination occurs in the compressed image data, it shall replace any previous
table specified for this destination, and shall be used whenever this destination is specified in the remaining scans in theframe or subsequent images represented in the abbreviated format for compressed image data. If a table specification for agiven destination occurs more than once in the compressed image data, each specification shall replace the previous
specification. The quantization table specification shall not be altered between progressive DCT scans of a given
component.
Tables or miscellaneous marker segment[

Marker]segment 1[

Marker]segment 2[

Marker]segment last
TISO0870-93/d023

Marker segment

Quantization table-specificationor
Huffman table-specificationorArithmetic conditioning table-specificationor
Restart interval definitionorComment
orApplication data

Figure B.5 – Tables/miscellaneous marker segment syntax
Figure B.5 [D23], = 7.5 cm = 293.%
B.2.4.1 Quantization table-specification syntax
Figure B.6 specifies the marker segment which defines one or more quantization tables.
Define quantization table segment
DQT

Lq

Pq Tq

Q0

Q1

Q 63
TISO0880-93/d024

Multiple (t = 1, ..., n)

Figure B.6 – Quantization table syntax
Figure B.6 [D24], = 3.5 cm = 136.%
The marker and parameters shown in Figure B.6 are defined below. The size and allowed values of each parameter are
given in Table B.4.
DQT: Define quantization table marker – Marks the beginning of quantization table-specification parameters.
Lq: Quantization table definition length – Specifies the length of all quantization table parameters shown in
Figure B.6 (see B.1.1.4).

CCITT Rec. T.81 (1992 E)

39ISO/IEC 10918-1 : 1993(E)Pq: Quantization table element precision – Specifies the precision of the Qk values. Value 0 indicates 8-bit Qk
values; value 1 indicates 16-bit Qk values. Pq shall be zero for 8 bit sample precision P (see B.2.2).
Tq: Quantization table destination identifier – Specifies one of four possible destinations at the decoder into
which the quantization table shall be installed.
Qk: Quantization table element – Specifies the kth element out of 64 elements, where k is the index in the zigzag ordering of the DCT coefficients. The quantization elements shall be specified in zig-zag scan order.
Table B.4 – Quantization table-specification parameter sizes and values
ValuesParameter

Size (bits)

Sequential DCT
Baseline

Progressive DCT

Lossless

Extended
n

2 + ∑

b 65

+ 64 × Pq(t )g

Lq

16 16

Pq

14 16

Tq

14 16

0-3

Undefined

Qk

18, 161-255, 1-65 535

Undefined

t =1

0

0, 1

Undefined
0, 1

Undefined

The value n in Table B.4 is the number of quantization tables specified in the DQT marker segment.
Once a quantization table has been defined for a particular destination, it replaces the previous tables stored in that
destination and shall be used, when referenced, in the remaining scans of the current image and in subsequent images
represented in the abbreviated format for compressed image data. If a table has never been defined for a particular
destination, then when this destination is specified in a frame header, the results are unpredictable.
An 8-bit DCT-based process shall not use a 16-bit precision quantization table.
B.2.4.2 Huffman table-specification syntax
Figure B.7 specifies the marker segment which defines one or more Huffman table specifications.
Define Huffman table segment

DHT

Lh

Tc Th

L1

L2

Symbol-length
assignment

L 16

Multiple (t = 1, ..., n)
Symbol-length assignment parameters
V1,1

V1,2

V1,L

1

V 2,1

V 2,2

V2,L

2

V16,1

V16,2

V16,L

16

TISO0890-93/d025

Figure B.7 – Huffman table syntax
Figure B.7 [D25], = 5.5 cm = 215.%

40

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)The marker and parameters shown in Figure B.7 are defined below. The size and allowed values of each parameter are
given in Table B.5.
DHT: Define Huffman table marker – Marks the beginning of Huffman table definition parameters.
Lh: Huffman table definition length – Specifies the length of all Huffman table parameters shown in Figure B.7(see B.1.1.4).
Tc: Table class – 0 = DC table or lossless table, 1 = AC table.
Th: Huffman table destination identifier – Specifies one of four possible destinations at the decoder into which
the Huffman table shall be installed.
Li: Number of Huffman codes of length i – Specifies the number of Huffman codes for each of the 16 possible
lengths allowed by this Specification. Li’s are the elements of the list BITS.
Vi,j: Value associated with each Huffman code – Specifies, for each i, the value associated with each Huffman
code of length i. The meaning of each value is determined by the Huffman coding model. The Vi,j’s are theelements of the list HUFFVAL.
Table B.5 – Huffman table specification parameter sizes and values

ValuesParameter

Size (bits)

Sequential DCT
Baseline

Progressive DCTnLh

Lossless

Extended

2 + ∑

16

t =1

+ mt h

c17

Tc

14

0, 1

0

Th

14

Li

18

0-255

Vi, j

18

0-255

0, 1

0-3

The value n in Table B.5 is the number of Huffman tables specified in the DHT marker segment. The value mt is thenumber of parameters which follow the 16 Li(t) parameters for Huffman table t, and is given by:
16

m t = ∑ Li
i =1

In general, mt is different for each table.
Once a Huffman table has been defined for a particular destination, it replaces the previous tables stored in that
destination and shall be used when referenced, in the remaining scans of the current image and in subsequent images
represented in the abbreviated format for compressed image data. If a table has never been defined for a particular
destination, then when this destination is specified in a scan header, the results are unpredictable.

CCITT Rec. T.81 (1992 E)

41

ISO/IEC 10918-1 : 1993(E)B.2.4.3 Arithmetic conditioning table-specification syntax
Figure B.8 specifies the marker segment which defines one or more arithmetic coding conditioning table specifications.
These replace the default arithmetic coding conditioning tables established by the SOI marker for arithmetic coding
processes. (See F.1.4.4.1.4 and F.1.4.4.2.1.)
Define arithmetic conditioning segment
DAC

La

Tc Tb

Cs
TISO0900-93/d026

Multiple (t = 1, ..., n)

Figure B.8 – Arithmetic conditioning table-specification syntax
Figure B.8 [D26], = 3 cm = 117.%
The marker and parameters shown in Figure B.8 are defined below. The size and allowed values of each parameter are
given in Table B.6.
DAC: Define arithmetic coding conditioning marker – Marks the beginning of the definition of arithmeticcoding conditioning parameters.
La: Arithmetic coding conditioning definition length – Specifies the length of all arithmetic coding
conditioning parameters shown in Figure B.8 (see B.1.1.4).
Tc: Table class – 0 = DC table or lossless table, 1 = AC table.
Tb: Arithmetic coding conditioning table destination identifier – Specifies one of four possible destinations at
the decoder into which the arithmetic coding conditioning table shall be installed.
Cs: Conditioning table value – Value in either the AC or the DC (and lossless) conditioning table. A single
value of Cs shall follow each value of Tb. For AC conditioning tables Tc shall be one and Cs shall contain avalue of Kx in the range 1 ≤ Kx ≤ 63. For DC (and lossless) conditioning tables Tc shall be zero and Cs shallcontain two 4-bit parameters, U and L. U and L shall be in the range 0 ≤ L ≤ U ≤ 15 and the value of Cs shall be
L + 16 × U.
The value n in Table B.6 is the number of arithmetic coding conditioning tables specified in the DAC marker segment.
The parameters L and U are the lower and upper conditioning bounds used in the arithmetic coding procedures definedfor DC coefficient coding and lossless coding. The separate value range 1-63 listed for DCT coding is the Kx conditioning
used in AC coefficient coding.
Table B.6 – Arithmetic coding conditioning table-specification parameter sizes and values
ValuesParameter

Size (bits)

Sequential DCT
Baseline

42

La

16

Undefined

Tc

14

UndefinedTb

14

Undefined

Cs

18

Undefined

CCITT Rec. T.81 (1992 E)

Progressive DCT

Lossless

Extended
2+2×n
0, 1

0-255
0-3

0-255 (Tc = 0), 1-63 (Tc = 1)

0-255

ISO/IEC 10918-1 : 1993(E)B.2.4.4 Restart interval definition syntax
Figure B.9 specifies the marker segment which defines the restart interval.
Define restart interval segment
DRI

Lr

Ri
TISO0910-93/d027

Figure B.9 – Restart interval definition syntax

Figure B.9 [D27], = 2.5 cm = 98.%
The marker and parameters shown in Figure B.9 are defined below. The size and allowed values of each parameter are
given in Table B.7.
DRI: Define restart interval marker – Marks the beginning of the parameters which define the restart interval.
Lr: Define restart interval segment length – Specifies the length of the parameters in the DRI segment shown in
Figure B.9 (see B.1.1.4).
Ri: Restart interval – Specifies the number of MCU in the restart interval.
In Table B.7 the value n is the number of rows of MCU in the restart interval. The value MCUR is the number of MCU
required to make up one line of samples of each component in the scan. The SOI marker disables the restart intervals. A
DRI marker segment with Ri nonzero shall be present to enable restart interval processing for the following scans. A DRI
marker segment with Ri equal to zero shall disable restart intervals for the following scans.
Table B.7 – Define restart interval segment parameter sizes and values
ValuesParameter

Size (bits)

Sequential DCT
Baseline

Lr

16

Ri

16

Progressive DCT

Lossless

Extended4n × MCUR

0-65 535

B.2.4.5 Comment syntax
Figure B.10 specifies the marker segment structure for a comment segment.
Comment segment
COM

Lc

Cm 1 . . . Cm Lc-2
TISO00920-93/d028

Figure B.10 – Comment segment syntax
Figure B.10 [D28], = 2.8cm = 98.%

CCITT Rec. T.81 (1992 E)

43ISO/IEC 10918-1 : 1993(E)The marker and parameters shown in Figure B.10 are defined below. The size and allowed values of each parameter are
given in Table B.8.
COM: Comment marker – Marks the beginning of a comment.
Lc: Comment segment length – Specifies the length of the comment segment shown in Figure B.10
(see B.1.1.4).
Cmi: Comment byte – The interpretation is left to the application.
Table B.8 – Comment segment parameter sizes and values
ValuesParameter

Size (bits)

Sequential DCT
Baseline

Progressive DCT

Lossless

ExtendedLc

16

2-65 535

Cmi

180-25522B.2.4.6 Application data syntax
Figure B.11 specifies the marker segment structure for an application data segment.
Application data segment
APP n

Lp

Ap 1 . . . Ap Lp-2
TISO0930-93/d029

Figure B.11 – Application data syntax
Figure B.11 [D29], = 2.8 cm = 98.%
The marker and parameters shown in Figure B.11 are defined below. The size and allowed values of each parameter are
given in Table B.9.
APPn: Application data marker – Marks the beginning of an application data segment.
Lp: Application data segment length – Specifies the length of the application data segment shown in
Figure B.11 (see B.1.1.4).
Api: Application data byte – The interpretation is left to the application.
The APPn (Application) segments are reserved for application use. Since these segments may be defined differently for
different applications, they should be removed when the data are exchanged between application environments.
Table B.9 – Application data segment parameter sizes and values
ValuesParameter

Size (bits)

Sequential DCT
Baseline

44

Progressive DCT

ExtendedLp

16

2-65 535Api

180-25522

CCITT Rec. T.81 (1992 E)

Lossless

ISO/IEC 10918-1 : 1993(E)
B.2.5

Define number of lines syntax

Figure B.12 specifies the marker segment for defining the number of lines. The DNL (Define Number of Lines) segmentprovides a mechanism for defining or redefining the number of lines in the frame (the Y parameter in the frame header) at
the end of the first scan. The value specified shall be consistent with the number of MCU-rows encoded in the first scan.
This segment, if used, shall only occur at the end of the first scan, and only after coding of an integer number of MCUrows. This marker segment is mandatory if the number of lines (Y) specified in the frame header has the value zero.
Define number of lines segment
DNL

Ld

NL
TISO0940-93/d030

Figure B.12 – Define number of lines syntax
Figure B.12 [D30], = 2.8 cm = 98.%
The marker and parameters shown in Figure B.12 are defined below. The size and allowed values of each parameter are
given in Table B.10.
DNL: Define number of lines marker – Marks the beginning of the define number of lines segment.
Ld: Define number of lines segment length – Specifies the length of the define number of lines segment shownin Figure B.12 (see B.1.1.4).
NL: Number of lines – Specifies the number of lines in the frame (see definition of Y in B.2.2).

Table B.10 – Define number of lines segment parameter sizes and values

ValuesParameter

Size (bits)

Sequential DCT
Baselinea)Progressive DCT

Lossless

Extended

Ld

164-65535a)NL

16

1-65 535a)

The value specified shall be consistent with the number of lines coded at the point where the DNL segment
terminates the compressed data segment.

B.3

Hierarchical syntax

B.3.1

High level hierarchical mode syntax

Figure B.13 specifies the order of the high level constituent parts of the interchange format for hierarchical encoding
processes.

CCITT Rec. T.81 (1992 E)

45

ISO/IEC 10918-1 : 1993(E)Compressed image data
SOI

[Tables/misc.]

DHP segment

Frame last

Frame 1EOI
TISO0950-93/d031

Figure B.13 – Syntax for the hierarchical mode of operation

Figure B.13 [D31], = 3 cm = 117.%
Hierarchical mode syntax requires a DHP marker segment that appears before the non-differential frame or frames. The
hierarchical mode compressed image data may include EXP marker segments and differential frames which shall follow
the initial non-differential frame. The frame structure in hierarchical mode is identical to the frame structure in nonhierarchical mode.
The non-differential frames in the hierarchical sequence shall use one of the coding processes specified for SOFn markers:
SOF0, SOF1, SOF2, SOF3, SOF9, SOF10 and SOF11. The differential frames shall use one of the processes specified for
SOF5, SOF6, SOF7, SOF13, SOF14 and SOF15. The allowed combinations of SOF markers within one hierarchicalsequence are specified in Annex J.
The sample precision (P) shall be constant for all frames and have the identical value as that coded in the DHP marker
segment. The number of samples per line (X) for all frames shall not exceed the value coded in the DHP marker segment.
If the number of lines (Y) is non-zero in the DHP marker segment, then the number of lines for all frames shall not exceed
the value in the DHP marker segment.

B.3.2

DHP segment syntax

The DHP segment defines the image components, size, and sampling factors for the completed hierarchical sequence offrames. The DHP segment shall precede the first frame; a single DHP segment shall occur in the compressed image data.
The DHP segment structure is identical to the frame header syntax, except that the DHP marker is used instead of the
SOFn marker. The figures and description of B.2.2 then apply, except that the quantization table destination selector
parameter shall be set to zero in the DHP segment.

B.3.3

EXP segment syntax

Figure B.14 specifies the marker segment structure for the EXP segment. The EXP segment shall be present if (and onlyif) expansion of the reference components is required either horizontally or vertically. The EXP segment parameters apply
only to the next frame (which shall be a differential frame) in the image. If required, the EXP segment shall be one of thetable-specification segments or miscellaneous marker segments preceding the frame header; the EXP segment shall not be
one of the table-specification segments or miscellaneous marker segments preceding a scan header or a DHP marker
segment.
Expand segment
EXP

Le

Eh Ev
TISO0960-93/d032

Figure B.14 – Syntax of the expand segment

Figure B.14 [D32], = 2.5 cm = 98.%

46

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)The marker and parameters shown in Figure B.14 are defined below. The size and allowed values of each parameter are
given in Table B.11.
EXP: Expand reference components marker – Marks the beginning of the expand reference components
segment.
Le: Expand reference components segment length – Specifies the length of the expand reference components
segment (see B.1.1.4).
Eh: Expand horizontally – If one, the reference components shall be expanded horizontally by a factor of two.
If horizontal expansion is not required, the value shall be zero.
Ev: Expand vertically – If one, the reference components shall be expanded vertically by a factor of two.
If vertical expansion is not required, the value shall be zero.
Both Eh and Ev shall be one if expansion is required both horizontally and vertically.
Table B.11 – Expand segment parameter sizes and values
ValuesParameter

Size (bits)

Sequential DCT
Baseline

B.4

Progressive DCT

Lossless

Extended

Le

16

3,1

Eh

14

0, 1

Ev

14

0, 1

Abbreviated format for compressed image data

Figure B.2 shows the high-level constituent parts of the interchange format. This format includes all table specifications
required for decoding. If an application environment provides methods for table specification other than by means of thecompressed image data, some or all of the table specifications may be omitted. Compressed image data which is missing
any table specification data required for decoding has the abbreviated format.

B.5

Abbreviated format for table-specification data

Figure B.2 shows the high-level constituent parts of the interchange format. If no frames are present in the compressed
image data, the only purpose of the compressed image data is to convey table specifications or miscellaneous marker
segments defined in B.2.4.1, B.2.4.2, B.2.4.5, and B.2.4.6. In this case the compressed image data has the abbreviatedformat for table specification data (see Figure B.15).
Compressed image data
SOI

[Tables/misc.]

EOI
TISO0970-93/d033

Figure B.15 – Abbreviated format for table-specification data syntax

Figure B.15 [D33], = 3 cm = 117.% dim. à 100

B.6

Summary

The order of the constituent parts of interchange format and all marker segment structures is summarized in Figures B.16
and B.17. Note that in Figure B.16 double-lined boxes enclose marker segments. In Figures B.16 and B.17 thick-lined
boxes enclose only markers.
The EXP segment can be mixed with the other tables/miscellaneous marker segments preceding the frame header but notwith the tables/miscellaneous marker segments preceding the DHP segment or the scan header.
CCITT Rec. T.81 (1992 E)

47

SOI

48

Tables/miscellaneous

CCITT Rec. T.81 (1992 E)
DHP

Figure à l'italienne B.16 [D34], = 21 cm = 821.%
SOFn

Tables/miscellaneous
SOS

Restart enabled

RST i(modulo 8)

i=0 to last-1

Restart not enabled

ECS i

Figure B.16 – Flow of compressed data syntax

Non-expansionof referencecomponents

EXP

Non-hierarchical mode

Tables/miscellaneous

Hierarchical mode

Abbreviated format for table-specification data

ECSlast

TISO0980-93/d034

From second
scan to last,
first scan when
number of lines
defined correctlyin frame header

DNL

Multi-scan

Multi-frame

EOI

ISO/IEC 10918-1 : 1993(E)

Le

Ld

Lf

Ls

Lf

Eh

NL

P

Ns

P

Lq

Lh

CCITT Rec. T.81 (1992 E)
Lp

Lc

Lr

La

Th

Tq

Nf

Taii

Nf

L1

Q0

Tc

Ap 1 . . . . Ap Lp-2

Tb

Hi

V1,1

Q 63

(=0)

Tq i

Al

Tq i

Default condition

L 16

Multiple (n times)

Q1

Vi

Figure B.17 – Flow of marker segment

Cs

Ah

Vi

i=1 to NfSeHi

i=1 to Nf

Multiple (n times)

Ci

Ss

Ci

Multiple (n times)

Tc

Pq

X

Td i

i=1 to Ns

X

Cm 1 . . . . Cm Lc-2

Ri

Ev

Y

Cs i

Y

Abbreviated format or some tables not in this position

APP nApplication

COM

Comment

DRI

Restart interval

DAC

Arithmetic coding table(s)DHT

Huffman coding table(s)DQT

Quantization table(s)(Tables/miscellaneous)

EXP(EXP segment)

DNL(DNL segment)

DHP(DHP segment)

SOS(Scan header)

SOFn(Frame header)

TISO0990-93/d035

V 16,L16

ISO/IEC 10918-1 : 1993(E)Figure à l'italienne B.17 [D35], = 21 cm = 821.%

49

ISO/IEC 10918-1 : 1993(E)Annex C
Huffman table specification(This annex forms an integral part of this Recommendation | International Standard)

A Huffman coding procedure may be used for entropy coding in any of the coding processes. Coding models for
Huffman encoding are defined in Annexes F, G, and H. In this Annex, the Huffman table specification is defined.

Huffman tables are specified in terms of a 16-byte list (BITS) giving the number of codes for each code length from
1 to 16. This is followed by a list of the 8-bit symbol values (HUFFVAL), each of which is assigned a Huffman code. The
symbol values are placed in the list in order of increasing code length. Code lengths greater than 16 bits are not allowed.
In addition, the codes shall be generated such that the all-1-bits code word of any length is reserved as a prefix for longer
code words.
NOTE – The order of the symbol values within HUFFVAL is determined only by code length. Within a given code length
the ordering of the symbol values is arbitrary.

This annex specifies the procedure by which the Huffman tables (of Huffman code words and their corresponding 8-bit
symbol values) are derived from the two lists (BITS and HUFFVAL) in the interchange format. However, the way inwhich these lists are generated is not specified. The lists should be generated in a manner which is consistent with therules for Huffman coding, and it shall observe the constraints discussed in the previous paragraph. Annex K contains an
example of a procedure for generating lists of Huffman code lengths and values which are in accord with these rules.
NOTE – There is no requirement in this Specification that any encoder or decoder shall implement the procedures inprecisely the manner specified by the flow charts in this annex. It is necessary only that an encoder or decoder implement the function
specified in this annex. The sole criterion for an encoder or decoder to be considered in compliance with this Specification is that it
satisfy the requirements given in clause 6 (for encoders) or clause 7 (for decoders), as determined by the compliance tests specified inPart 2.

C.1

Marker segments for Huffman table specification

The DHT marker identifies the start of Huffman table definitions within the compressed image data. B.2.4.2 specifies thesyntax for Huffman table specification.

C.2

Conversion of Huffman table specifications to tables of codes and code lengths

Conversion of Huffman table specifications to tables of codes and code lengths uses three procedures. The first procedure(Figure C.1) generates a table of Huffman code sizes. The second procedure (Figure C.2) generates the Huffman codesfrom the table built in Figure C.1. The third procedure (Figure C.3) generates the Huffman codes in symbol value order.

Given a list BITS (1 to 16) containing the number of codes of each size, and a list HUFFVAL containing the symbol
values to be associated with those codes as described above, two tables are generated. The HUFFSIZE table contains a listof code lengths; the HUFFCODE table contains the Huffman codes corresponding to those lengths.

Note that the variable LASTK is set to the index of the last entry in the table.

50

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Generate_size_table

K=0
I=1
J=1

HUFFSIZE(K) = I
K=K+1
J=J+1

No

J > BITS(I)
?
Yes
I=I+1
J=1

No

I > 16?
Yes
HUFFSIZE(K) = 0
LASTK = K

Done

TISO1000-93/d036

Figure C.1 – Generation of table of Huffman code sizes

Figure C.1 [D36], = 16 cm = 625 %CCITT Rec. T.81 (1992 E)

51

ISO/IEC 10918-1 : 1993(E)A Huffman code table, HUFFCODE, containing a code for each size in HUFFSIZE is generated by the procedure in
Figure C.2. The notation “SLL CODE 1” in Figure C.2 indicates a shift-left-logical of CODE by one bit position.

Generate_code_table

K= 0
CODE = 0
SI = HUFFSIZE(0)HUFFCODE(K) = CODE
CODE = CODE + 1
K=K+1

Yes

HUFFSIZE(K) = SI?
No
HUFFSIZE(K) = 0
?

Yes

No

CODE = SLL CODE 1
SI = SI + 1

Done

TISO1010-93/d037

Yes

HUFFSIZE(K) = SI?

No

Figure C.2 – Generation of table of Huffman codes

Figure C.2 [D37], = 16.5 cm = 645.%

Two tables, HUFFCODE and HUFFSIZE, have now been generated. The entries in the tables are ordered according toincreasing Huffman code numeric value and length.

The encoding procedure code tables, EHUFCO and EHUFSI, are created by reordering the codes specified by
HUFFCODE and HUFFSIZE according to the symbol values assigned to each code in HUFFVAL.

52

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Figure C.3 illustrates this ordering procedure.

Order_codes

K=0

I = HUFFVAL(K)EHUFCO(I) = HUFFCODE(K)EHUFSI(I) = HUFFSIZE(K)
K=K+1

Yes

K < LASTK
?
No

Done

TISO1020-93/d038

Figure C.3 – Ordering procedure for encoding procedure code tables
Figure C.3 [D38], = 11.5 cm = 449.%

C.3

Bit ordering within bytes

The root of a Huffman code is placed toward the MSB (most-significant-bit) of the byte, and successive bits are placed in
the direction MSB to LSB (least-significant-bit) of the byte. Remaining bits, if any, go into the next byte following thesame rules.
Integers associated with Huffman codes are appended with the MSB adjacent to the LSB of the preceding Huffman code.

CCITT Rec. T.81 (1992 E)

53

ISO/IEC 10918-1 : 1993(E)Annex D
Arithmetic coding(This annex forms an integral part of this Recommendation | International Standard)

An adaptive binary arithmetic coding procedure may be used for entropy coding in any of the coding processes except
the baseline sequential process. Coding models for adaptive binary arithmetic coding are defined in Annexes F, G,
and H. In this annex the arithmetic encoding and decoding procedures used in those models are defined.
In K.4 a simple test example is given which should be helpful in determining if a given implementation is correct.
NOTE – There is no requirement in this Specification that any encoder or decoder shall implement the procedures inprecisely the manner specified by the flow charts in this annex. It is necessary only that an encoder or decoder implement the function
specified in this annex. The sole criterion for an encoder or decoder to be considered in compliance with this Specification is that it
satisfy the requirements given in clause 6 (for encoders) or clause 7 (for decoders), as determined by the compliance tests specified inPart 2.

D.1

Arithmetic encoding procedures

Four arithmetic encoding procedures are required in a system with arithmetic coding (see Table D.1).
Table D.1 – Procedures for binary arithmetic encoding
Procedure

Purpose

Code_0(S)Code a “0” binary decision with context-index S

Code_1(S)Code a “1” binary decision with context-index S

Initenc

Initialize the encoder

Flush

Terminate entropy-coded segment

The “Code_0(S)”and “Code_1(S)” procedures code the 0-decision and 1-decision respectively; S is a context-index
which identifies a particular conditional probability estimate used in coding the binary decision. The “Initenc” procedure
initializes the arithmetic coding entropy encoder. The “Flush” procedure terminates the entropy-coded segment in
preparation for the marker which follows.
D.1.1

Binary arithmetic encoding principles

The arithmetic coder encodes a series of binary symbols, zeros and ones, each symbol representing one possible result of abinary decision.
Each “binary decision” provides a choice between two alternatives. The binary decision might be between positive andnegative signs, a magnitude being zero or nonzero, or a particular bit in a sequence of binary digits being zero or one.
The output bit stream (entropy-coded data segment) represents a binary fraction which increases in precision as bytes areappended by the encoding process.
D.1.1.1 Recursive interval subdivision
Recursive probability interval subdivision is the basis for the binary arithmetic encoding procedures. With each binary
decision the current probability interval is subdivided into two sub-intervals, and the bit stream is modified (if necessary)so that it points to the base (the lower bound) of the probability sub-interval assigned to the symbol which occurred.
In the partitioning of the current probability interval into two sub-intervals, the sub-interval for the less probable symbol(LPS) and the sub-interval for the more probable symbol (MPS) are ordered such that usually the MPS sub-interval iscloser to zero. Therefore, when the LPS is coded, the MPS sub-interval size is added to the bit stream. This coding
convention requires that symbols be recognized as either MPS or LPS rather than 0 or 1. Consequently, the size of the
LPS sub-interval and the sense of the MPS for each decision must be known in order to encode that decision.
54

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)The subdivision of the current probability interval would ideally require a multiplication of the interval by the probability
estimate for the LPS. Because this subdivision is done approximately, it is possible for the LPS sub-interval to be larger
than the MPS sub-interval. When that happens a “conditional exchange” interchanges the assignment of the sub-intervals
such that the MPS is given the larger sub-interval.
Since the encoding procedure involves addition of binary fractions rather than concatenation of integer code words, themore probable binary decisions can sometimes be coded at a cost of much less than one bit per decision.
D.1.1.2 Conditioning of probability estimates
An adaptive binary arithmetic coder requires a statistical model – a model for selecting conditional probability estimates tobe used in the coding of each binary decision. When a given binary decision probability estimate is dependent on aparticular feature or features (the context) already coded, it is “conditioned” on that feature. The conditioning ofprobability estimates on previously coded decisions must be identical in encoder and decoder, and therefore can use only
information known to both.
Each conditional probability estimate required by the statistical model is kept in a separate storage location or “bin”
identified by a unique context-index S. The arithmetic coder is adaptive, which means that the probability estimates at
each context-index are developed and maintained by the arithmetic coding system on the basis of prior coding decisions
for that context-index.
D.1.2

Encoding conventions and approximations

The encoding procedures use fixed precision integer arithmetic and an integer representation of fractional values in which
X’8000’ can be regarded as the decimal value 0.75. The probability interval, A, is kept in the integer
range X’8000’ ≤ A < X’10000’ by doubling it whenever its integer value falls below X’8000’. This is equivalent tokeeping A in the decimal range 0.75 ≤ A < 1.5. This doubling procedure is called renormalization.
The code register, C, contains the trailing bits of the bit stream. C is also doubled each time A is doubled. Periodically– to keep C from overflowing – a byte of data is removed from the high order bits of the C-register and placed in theentropy-coded segment.
Carry-over into the entropy-coded segment is limited by delaying X’FF’ output bytes until the carry-over is resolved. Zerobytes are stuffed after each X’FF’ byte in the entropy-coded segment in order to avoid the accidental generation ofmarkers in the entropy-coded segment.
Keeping A in the range 0.75 ≤ A < 1.5 allows a simple arithmetic approximation to be used in the probability interval
subdivision. Normally, if the current estimate of the LPS probability for context-index S is Qe(S), precise calculation of
the sub-intervals would require:
Qe(S) × A
Probability sub-interval for the LPS;
A – (Qe(S) × A) Probability sub-interval for the MPS.
Because the decimal value of A is of order unity, these can be approximated byQe(S)A – Qe(S)Probability sub-interval for the LPS;
Probability sub-interval for the MPS.

Whenever the LPS is coded, the value of A – Qe(S) is added to the code register and the probability interval is reduced toQe(S). Whenever the MPS is coded, the code register is left unchanged and the interval is reduced to A – Qe(S). The
precision range required for A is then restored, if necessary, by renormalization of both A and C.
With the procedure described above, the approximations in the probability interval subdivision process can sometimes
make the LPS sub-interval larger than the MPS sub-interval. If, for example, the value of Qe(S) is 0.5 and A is at theminimum allowed value of 0.75, the approximate scaling gives one-third of the probability interval to the MPS and twothirds to the LPS. To avoid this size inversion, conditional exchange is used. The probability interval is subdivided using
the simple approximation, but the MPS and LPS sub-interval assignments are exchanged whenever the LPS sub-interval islarger than the MPS sub-interval. This MPS/LPS conditional exchange can only occur when a renormalization will beneeded.
Each binary decision uses a context. A context is the set of prior coding decisions which determine the context-index, S,
identifying the probability estimate used in coding the decision.
Whenever a renormalization occurs, a probability estimation procedure is invoked which determines a new probability
estimate for the context currently being coded. No explicit symbol counts are needed for the estimation. The relative
probabilities of renormalization after coding of LPS and MPS provide, by means of a table-based probability estimation
state machine, a direct estimate of the probabilities.
CCITT Rec. T.81 (1992 E)

55

ISO/IEC 10918-1 : 1993(E)D.1.3

Encoder code register conventions

The flow charts in this annex assume the register structures for the encoder as shown in Table D.2.

Table D.2 – Encoder register connections

MSB

LSB

C-register

0000cbbb,

bbbbbsss,

xxxxxxxx,

xxxxxxxx

A-register

00000000,

00000000,

aaaaaaaa,

aaaaaaaa

The “a” bits are the fractional bits in the A-register (the current probability interval value) and the “x” bits are thefractional bits in the code register. The “s” bits are optional spacer bits which provide useful constraints on carry-over, andthe “b” bits indicate the bit positions from which the completed bytes of data are removed from the C-register. The “c” bitis a carry bit. Except at the time of initialization, bit 15 of the A-register is always set and bit 16 is always clear (the LSB
is bit 0).
These register conventions illustrate one possible implementation. However, any register conventions which allow
resolution of carry-over in the encoder and which produce the same entropy-coded segment may be used. The handling ofcarry-over and the byte stuffing following X’FF’ will be described in a later part of this annex.
D.1.4

Code_1(S) and Code_0(S) procedures

When a given binary decision is coded, one of two possibilities occurs – either a 1-decision or a 0-decision is coded.
Code_1(S) and Code_0(S) are shown in Figures D.1 and D.2. The Code_1(S) and Code_0(S) procedures use probability
estimates with a context-index S. The context-index S is determined by the statistical model and is, in general, a functionof the previous coding decisions; each value of S identifies a particular conditional probability estimate which is used in
encoding the binary decision.

Code_1(S)No

MPS(S) = 1?

Yes

Code_MPS(S)

Code_LPS(S)TISO1800-93/d039

Done

Figure D.1 – Code_1(S) procedure
Figure D.1 [D39], = 9 cm = 352.%

56

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)

Code_0(S)No

MSP(S) = 0?

Yes

Code_LPS(S)

Code_MPS(S)TISO1030-93/d040

Done

Figure D.2 – Code_0(S) procedure

Figure D.2 [D40], = 9 cm = 352 %The context-index S selects a storage location which contains Index(S), an index to the tables which make up theprobability estimation state machine. When coding a binary decision, the symbol being coded is either the more probable
symbol or the less probable symbol. Therefore, additional information is stored at each context-index identifying the senseof the more probable symbol, MPS(S).

For simplicity, the flow charts in this subclause assume that the context storage for each context-index S has an additional
storage field for Qe(S) containing the value of Qe(Index(S)). If only the value of Index(S) and MPS(S) are stored, allreferences to Qe(S) should be replaced by Qe(Index(S)).

The Code_LPS(S) procedure normally consists of the addition of the MPS sub-interval A – Qe(S) to the bit stream and ascaling of the interval to the sub-interval, Qe(S). It is always followed by the procedures for obtaining a new LPS
probability estimate (Estimate_Qe(S)_after_LPS) and renormalization (Renorm_e) (see Figure D.3).

However, in the event that the LPS sub-interval is larger than the MPS sub-interval, the conditional MPS/LPS exchange
occurs and the MPS sub-interval is coded.

The Code_MPS(S) procedure normally reduces the size of the probability interval to the MPS sub-interval. However, if
the LPS sub-interval is larger than the MPS sub-interval, the conditional exchange occurs and the LPS sub-interval iscoded instead. Note that conditional exchange cannot occur unless the procedures for obtaining a new LPS probability
estimate (Estimate_Qe(S)_after_MPS) and renormalization (Renorm_e) are required after the coding of the symbol (seeFigure D.4).

CCITT Rec. T.81 (1992 E)

57

ISO/IEC 10918-1 : 1993(E)

Code_LPS(S)A = A – Qe(S)A < Qe(S)
?

Yes

No
C=C+A
A = Qe(S)Estimate_Qe(S)_after_LPS
Renorm_e

Done

TISO1040-93/d041

Figure D.3 – Code_LPS(S) procedure with conditional MPS/LPS exchange

Figure D.3 [D41], = 13.5 cm = 528.%

58

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)

Code_MPS(S)A = A – Qe(S)No

A < X’8000’
?

No

Yes

A < Qe(S)
?

Yes

C=C+A
A = Qe(S)Estimate_Qe(S)_after_MPS
Renorm_e

Done
TISO1050-93/d042

Figure D.4 – Code_MPS(S) procedure with conditional MPS/LPS exchange
Figure D.4 [D42], = 16.5 cm = 645.%
D.1.5

Probability estimation in the encoder

D.1.5.1 Probability estimation state machine
The probability estimation state machine consists of a number of sequences of probability estimates. These sequences areinterlinked in a manner which provides probability estimates based on approximate symbol counts derived from thearithmetic coder renormalization. Some of these sequences are used during the initial “learning” stages of probability
estimation; the rest are used for “steady state” estimation.
Each entry in the probability estimation state machine is assigned an index, and each index has associated with it a
Qe value and two Next_Index values. The Next_Index_MPS gives the index to the new probability estimate after an MPS
renormalization; the Next_Index_LPS gives the index to the new probability estimate after an LPS renormalization. Notethat both the index to the estimation state machine and the sense of the MPS are kept for each context-index S. The senseof the MPS is changed whenever the entry in the Switch_MPS is one.
The probability estimation state machine is given in Table D.3. Initialization of the arithmetic coder is always withan MPS sense of zero and a Qe index of zero in Table D.3.
The Qe values listed in Table D.3 are expressed as hexadecimal integers. To approximately convert the 15-bit integer
representation of Qe to a decimal probability, divide the Qe values by (4/3) × (X’8000’).

CCITT Rec. T.81 (1992 E)

59

ISO/IEC 10918-1 : 1993(E)Table D.3 – Qe values and probability estimation state machine

Index

10
11
12
13
14
15
16
17
18
19
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56

60

Qe

Next_ Index

Switch_Value

_LPS

_MPS

_MPS

X’5A1D’
X’2586’
X’1114’
X’080B’X’03D8’
X’01DA’X’00E5’
X’006F’
X’0036’
X’001A’
X’000D’
X’0006’
X’0003’
X’0001’
X’5A7F’X’3F25’
X’2CF2’
X’207C’X’17B9’X’1182’
X’0CEF’
X’09A1’
X’072F’
X’055C’
X’0406’
X’0303’
X’0240’
X’01B1’
X’0144’
X’00F5’
X’00B7’
X’008A’
X’0068’X’004E’
X’003B’
X’002C’X’5AE1’
X’484C’X’3A0D’
X’2EF1’
X’261F’X’1F33’
X’19A8’
X’1518’
X’1177’
X’0E74’
X’0BFB’
X’09F8’
X’0861’
X’0706’
X’05CD’
X’04DE’
X’040F’
X’0363’
X’02D4’
X’025C’X’01F8’

11
14
16
18
20
23
25
28
30
33
35
19
10
12
15
36
38
39
40
42
43
45
46
48
49
51
52
54
56
57
59
60
62
63
32
33
37
64
65
67
68
69
70
72
73
74
75
77
78
79
48
50
50
51
52
53
54

11
12
13
14
15
16
17
18
19
10
11
12
13
13
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
19
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57

1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

CCITT Rec. T.81 (1992 E)

Index

157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
100
101
102
103
104
105
106
107
108
109
110
111
112

Qe

Next_ Index

Switch_Value

_LPS

_MPS

_MPS

X’01A4’
X’0160’
X’0125’
X’00F6’
X’00CB’
X’00AB’
X’008F’X’5B12’
X’4D04’
X’412C’X’37D8’
X’2FE8’X’293C’
X’2379’X’1EDF’X’1AA9’X’174E’
X’1424’
X’119C’X’0F6B’X’0D51’
X’0BB6’
X’0A40’X’5832’
X’4D1C’
X’438E’X’3BDD’
X’34EE’X’2EAE’
X’299A’
X’2516’
X’5570’
X’4CA9’
X’44D9’X’3E22’
X’3824’
X’32B4’X’2E17’
X’56A8’
X’4F46’
X’47E5’
X’41CF’X’3C3D’
X’375E’
X’5231’
X’4C0F’
X’4639’X’415E’
X’5627’
X’50E7’
X’4B85’
X’5597’
X’504F’X’5A10’
X’5522’
X’59EB’

155
156
157
158
159
161
161
165
180
181
182
183
184
186
187
187
172
172
174
174
175
177
177
180
188
189
190
191
192
193
186
188
195
196
197
199
199
193
195
101
102
103
104
199
105
106
107
103
105
108
109
110
111
110
112
112

158
159
160
161
162
163
132
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
148
181
182
183
184
185
186
187
171
189
190
191
192
193
194
186
196
197
198
199
100
193
102
103
104
199
106
107
103
109
107
111
109
111

0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1

ISO/IEC 10918-1 : 1993(E)D.1.5.2 Renormalization driven estimation

The change in state in Table D.3 occurs only when the arithmetic coder interval register is renormalized. This must always
be done after coding an LPS, and whenever the probability interval register is less than X'8000' (0.75 in decimal notation)
after coding an MPS.

When the LPS renormalization is required, Next_Index_LPS gives the new index for the LPS probability estimate. Whenthe MPS renormalization is required, Next_Index_MPS gives the new index for the LPS probability estimate. If
Switch_MPS is 1 for the old index, the MPS symbol sense must be inverted after an LPS.

D.1.5.3 Estimation following renormalization after MPS

The procedure for estimating the probability on the MPS renormalization path is given in Figure D.5. Index(S) is part ofthe information stored for context-index S. The new value of Index(S) is obtained from Table D.3 from the column labeled
Next_Index_MPS, as that is the next index after an MPS renormalization. This next index is stored as the new value of
Index(S) in the context storage at context-index S, and the value of Qe at this new Index(S) becomes the new Qe(S).
MPS(S) does not change.

Estimate_Qe(S)_after_MPS

I = Index(S)I = Next_Index_MPS(I)
Index(S) = I
Qe(S) = Qe_Value(I)

Done

TISO1060-93/d043

Figure D.5 – Probability estimation on MPS renormalization path

Figure D.5 [D43], = 7 cm = 273.%

CCITT Rec. T.81 (1992 E)

61

ISO/IEC 10918-1 : 1993(E)D.1.5.4 Estimation following renormalization after LPS
The procedure for estimating the probability on the LPS renormalization path is shown in Figure D.6. The procedure issimilar to that of Figure D.5 except that when Switch_MPS(I) is 1, the sense of MPS(S) must be inverted.

Estimate_Qe(S)_after_LPS

I = Index(S)No

Switch_MPS(I) = 1?

Yes

MPS(S) = 1 – MPS(S)I = Next_Index_LPS(I)
Index(S) = I
Qe(S) = Qe_Value(I)

Done
TISO1070-93/d044

Figure D.6 – Probability estimation on LPS renormalization path
Figure D.6 [D44], = 14 cm = 547.%

D.1.6

Renormalization in the encoder

The Renorm_e procedure for the encoder renormalization is shown in Figure D.7. Both the probability interval register A
and the code register C are shifted, one bit at a time. The number of shifts is counted in the counter CT; when CT is zero,
a byte of compressed data is removed from C by the procedure Byte_out and CT is reset to 8. Renormalization continues
until A is no longer less than X’8000’.

62

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Renorm_e

A = SLL A 1
C = SLL C 1
CT = CT – 1

No

CT = 0?
Yes
Byte_out

CT = 8A < X’8000’
?

Yes

No
Done

TISO1080-93/d045

Figure D.7 – Encoder renormalization procedure

Figure D.7 [D45], = 16.5 cm = 645.%

The Byte_out procedure used in Renorm_e is shown in Figure D.8. This procedure uses byte-stuffing procedures which
prevent accidental generation of markers by the arithmetic encoding procedures. It also includes an example of aprocedure for resolving carry-over. For simplicity of exposition, the buffer holding the entropy-coded segment is assumed
to be large enough to contain the entire segment.

In Figure D.8 BP is the entropy-coded segment pointer and B is the compressed data byte pointed to by BP. T in Byte_out
is a temporary variable which is used to hold the output byte and carry bit. ST is the stack counter which is used to count
X’FF’ output bytes until any carry-over through the X’FF’ sequence has been resolved. The value of ST rarely exceeds 3.
However, since the upper limit for the value of ST is bounded only by the total entropy-coded segment size, a precision of
32 bits is recommended for ST.

Since large values of ST represent a latent output of compressed data, the following procedure may be needed in highspeed synchronous encoding systems for handling the burst of output data which occurs when the carry is resolved.

CCITT Rec. T.81 (1992 E)

63

ISO/IEC 10918-1 : 1993(E)Byte_out

T = SRL C 19

B=B+1

Yes

T > X’FF’
?

No

Yes

Stuff_0

T = X’FF’?
No

Output_stacked_
zeros

ST = ST + 1

BP = BP + 1
B=T

Output_stacked_
X’FF’sBP = BP + 1
B=T

C = C AND X’7FFFF’Done
TISO1090-93/d046

Figure D.8 – Byte_out procedure for encoder

Figure D.8 [D46], = 18 cm = 704.%

When the stack count reaches an upper bound determined by output channel capacity, the stack is emptied and the stacked
X’FF’ bytes (and stuffed zero bytes) are added to the compressed data before the carry-over is resolved. If a carry-overthen occurs, the carry is added to the final stuffed zero, thereby converting the final X’FF00’ sequence to the X’FF01’
temporary private marker. The entropy-coded segment must then be post-processed to resolve the carry-over and remove
the temporary marker code. For any reasonable bound on ST this post processing is very unlikely.

Referring to Figure D.8, the shift of the code register by 19 bits aligns the output bits with the low order bits of T. The
first test then determines if a carry-over has occurred. If so, the carry must be added to the previous output byte before
advancing the segment pointer BP. The Stuff_0 procedure stuffs a zero byte whenever the addition of the carry to the data
already in the entropy-coded segments creates a X’FF’ byte. Any stacked output bytes – converted to zeros by the carryover – are then placed in the entropy-coded segment. Note that when the output byte is later transferred from T to theentropy-coded segment (to byte B), the carry bit is ignored if it is set.

64

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)If a carry has not occurred, the output byte is tested to see if it is X’FF’. If so, the stack count ST is incremented, as theoutput must be delayed until the carry-over is resolved. If not, the carry-over has been resolved, and any stacked X’FF’
bytes must then be placed in the entropy-coded segment. Note that a zero byte is stuffed following each X’FF’.

The procedures used by Byte_out are defined in Figures D.9 through D.11.

Output_stacked_
zeros

ST = 0?

Yes

No
BP = BP + 1
B=0
ST = ST – 1

Done

TISO1810-93/d047

Figure D.9 – Output_stacked_zeros procedure for encoder

Figure D.9 [D47], = 8.5 cm = 332.%

Output_stacked_
X’FF’sST = 0?

Yes

No
BP = BP + 1
B = X’FF’
BP = BP + 1
B=0
ST = ST – 1

Done

TISO1100-93/d048

Figure D.10 – Output_stacked_X’FF’s procedure for encoder

Figure D.10 [D48], = 8.5 cm = 332.%

CCITT Rec. T.81 (1992 E)

65

ISO/IEC 10918-1 : 1993(E)Stuff_0

No

B = X’FF’?
Yes
BP = BP + 1
B=0

Done
TISO1110-93/d049

Figure D.11 – Stuff_0 procedure for encoder

Figure D.11 [D49], = 10 cm = 391.%

D.1.7

Initialization of the encoder

The Initenc procedure is used to start the arithmetic coder. The basic steps are shown in Figure D.12.

Initenc

Initialize statistics areas
ST = 0A = X’10000’
A = (see Note below)
C=0
CT = 11
BP = BPST – 1

Done

TISO1120-93/d050

Figure D.12 – Initialization of the encoder

Figure D.12 [D50], = 9 cm = 352.%

66

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)The probability estimation tables are defined by Table D.3. The statistics areas are initialized to an MPS sense of 0 and a
Qe index of zero as defined by Table D.3. The stack count (ST) is cleared, the code register (C) is cleared, and the intervalregister is set to X’10000’. The counter (CT) is set to 11, reflecting the fact that when A is initialized to X’10000’ threespacer bits plus eight output bits in C must be filled before the first byte is removed. Note that BP is initialized to point tothe byte before the start of the entropy-coded segment (which is at BPST). Note also that the statistics areas are initialized
for all values of context-index S to MPS(S) = 0 and Index(S) = 0.
NOTE – Although the probability interval is initialized to X’10000’ in both Initenc and Initdec, the precision of
the probability interval register can still be limited to 16 bits. When the precision of the interval register is 16 bits, it is initialized to
zero.

D.1.8

Termination of encoding

The Flush procedure is used to terminate the arithmetic encoding procedures and prepare the entropy-coded segment for
the addition of the X’FF’ prefix of the marker which follows the arithmetically coded data. Figure D.13 shows this flushprocedure. The first step in the procedure is to set as many low order bits of the code register to zero as possible without
pointing outside of the final interval. Then, the output byte is aligned by shifting it left by CT bits; Byte_out then removes
it from C. C is then shifted left by 8 bits to align the second output byte and Byte_out is used a second time. The
remaining low order bits in C are guaranteed to be zero, and these trailing zero bits shall not be written to the entropycoded segment.

Flush

Clear_final_bits

C = SLL C CT

Byte_out

C = SLL C 8

Byte_out
Discard_final_zeros

Done
TISO1130-93/d051

Figure D.13 – Flush procedure
Figure D.13 [D51], = 15.5 cm = 606.%

CCITT Rec. T.81 (1992 E)

67

ISO/IEC 10918-1 : 1993(E)Any trailing zero bytes already written to the entropy-coded segment and not preceded by a X’FF’ may, optionally, be
discarded. This is done in the Discard_final_zeros procedure. Stuffed zero bytes shall not be discarded.

Entropy coded segments are always followed by a marker. For this reason, the final zero bits needed to complete decoding
shall not be included in the entropy coded segment. Instead, when the decoder encounters a marker, zero bits shall be
supplied to the decoding procedure until decoding is complete. This convention guarantees that when a DNL marker isused, the decoder will intercept it in time to correctly terminate the decoding procedure.

Clear_final_bits

T=C+A–1
T = T ANDT = X’FFFF0000’

T<C
?

No

Yes
T = T + X’8000’

C=T

Done

TISO1140-93/d052

Figure D.14 – Clear_final_bits procedure in Flush

Figure D.14 [D52], = 14 cm = 547.%

68

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Discard_final_zeros

Yes

BP < BPST?
No
Yes
BP = BP – 1

B=0
?
No

Yes
BP = BP + 1

B = X’FF’
?
No

Done
TISO1150-93/d053

Figure D.15 – Discard_final_zeros procedure in Flush
Figure D.15 [D53], = 12.5cm = 489.%

D.2

Arithmetic decoding procedures

Two arithmetic decoding procedures are used for arithmetic decoding (see Table D.4).
The “Decode(S)” procedure decodes the binary decision for a given context-index S and returns a value of either 0 or 1. It
is the inverse of the “Code_0(S)” and “Code_1(S)” procedures described in D.1. “Initdec” initializes the arithmeticcoding entropy decoder.
Table D.4 – Procedures for binary arithmetic decoding

Procedure

Purpose

Decode(S)Decode a binary decision with context-index S

Initdec

Initialize the decoder

CCITT Rec. T.81 (1992 E)

69

ISO/IEC 10918-1 : 1993(E)D.2.1

Binary arithmetic decoding principles

The probability interval subdivision and sub-interval ordering defined for the arithmetic encoding procedures also apply tothe arithmetic decoding procedures.
Since the bit stream always points within the current probability interval, the decoding process is a matter of determining,for each decision, which sub-interval is pointed to by the bit stream. This is done recursively, using the same probability
interval sub-division process as in the encoder. Each time a decision is decoded, the decoder subtracts from the bit stream
any interval the encoder added to the bit stream. Therefore, the code register in the decoder is a pointer into the current
probability interval relative to the base of the interval.
If the size of the sub-interval allocated to the LPS is larger than the sub-interval allocated to the MPS, the encoder invokes
the conditional exchange procedure. When the interval sizes are inverted in the decoder, the sense of the symbol decoded
must be inverted.
D.2.2

Decoding conventions and approximations

The approximations and integer arithmetic defined for the probability interval subdivision in the encoder must also be
used in the decoder. However, where the encoder would have added to the code register, the decoder subtracts from thecode register.
D.2.3

Decoder code register conventions

The flow charts given in this section assume the register structures for the decoder as shown in Table D.5:

Table D.5 – Decoder register conventions

MSB

LSB

Cx register

xxxxxxxx,

xxxxxxxx

C-low

bbbbbbbb,

00000000

A-register

aaaaaaaa,

aaaaaaaa

Cx and C-low can be regarded as one 32-bit C-register, in that renormalization of C shifts a bit of new data from bit 15 of
C-low to bit 0 of Cx. However, the decoding comparisons use Cx alone. New data are inserted into the “b” bits of C-low
one byte at a time.
NOTE – The comparisons shown in the various procedures use arithmetic comparisons, and therefore assume precisions
greater than 16 bits for the variables. Unsigned (logical) comparisons should be used in 16-bit precision implementations.

D.2.4

The decode procedure

The decoder decodes one binary decision at a time. After decoding the decision, the decoder subtracts any amount fromthe code register that the encoder added. The amount left in the code register is the offset from the base of the current
probability interval to the sub-interval allocated to the binary decisions not yet decoded. In the first test in the decode
procedure shown in Figure D.16 the code register is compared to the size of the MPS sub-interval. Unless a conditional
exchange is needed, this test determines whether the MPS or LPS for context-index S is decoded. Note that the LPS forcontext-index S is given by 1 – MPS(S).

70

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)When a renormalization is needed, the MPS/LPS conditional exchange may also be needed. For the LPS path, theconditional exchange procedure is shown in Figure D.17. Note that the probability estimation in the decoder is identicalto the probability estimation in the encoder (Figures D.5 and D.6).

Decode(S)A = A – Qe(S)Yes

A < X’8000’

Cx < A
?

No

No

Yes
Di=iCond_MPS_exchange(S)Renorm_d

D = MPS(S)D = Cond_LPS_exchange(S)Renorm_d

TISO1160-93/d054

Return D

Figure D.16 – Decode(S) procedure
Figure D.16 [D54], = 13.5 cm = 528.%

For the MPS path of the decoder the conditional exchange procedure is given in Figure D.18.

CCITT Rec. T.81 (1992 E)

71

ISO/IEC 10918-1 : 1993(E)Cond_LPS_
exchange(S)Yes

A < Qe(S)?

No

D = MPS(S)Cx = Cx – A
A = Qe(S)D = 1 – MPS(S)Cx = Cx – A
A = Qe(S)Estimate_Qe(S)_after_MPS

Estimate_Qe(S)_after_LPS

Return D
TISO1170-93/d055

Figure D.17 – Decoder LPS path conditional exchange procedure
Figure D.17 [D55], = 12 cm = 469.%

Cond_MPS_
exchange(S)Yes

A < Qe(S)?

No

D = 1 – MPS(S)D = MPS(S)

Estimate_Qe(S)_after_LPS

Estimate_Qe(S)_after_MPS

Return D
TISO1180-93/d056

Figure D.18 – Decoder MPS path conditional exchange procedure
Figure D.18 [D56], = 12 cm = 469.%

72

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)D.2.5

Probability estimation in the decoder

The procedures defined for obtaining a new LPS probability estimate in the encoder are also used in the decoder.

D.2.6

Renormalization in the decoder

The Renorm_d procedure for the decoder renormalization is shown in Figure D.19. CT is a counter which keeps track of
the number of compressed bits in the C-low section of the C-register. When CT is zero, a new byte is inserted into C-low
by the procedure Byte_in and CT is reset to 8.
Both the probability interval register A and the code register C are shifted, one bit at a time, until A is no longer less thanX’8000’.

Renorm_dNo

CT = 0?
Yes
Byte_in

CT = 8A = SLL A 1
C = SLL C 1
CT = CT – 1

A < X’8000’
?

Yes

No

Done

TISO1190-93/d057

Figure D.19 – Decoder renormalization procedure
Figure D.19 [D57], = 16.5 cm = 645.%

CCITT Rec. T.81 (1992 E)

73

ISO/IEC 10918-1 : 1993(E)The Byte_in procedure used in Renorm_d is shown in Figure D.20. This procedure fetches one byte of data,compensating for the stuffed zero byte which follows any X’FF’ byte. It also detects the marker which must follow theentropy-coded segment. The C-register in this procedure is the concatenation of the Cx and C-low registers. For simplicity
of exposition, the buffer holding the entropy-coded segment is assumed to be large enough to contain the entire segment.

B is the byte pointed to by the entropy-coded segment pointer BP. BP is first incremented. If the new value of B is not a
X’FF’, it is inserted into the high order 8 bits of C-low.

Byte_in

BP = BP + 1

Yes

B = X’FF’?

Unstuff_0

No

C = C + SLL B 8

Done
TISO1200-93/d058

Figure D.20 – Byte_in procedure for decoder

Figure D.20 [D58], = 12 cm = 469.%

74

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)The Unstuff_0 procedure is shown in Figure D.21. If the new value of B is X’FF’, BP is incremented to point to the next
byte and this next B is tested to see if it is zero. If so, B contains a stuffed byte which must be skipped. The zero B is
ignored, and the X’FF’ B value which preceded it is inserted in the C-register.

If the value of B after a X’FF’ byte is not zero, then a marker has been detected. The marker is interpreted as required andthe entropy-coded segment pointer is adjusted (“Adjust BP” in Figure D.21) so that 0-bytes will be fed to the decoder
until decoding is complete. One way of accomplishing this is to point BP to the byte preceding the marker which follows
the entropy-coded segment.

Unstuff_0

BP = BP + 1

Yes

B=0
?

No

Interpret_marker
Adjust BP

C = C OR X’FF00’

Done
TISO1210-93/d059

Figure D.21 – Unstuff_0 procedure for decoder

Figure D.21 [D59], = 12 cm = 469.%

CCITT Rec. T.81 (1992 E)

75

ISO/IEC 10918-1 : 1993(E)D.2.7

Initialization of the decoder

The Initdec procedure is used to start the arithmetic decoder. The basic steps are shown in Figure D.22.

Initdec

Initialize statistics areas
BP = BPST – 1
A = X’0000’
A = (see Note below)
C=0

Byte_in

C = SLL C 8

Byte_in

C = SLL C 8
CT = 0Done
TISO1220-93/d060

Figure D.22 – Initialization of the decoder
Figure D.22 [D60], = 16 cm = 625.%
The estimation tables are defined by Table D.3. The statistics areas are initialized to an MPS sense of 0 and a Qe index ofzero as defined by Table D.3. BP, the pointer to the entropy-coded segment, is then initialized to point to the byte before
the start of the entropy-coded segment at BPST, and the interval register is set to the same starting value as in the encoder.
The first byte of compressed data is fetched and shifted into Cx. The second byte is then fetched and shifted into Cx. The
count is set to zero, so that a new byte of data will be fetched by Renorm_d.
NOTE – Although the probability interval is initialized to X’10000’ in both Initenc and Initdec, the precision of
the probability interval register can still be limited to 16 bits. When the precision of the interval register is 16 bits, it is initialized to
zero.

D.3

Bit ordering within bytes

The arithmetically encoded entropy-coded segment is an integer of variable length. Therefore, the ordering of bytes andthe bit ordering within bytes is the same as for parameters (see B.1.1.1).

76

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Annex E
Encoder and decoder control procedures(This annex forms an integral part of this Recommendation | International Standard)This annex describes the encoder and decoder control procedures for the sequential, progressive, and lossless modes ofoperation.
The encoding and decoding control procedures for the hierarchical processes are specified in Annex J.
NOTES
1There is no requirement in this Specification that any encoder or decoder shall implement the procedures in precisely
the manner specified by the flow charts in this annex. It is necessary only that an encoder or decoder implement the function specified
in this annex. The sole criterion for an encoder or decoder to be considered in compliance with this Specification is that it satisfy therequirements given in clause 6 (for encoders) or clause 7 (for decoders), as determined by the compliance tests specified in Part 2.
2

Implementation-specific setup steps are not indicated in this annex and may be necessary.

E.1

Encoder control procedures

E.1.1

Control procedure for encoding an image

The encoder control procedure for encoding an image is shown in Figure E.1.

Encode_image

Append SOI marker

Encode_frame

Append EOI marker

Done

TISO1230-93/d061

Figure E.1 – Control procedure for encoding an image
Figure E.1 [D61], = 11.5 cm = 449.%

CCITT Rec. T.81 (1992 E)

77ISO/IEC 10918-1 : 1993(E)E.1.2

Control procedure for encoding a frame

In all cases where markers are appended to the compressed data, optional X’FF’ fill bytes may precede the marker.
The control procedure for encoding a frame is oriented around the scans in the frame. The frame header is first appended,and then the scans are coded. Table specifications and other marker segments may precede the SOFn marker, as indicatedby [tables/miscellaneous] in Figure E.2.
Figure E.2 shows the encoding process frame control procedure.

Encode_frame[Append tables/miscellaneous]
Append SOF n marker and restof frame header

Encode_scan

First scan?

Yes

[Append DNL
segment]

No

Yes

More scans
?
No

Done
TISO1240-93/d062

Figure E.2 – Control procedure for encoding a frame
Figure E.2 [D62], = 14 cm = 547.%

E.1.3

Control procedure for encoding a scan

A scan consists of a single pass through the data of each component in the scan. Table specifications and other marker
segments may precede the SOS marker. If more than one component is coded in the scan, the data are interleaved. If
restart is enabled, the data are segmented into restart intervals. If restart is enabled, a RSTm marker is placed in the coded
data between restart intervals. If restart is disabled, the control procedure is the same, except that the entire scan contains asingle restart interval. The compressed image data generated by a scan is always followed by a marker, either the EOI
marker or the marker of the next marker segment.

78

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Figure E.3 shows the encoding process scan control procedure. The loop is terminated when the encoding process has
coded the number of restart intervals which make up the scan. “m” is the restart interval modulo counter needed for the
RSTm marker. The modulo arithmetic for this counter is shown after the “Append RSTm marker” procedure.

Encode_scan[Append tables/miscellaneous]
Append SOS marker and rest ofscan header
m=0

Encode_restart_
intervalMore intervals
?

No

Yes
Append RST m marker
m = (m + 1) AND 7

Done
TISO1250-93/d063

Figure E.3 – Control procedure for encoding a scanFigure E.3 [D63], = 13 cm = 508.%

CCITT Rec. T.81 (1992 E)

79ISO/IEC 10918-1 : 1993(E)E.1.4

Control procedure for encoding a restart interval

Figure E.4 shows the encoding process control procedure for a restart interval. The loop is terminated either when theencoding process has coded the number of minimum coded units (MCU) in the restart interval or when it has completed
the image scan.

Encode_restart_
interval

Reset_encoder

Encode_MCU

More MCU?

No

Prepare_for_marker

Yes
Done
TISO1260-93/d064

Figure E.4 – Control procedure for encoding a restart interval
Figure E.4 [D64], = 12 cm = 469.%

The “Reset_encoder” procedure consists at least of the following:a)

if arithmetic coding is used, initialize the arithmetic encoder using the “Initenc” procedure describedin D.1.7;b)for DCT-based processes, set the DC prediction (PRED) to zero for all components in the scan(see F.1.1.5.1);c)for lossless processes, reset the prediction to a default value for all components in the scan (see H.1.1);d)do all other implementation-dependent setups that may be necessary.

The procedure “Prepare_for_marker” terminates the entropy-coded segment by:a)padding a Huffman entropy-coded segment with 1-bits to complete the final byte (and if needed stuffing azero byte) (see F.1.2.3); orb)

invoking the procedure “Flush” (see D.1.8) to terminate an arithmetic entropy-coded segment.

NOTE – The number of minimum coded units (MCU) in the final restart interval must be adjusted to match the numberof MCU in the scan. The number of MCU is calculated from the frame and scan parameters. (See Annex B.)

80

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)E.1.5

Control procedure for encoding a minimum coded unit (MCU)

The minimum coded unit is defined in A.2. Within a given MCU the data units are coded in the order in which they occur
in the MCU. The control procedure for encoding a MCU is shown in Figure E.5.

Encode_MCU

N =0

N=N+1
Encode data unitNo

N = Nb?
Yes

Done
TISO1270-93/d065

Figure E.5 – Control procedure for encoding a minimum coded unit (MCU)
Figure E.5 [D65], = 12 cm = 469.%
In Figure E.5, Nb refers to the number of data units in the MCU. The order in which data units occur in the MCU isdefined in A.2. The data unit is an 8 × 8 block for DCT-based processes, and a single sample for lossless processes.
The procedures for encoding a data unit are specified in Annexes F, G, and H.

E.2

Decoder control procedures

E.2.1

Control procedure for decoding compressed image data

Figure E.6 shows the decoding process control for compressed image data.
Decoding control centers around identification of various markers. The first marker must be the SOI (Start Of Image)marker. The “Decoder_setup” procedure resets the restart interval (Ri = 0) and, if the decoder has arithmetic decoding
capabilities, sets the conditioning tables for the arithmetic coding to their default values. (See F.1.4.4.1.4 and F.1.4.4.2.1.)
The next marker is normally a SOFn (Start Of Frame) marker; if this is not found, one of the marker segments listed inTable E.1 has been received.

CCITT Rec. T.81 (1992 E)

81ISO/IEC 10918-1 : 1993(E)Decode_image

SOI marker
?

No

Yes
Decoder_setup

SOFn marker
?

Error

No

Interpret markers

Yes
Decode_frame

Done
TISO1280-93/d066

Figure E.6 – Control procedure for decoding compressed image data

Figure E.6 [D66], = 14 cm = 547 %Table E.1 – Markers recognized by “Interpret markers”
MarkerPurposeDHT

Define Huffman Tables

DAC

Define Arithmetic Conditioning

DQT

Define Quantization Tables

DRI

Define Restart Interval

APPn

Application defined marker

COM

Comment

Note that optional X’FF’ fill bytes which may precede any marker shall be discarded before determining which marker ispresent.

82

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)The additional logic to interpret these various markers is contained in the box labeled “Interpret markers”. DHT markers
shall be interpreted by processes using Huffman coding. DAC markers shall be interpreted by processes using arithmeticcoding. DQT markers shall be interpreted by DCT-based decoders. DRI markers shall be interpreted by all decoders.
APPn and COM markers shall be interpreted only to the extent that they do not interfere with the decoding.
By definition, the procedures in “Interpret markers” leave the system at the next marker. Note that if the expected SOI
marker is missing at the start of the compressed image data, an error condition has occurred. The techniques for detecting
and managing error conditions can be as elaborate or as simple as desired.

E.2.2

Control procedure for decoding a frame

Figure E.7 shows the control procedure for the decoding of a frame.

Decode_frame

Interpret frame header

SOS marker?

No

Interpret markers

Yes
Decode_scan

No

EOI marker
?
Yes

Done
TISO1290-93/d067

Figure E.7 – Control procedure for decoding a frame
Figure E.7 [D67], = 13.5 cm = 528.%

The loop is terminated if the EOI marker is found at the end of the scan.
The markers recognized by “Interpret markers” are listed in Table E.1. Subclause E.2.1 describes the extent to which thevarious markers shall be interpreted.

CCITT Rec. T.81 (1992 E)

83ISO/IEC 10918-1 : 1993(E)E.2.3

Control procedure for decoding a scanFigure E.8 shows the decoding of a scan.
The loop is terminated when the expected number of restart intervals has been decoded.

Decode_scan

Interpret scan header
m= 0

Decode_restart_
intervalMore intervals
?

No

Yes
Done
TISO1300-93/d068

Figure E.8 – Control procedure for decoding a scanFigure E.8 [D68], = 11.5cm = 449.%

84

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)E.2.4

Control procedure for decoding a restart interval

The procedure for decoding a restart interval is shown in Figure E.9. The “Reset_decoder” procedure consists at least of
the following:a)

if arithmetic coding is used, initialize the arithmetic decoder using the “Initdec” procedure describedin D.2.7;b)for DCT-based processes, set the DC prediction (PRED) to zero for all components in the scan(see F.2.1.3.1);c)for lossless process, reset the prediction to a default value for all components in the scan (see H.2.1);d)do all other implementation-dependent setups that may be necessary.

Decode_restart_
interval

Reset_decoder

Decode_MCU

More MCU?

No

Find marker

Yes

Done
TISO1310-93/d069

Figure E.9 – Control procedure for decoding a restart interval
Figure E.9 [D69], = 12 cm = 469.%

At the end of the restart interval, the next marker is located. If a problem is detected in locating this marker, error handlin gprocedures may be invoked. While such procedures are optional, the decoder shall be able to correctly recognize restartmarkers in the compressed data and reset the decoder when they are encountered. The decoder shall also be able torecognize the DNL marker, set the number of lines defined in the DNL segment, and end the “Decode_restart_interval”
procedure.
NOTE – The final restart interval may be smaller than the size specified by the DRI marker segment, as it includes only the
number of MCUs remaining in the scan.

CCITT Rec. T.81 (1992 E)

85

ISO/IEC 10918-1 : 1993(E)E.2.5

Control procedure for decoding a minimum coded unit (MCU)

The procedure for decoding a minimum coded unit (MCU) is shown in Figure E.10.
In Figure E.10 Nb is the number of data units in a MCU.
The procedures for decoding a data unit are specified in Annexes F, G, and H.

Decode_MCU

N=0

N=N+1
Decode_data_unit

No

N = Nb?
Yes

Done
TISO1320-93/d070

Figure E.10 – Control procedure for decoding a minimum coded unit (MCU)
Figure E.106 [D70], = 11.5 cm = 449.%

86

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Annex F
Sequential DCT-based mode of operation(This annex forms an integral part of this Recommendation | International Standard)
ISO/IEC 10918-1 : 1993(E)
CCITT Rec. T.81 (1992 E)

This annex provides a functional specification of the following coding processes for the sequential DCT-based mode ofoperation:1)

baseline sequential;

2)extended sequential, Huffman coding, 8-bit sample precision;

3)

extended sequential, arithmetic coding, 8-bit sample precision;

4)extended sequential, Huffman coding, 12-bit sample precision;

5)extended sequential, arithmetic coding, 12-bit sample precision.

For each of these, the encoding process is specified in F.1, and the decoding process is specified in F.2. The functional
specification is presented by means of specific flow charts for the various procedures which comprise these coding
processes.
NOTE – There is no requirement in this Specification that any encoder or decoder which embodies one of the above-named
processes shall implement the procedures in precisely the manner specified by the flow charts in this annex. It is necessary only that an
encoder or decoder implement the function specified in this annex. The sole criterion for an encoder or decoder to be considered incompliance with this Specification is that it satisfy the requirements given in clause 6 (for encoders) or clause 7 (for decoders), as
determined by the compliance tests specified in Part 2.

F.1

Sequential DCT-based encoding processes

F.1.1

Sequential DCT-based control procedures and coding models

F.1.1.1

Control procedures for sequential DCT-based encoders

The control procedures for encoding an image and its constituent parts – the frame, scan, restart interval and
MCU – are given in Figures E.1 to E.5. The procedure for encoding a MCU (see Figure E.5) repetitively calls theprocedure for encoding a data unit. For DCT-based encoders the data unit is an 8 × 8 block of samples.
F.1.1.2

Procedure for encoding an 8 × 8 block data unit

For the sequential DCT-based processes encoding an 8 × 8 block data unit consists of the following procedures:

F.1.1.3

a)level shift, calculate forward 8 × 8 DCT and quantize the resulting coefficients using table destination
specified in frame header;b)

encode DC coefficient for 8 × 8 block using DC table destination specified in scan header;c)encode AC coefficients for 8 × 8 block using AC table destination specified in scan header.

Level shift and forward DCT (FDCT)The mathematical definition of the FDCT is given in A.3.3.
Prior to computing the FDCT the input data are level shifted to a signed two’s complement representation as described in
A.3.1. For 8-bit input precision the level shift is achieved by subtracting 128. For 12-bit input precision the level shift isachieved by subtracting 2048.
F.1.1.4

Quantization of the FDCTThe uniform quantization procedure described in Annex A is used to quantize the DCT coefficients. One of four
quantization tables may be used by the encoder. No default quantization tables are specified in this Specification.
However, some typical quantization tables are given in Annex K.
The quantized DCT coefficient values are signed, two’s complement integers with 11-bit precision for 8-bit input
precision and 15-bit precision for 12-bit input precision.
CCITT Rec. T.81 (1992 E)

87ISO/IEC 10918-1 : 1993(E)F.1.1.5

Encoding models for the sequential DCT procedures

The two dimensional array of quantized DCT coefficients is rearranged in a zig-zag sequence order defined in A.3.6. The
zig-zag order coefficients are denoted ZZ (0) through ZZ(63) with:
ZZ(0) = Sq00,ZZ(1) = Sq01,ZZ(2) = Sq10,•,•,•,ZZ(63) = Sq77

Sqvu are defined in Figure A.6.
Two coding procedures are used, one for the DC coefficient ZZ(0) and the other for the AC coefficients ZZ(1)..ZZ(63).
The coefficients are encoded in the order in which they occur in zig-zag sequence order, starting with the DC coefficient.
The coefficients are represented as two’s complement integers.
F.1.1.5.1

Encoding model for DC coefficientsThe DC coefficients are coded differentially, using a one-dimensional predictor, PRED, which is the quantized DC value
from the most recently coded 8 × 8 block from the same component. The difference, DIFF, is obtained from
DIFF = ZZ(0) – PRED
At the beginning of the scan and at the beginning of each restart interval, the prediction for the DC coefficient prediction
is initialized to 0. (Recall that the input data have been level shifted to two’s complement representation.)
F.1.1.5.2

Encoding model for AC coefficients

Since many coefficients are zero, runs of zeros are identified and coded efficiently. In addition, if the remaining
coefficients in the zig-zag sequence order are all zero, this is coded explicitly as an end-of-block (EOB).
F.1.2

Baseline Huffman encoding procedures

The baseline encoding procedure is for 8-bit sample precision. The encoder may employ up to two DC and two AC
Huffman tables within one scan.
F.1.2.1

Huffman encoding of DC coefficients

F.1.2.1.1

Structure of DC code table

The DC code table consists of a set of Huffman codes (maximum length 16 bits) and appended additional bits (in mostcases) which can code any possible value of DIFF, the difference between the current DC coefficient and the prediction.
The Huffman codes for the difference categories are generated in such a way that no code consists entirely of 1-bits(X’FF’ prefix marker code avoided).
The two’s complement difference magnitudes are grouped into 12 categories, SSSS, and a Huffman code is created foreach of the 12 difference magnitude categories (see Table F.1).
For each category, except SSSS = 0, an additional bits field is appended to the code word to uniquely identify which
difference in that category actually occurred. The number of extra bits is given by SSSS; the extra bits are appended to the
LSB of the preceding Huffman code, most significant bit first. When DIFF is positive, the SSSS low order bits of DIFF
are appended. When DIFF is negative, the SSSS low order bits of (DIFF – 1) are appended. Note that the most significant
bit of the appended bit sequence is 0 for negative differences and 1 for positive differences.
F.1.2.1.2

Defining Huffman tables for the DC coefficients

The syntax for specifying the Huffman tables is given in Annex B. The procedure for creating a code table from thisinformation is described in Annex C. No more than two Huffman tables may be defined for coding of DC coefficients.
Two examples of Huffman tables for coding of DC coefficients are provided in Annex K.

88

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Table F.1 – Difference magnitude categories for DC coding

F.1.2.1.3

SSSS

DIFF values

10

0

11

–1,1

12

–3,–2,2,3

13–7..–4,4..7

14–15..–8,8..15

15–31..–16,16..31

16–63..–32,32..6317–127..–64,64..12718–255..–128,128..255

19–511..–256,256..511

10–1 023..–512,512..1 023

11–2 047..–1 024,1 024..2 047

Huffman encoding procedures for DC coefficients

The encoding procedure is defined in terms of a set of extended tables, XHUFCO and XHUFSI, which contain thecomplete set of Huffman codes and sizes for all possible difference values. For full 12-bit precision the tables are relatively
large. For the baseline system, however, the precision of the differences may be small enough to make this description
practical.
XHUFCO and XHUFSI are generated from the encoder tables EHUFCO and EHUFSI (see Annex C) by appending to the
Huffman codes for each difference category the additional bits that completely define the difference. By definition,
XHUFCO and XHUFSI have entries for each possible difference value. XHUFCO contains the concatenated bit pattern of
the Huffman code and the additional bits field; XHUFSI contains the total length in bits of this concatenated bit pattern.
Both are indexed by DIFF, the difference between the DC coefficient and the prediction.
The Huffman encoding procedure for the DC difference, DIFF, is:
SIZE = XHUFSI(DIFF)
CODE = XHUFCO(DIFF)
code SIZE bits of CODE
where DC is the quantized DC coefficient value and PRED is the predicted quantized DC value. The Huffman code
(CODE) (including any additional bits) is obtained from XHUFCO and SIZE (length of the code including additionalbits) is obtained from XHUFSI, using DIFF as the index to the two tables.
F.1.2.2

Huffman encoding of AC coefficients

F.1.2.2.1

Structure of AC code table

Each non-zero AC coefficient in ZZ is described by a composite 8-bit value, RS, of the form
RS = binary ’RRRRSSSS’CCITT Rec. T.81 (1992 E)

89ISO/IEC 10918-1 : 1993(E)The 4 least significant bits, ’SSSS’, define a category for the amplitude of the next non-zero coefficient in ZZ, and the 4
most significant bits, ’RRRR’, give the position of the coefficient in ZZ relative to the previous non-zero coefficient (i.e.
the run-length of zero coefficients between non-zero coefficients). Since the run length of zero coefficients may exceed
15, the value ’RRRRSSSS’ = X’F0’ is defined to represent a run length of 15 zero coefficients followed by a coefficientof zero amplitude. (This can be interpreted as a run length of 16 zero coefficients.) In addition, a special value’RRRRSSSS’ = ’00000000’ is used to code the end-of-block (EOB), when all remaining coefficients in the block arezero.
The general structure of the code table is illustrated in Figure F.1. The entries marked “N/A” are undefined for thebaseline procedure.

00.
RRRR .
.
15

EOB
N/A
N/A
N/A
ZRL

1

2

SSSS
. .

.

9

10

COMPOSITE VALUESTISO1330-93/d071

Figure F.1 – Two-dimensional value array for Huffman coding

Figure F.1 [D71] =4 cm = 156 %The magnitude ranges assigned to each value of SSSS are defined in Table F.2.
Table F.2 – Categories assigned to coefficient values

SSSS

AC coefficients

11

–1,1

12

–3,–2,2,3

13–7..–4,4..7

14–15..–8,8..15

15–31..–16,16..31

16–63..–32,32..6317–127..–64,64..12718–255..–128,128..255

19–511..–256,256..511

10–1 023..–512,512..1 023

The composite value, RRRRSSSS, is Huffman coded and each Huffman code is followed by additional bits which specify
the sign and exact amplitude of the coefficient.
The AC code table consists of one Huffman code (maximum length 16 bits, not including additional bits) for eachpossible composite value. The Huffman codes for the 8-bit composite values are generated in such a way that no code
consists entirely of 1-bits.

90

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)The format for the additional bits is the same as in the coding of the DC coefficients. The value of SSSS gives the numberof additional bits required to specify the sign and precise amplitude of the coefficient. The additional bits are either the
low-order SSSS bits of ZZ(K) when ZZ(K) is positive or the low-order SSSS bits of ZZ(K) – 1 when ZZ(K) is negative.
ZZ(K) is the Kth coefficient in the zig-zag sequence of coefficients being coded.
F.1.2.2.2

Defining Huffman tables for the AC coefficients

The syntax for specifying the Huffman tables is given in Annex B. The procedure for creating a code table from thisinformation is described in Annex C.
In the baseline system no more than two Huffman tables may be defined for coding of AC coefficients. Two examples ofHuffman tables for coding of AC coefficients are provided in Annex K.
F.1.2.2.3

Huffman encoding procedures for AC coefficients

As defined in Annex C, the Huffman code table is assumed to be available as a pair of tables, EHUFCO (containing thecode bits) and EHUFSI (containing the length of each code in bits), both indexed by the composite value defined above.
The procedure for encoding the AC coefficients in a block is shown in Figures F.2 and F.3. In Figure F.2, K is the index
to the zig-zag scan position and R is the run length of zero coefficients.
The procedure “Append EHUFSI(X’F0’) bits of EHUFCO(X’F0’)” codes a run of 16 zero coefficients (ZRL code of
Figure F.1). The procedure “Code EHUFSI(0) bits of EHUFCO(0)” codes the end-of-block (EOB code). If the lastcoefficient (K = 63) is not zero, the EOB code is bypassed.
CSIZE is a procedure which maps an AC coefficient to the SSSS value as defined in Table F.2.
F.1.2.3

Byte stuffing

In order to provide code space for marker codes which can be located in the compressed image data without decoding,byte stuffing is used.
Whenever, in the course of normal encoding, the byte value X’FF’ is created in the code string, a X’00’ byte is stuffed
into the code string.
If a X’00’ byte is detected after a X’FF’ byte, the decoder must discard it. If the byte is not zero, a marker has been
detected, and shall be interpreted to the extent needed to complete the decoding of the scan.
Byte alignment of markers is achieved by padding incomplete bytes with 1-bits. If padding with 1-bits creates a X’FF’
value, a zero byte is stuffed before adding the marker.
F.1.3

Extended sequential DCT-based Huffman encoding process for 8-bit sample precisionThis process is identical to the Baseline encoding process described in F.1.2, with the exception that the number of sets ofHuffman table destinations which may be used within the same scan is increased to four. Four DC and four AC Huffman
table destinations is the maximum allowed by this Specification.
F.1.4

Extended sequential DCT-based arithmetic encoding process for 8-bit sample precisionThis subclause describes the use of arithmetic coding procedures in the sequential DCT-based encoding process.
NOTE – The arithmetic coding procedures in this Specification are defined for the maximum precision to encourageinterchangeability.

The arithmetic coding extensions have the same DCT model as the Baseline DCT encoder. Therefore, Annex F.1.1 also
applies to arithmetic coding. As with the Huffman coding technique, the binary arithmetic coding technique is lossless. It
is possible to transcode between the two systems without either FDCT or IDCT computations, and without modification of
the reconstructed image.
The basic principles of adaptive binary arithmetic coding are described in Annex D. Up to four DC and four AC
conditioning table destinations and associated statistics areas may be used within one scan.
The arithmetic encoding procedures for encoding binary decisions, initializing the statistics area, initializing the encoder,terminating the code string, and adding restart markers are listed in Table D.1 of Annex D.

CCITT Rec. T.81 (1992 E)

91ISO/IEC 10918-1 : 1993(E)Encode_AC_
coefficients

K=0
R=0

K=K+1

ZZ(K) = 0
?

R=R+1

Yes

No
Append EHUFSI(X’F0’) bitsof EHUFCO(X’F0’)
R = R – 16

Yes

K = 63?

No

Yes

Append EHUFSI(X’00’) bitsof EHUFCO(X’00’)

R > 15?
No
Encode_R,ZZ(K)

R=0

No

K = 63?

Yes

Done
TISO1340-93/d072

Figure F.2 – Procedure for sequential encoding of AC coefficients with Huffman coding
Figure F.2 [D72] = 21 cm = 821 %92

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Encode_R,ZZ(K)SSSS = CSIZE(ZZ(K))
RS = (16 × R) + SSSS
Append EHUFSI(RS) bitsof EHUFCO(RS)Yes

ZZ(K) < 0?

No
ZZ(K) = ZZ(K) – 1

Append SSSS
low order bits of ZZ(K)Done

TISO1350-93/d073

Figure F.3 – Sequential encoding of a non-zero AC coefficient
Figure F.3 [D73] 14 cm = 547 %Some of the procedures in Table D.1 are used in the higher level control structure for scans and restart intervals describedin Annex E. At the beginning of scans and restart intervals, the probability estimates used in the arithmetic coder are resetto the standard initial value as part of the Initenc procedure which restarts the arithmetic coder. At the end of scans andrestart intervals, the Flush procedure is invoked to empty the code register before the next marker is appended.

F.1.4.1

Arithmetic encoding of DC coefficients

The basic structure of the decision sequence for encoding a DC difference value, DIFF, is shown in Figure F.4.
The context-index S0 and other context-indices used in the DC coding procedures are defined in Table F.4(see F.1.4.4.1.3). A 0-decision is coded if the difference value is zero and a 1-decision is coded if the difference is not
zero. If the difference is not zero, the sign and magnitude are coded using the procedure Encode_V(S0), which is
described in F.1.4.3.1.

F.1.4.2

Arithmetic encoding of AC coefficients

The AC coefficients are coded in the order in which they occur in the zig-zag sequence ZZ(1,...,63). An end-of-block(EOB) binary decision is coded before coding the first AC coefficient in ZZ, and after each non-zero coefficient. If the
EOB occurs, all remaining coefficients in ZZ are zero. Figure F.5 illustrates the decision sequence. The equivalent
procedure for the Huffman coder is found in Figure F.2.

CCITT Rec. T.81 (1992 E)

93ISO/IEC 10918-1 : 1993(E)Encode_DC_DIFF

V = DIFF

No

V=0
?

Code_1(S0)
Encode_V(S0)

Yes

Code_0(S0)

Done
TISO1360-93/d074

Figure F.4 – Coding model for arithmetic coding of DC difference
Figure F.4 [D74] = 11.5 cm = 449 %The context-indices SE and S0 used in the AC coding procedures are defined in Table F.5 (see F.1.4.4.2). In Figure F.5,
K is the index to the zig-zag sequence position. For the sequential scan, Kmin is 1 and Se is 63. The V = 0 decision is partof a loop which codes runs of zero coefficients. Whenever the coefficient is non-zero, “Encode_V(S0)” codes the sign andmagnitude of the coefficient. Each time a non-zero coefficient is coded, it is followed by an EOB decision. If the EOB
occurs, a 1-decision is coded to indicate that the coding of the block is complete. If the coefficient for K = Se is not zero,
the EOB decision is skipped.
F.1.4.3

Encoding the binary decision sequence for non-zero DC differences and AC coefficients

Both the DC difference and the AC coefficients are represented as signed two’s complement integer values. The
decomposition of these signed integer values into a binary decision tree is done in the same way for both the DC and AC
coding models.
Although the binary decision trees for this section of the DC and AC coding models are the same, the statistical models
for assigning statistics bins to the binary decisions in the tree are quite different.
F.1.4.3.1

Structure of the encoding decision sequence

The encoding sequence can be separated into three procedures, a procedure which encodes the sign, a second procedure
which identifies the magnitude category, and a third procedure which identifies precisely which magnitude occurred
within the category identified in the second procedure.
At the point where the binary decision sequence in Encode_V(S0) starts, the coefficient or difference has already been
determined to be non-zero. That determination was made in the procedures in Figures F.4 and F.5.
Denoting either DC differences (DIFF) or AC coefficients as V, the non-zero signed integer value of V is encoded by thesequence shown in Figure F.6. This sequence first codes the sign of V. It then (after converting V to a magnitude anddecrementing it by 1 to give Sz) codes the magnitude category of Sz (code_log2_Sz), and then codes the low ordermagnitude bits (code_Sz_bits) to identify the exact magnitude value.

94

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)There are two significant differences between this sequence and the similar set of operations described in F.1.2 for
Huffman coding. First, the sign is encoded before the magnitude category is identified, and second, the magnitude isdecremented by 1 before the magnitude category is identified.

Encode_AC_
Coefficients

K = Kmin

K = EOB?

Yes

Code_1(SE)No
Code_0(SE)

K=K+1

K=K+1

V = ZZ(K)

V=0
?

Yes

Code_0(S0)No
Code_1(S0)
Encode_V(S0)No

K = Se
?

Yes

Done

TISO1370-93/d075

Figure F.5 – AC coding model for arithmetic coding

Figure F.5 [D75] = 21 cm = 821 %CCITT Rec. T.81 (1992 E)

95ISO/IEC 10918-1 : 1993(E)Encode_V(S)

Encode_sign_of_V

Sz = | V | – 1

Encode_log2_Sz

Encode_Sz_bits

Done

TISO1380-93/d076

Figure F.6 – Sequence of procedures in encoding non-zero values of V
Figure F.6 [D76] = 13.5 cm = 528 %F.1.4.3.1.1

Encoding the sign

The sign is encoded by coding a 0-decision when the sign is positive and a 1-decision when the sign is negative(see Figure F.7).
The context-indices SS, SN and SP are defined for DC coding in Table F.4 and for AC coding in Table F.5. After the sign
is coded, the context-index S is set to either SN or SP, establishing an initial value for Encode_log2_Sz.
F.1.4.3.1.2

Encoding the magnitude category

The magnitude category is determined by a sequence of binary decisions which compares Sz against an exponentially
increasing bound (which is a power of 2) in order to determine the position of the leading 1-bit. This establishes themagnitude category in much the same way that the Huffman encoder generates a code for the value associated with thedifference category. The flow chart for this procedure is shown in Figure F.8.
The starting value of the context-index S is determined in Encode_sign_of_V, and the context-index values X1 and X2
are defined for DC coding in Table F.4 and for AC coding in Table F.5. In Figure F.8, M is the exclusive upper bound forthe magnitude and the abbreviations “SLL” and “SRL” refer to the shift-left-logical and shift-right-logical operations – inthis case by one bit position. The SRL operation at the completion of the procedure aligns M with the most significant bitof Sz (see Table F.3).
The highest precision allowed for the DCT is 15 bits. Therefore, the highest precision required for the coding decision
tree is 16 bits for the DC coefficient difference and 15 bits for the AC coefficients, including the sign bit.

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ISO/IEC 10918-1 : 1993(E)Encode_sign_of_V

Yes

V<0
?

No

Code_1(SS)

Code_0(SS)S = SNS = SP

Done
TISO1390-93/d077

Figure F.7 – Encoding the sign of V
Figure F.7 [D77] = 11 cm = 430 %Table F.3 – Categories for each maximum boundExclusive upperbound (M)Sz range

Number of low ordermagnitude bits

11111

0

10

11112

1

10

11114

2,3

11

11118

4,...,7

1211116

8,...,15

13

32332

16,...,31

14

66464

32,...,63

15

12128

64,...,127

16

25256

128,...,255

17

15512

256,...,511

18

11 024

512,...,1 023

19

22 048

1 024,...,2 047

10

14 096

2 048,...,4 095

11

18 192

4 096,...,8 191

12

16 3848 192,...,16 383

13

32 76816 384,...,32 767

14

CCITT Rec. T.81 (1992 E)

97ISO/IEC 10918-1 : 1993(E)Encode_log2_Sz

M=1

Sz < M?

Yes

No
Code_1(S)

M=2
S = X1

Sz < M?

Yes

No
Code_1(S)

M=4
S = X2

Sz < M?

Yes

No
Code_1(S)Code_0(S)M = SLL M 1
S=S+1

M = SRL M 1

Done

TISO1400-93/d078

Figure F.8 – Decision sequence to establish the magnitude category

98

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ISO/IEC 10918-1 : 1993(E)F.1.4.3.1.3

Encoding the exact value of the magnitude

After the magnitude category is encoded, the low order magnitude bits are encoded. These bits are encoded in order ofdecreasing bit significance. The procedure is shown in Figure F.9. The abbreviation “SRL” indicates the shift-rightlogical operation, and M is the exclusive bound established in Figure F.8. Note that M has only one bit set – shifting M
right converts it into a bit mask for the logical “AND” operation.
The starting value of the context-index S is determined in Encode_log2_Sz. The increment of S by 14 at the beginning of
this procedure sets the context-index to the value required in Tables F.4 and F.5.

Encode_Sz-bits

S = S + 14

M = SRL M 1

M=0
?

Yes

No

T = M AND Sz

Yes

Code_0(S)

T=0
?

Done

No

Code_1(S)TISO1410-93/d079

Figure F.9 – Decision sequence to code the magnitude bit patternFigure F.9 [D79] = 16.5 cm = 645 %CCITT Rec. T.81 (1992 E)

99ISO/IEC 10918-1 : 1993(E)F.1.4.4

Statistical models

An adaptive binary arithmetic coder requires a statistical model. The statistical model defines the contexts which are used
to select the conditional probability estimates used in the encoding and decoding procedures.
Each decision in the binary decision trees is associated with one or more contexts. These contexts identify the sense of the
MPS and the index in Table D.3 of the conditional probability estimate Qe which is used to encode and decode the binary
decision.
The arithmetic coder is adaptive, which means that the probability estimates for each context are developed andmaintained by the arithmetic coding system on the basis of prior coding decisions for that context.
F.1.4.4.1

Statistical model for coding DC prediction differences

The statistical model for coding the DC difference conditions some of the probability estimates for the binary decisions on
previous DC coding decisions.
F.1.4.4.1.1

Statistical conditioning on sign

In coding the DC coefficients, four separate statistics bins (probability estimates) are used in coding the zero/not-zero (V =0) decision, the sign decision and the first magnitude category decision. Two of these bins are used to code the V = 0
decision and the sign decision. The other two bins are used in coding the first magnitude decision, Sz < 1; one of thesebins is used when the sign is positive, and the other is used when the sign is negative. Thus, the first magnitude decision
probability estimate is conditioned on the sign of V.
F.1.4.4.1.2

Statistical conditioning on DC difference in previous block

The probability estimates for these first three decisions are also conditioned on Da, the difference value coded for theprevious DCT block of the same component. The differences are classified into five groups: zero, small positive, small
negative, large positive and large negative. The relationship between the default classification and the quantization scale isshown in Figure F.10.

. . . –5

–4

–3

– large

–2

–1

0

+1

+2

– small0+ small+3+4+5 . . . DC difference+ large

Classification

TISO1420-93/d080

Figure F.10 – Conditioning classification of difference values

Figure F.10 [D80] = 3 cm = 117 %The bounds for the “small” difference category determine the classification. Defining L and U as integers in the range 0 to
15 inclusive, the lower bound (exclusive) for difference magnitudes classified as “small” is zero for L = 0, and is 2L–1 for
L > 0.
The upper bound (inclusive) for difference magnitudes classified as “small” is 2U.
L shall be less than or equal to U.
These bounds for the conditioning category provide a segmentation which is identical to that listed in Table F.3.
F.1.4.4.1.3

Assignment of statistical bins to the DC binary decision tree

As shown in Table F.4, each statistics area for DC coding consists of a set of 49 statistics bins. In the following
explanation, it is assumed that the bins are contiguous. The first 20 bins consist of five sets of four bins selected by acontext-index S0. The value of S0 is given by DC_Context(Da), which provides a value of 0, 4, 8, 12 or 16, depending on
the difference classification of Da (see F.1.4.4.1.2). The remaining 29 bins, X1,...,X15,M2,...,M15, are used to code
magnitude category decisions and magnitude bits.

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ISO/IEC 10918-1 : 1993(E)Table F.4 – Statistical model for DC coefficient coding
Context-index
S0
SS
SP
SN
X1
X2
X3
.
.
X15
M2
M3
.
.
M15

F.1.4.4.1.4

Value
DC_Context(Da)S0 + 1S0 + 2S0 + 320
X1 + 1X1 + 2.
.
X1 + 14
X2 + 14
X3 + 14.
.
X15 + 14

Coding decision
V=0
Sign of V
Sz < 1 if V > 0
Sz < 1 if V < 0
Sz < 2
Sz < 4
Sz < 8.
.
Sz < 215
Magnitude bits if Sz < 4
Magnitude bits if Sz < 8.
.
Magnitude bits if Sz < 215

Default conditioning for DC statistical model

The bounds, L and U, for determining the conditioning category have the default values L = 0 and U = 1. Other bounds
may be set using the DAC (Define Arithmetic coding Conditioning) marker segment, as described in Annex B.
F.1.4.4.1.5

Initial conditions for DC statistical model

At the start of a scan and at the beginning of each restart interval, the difference for the previous DC value is defined to be
zero in determining the conditioning state.
F.1.4.4.2

Statistical model for coding the AC coefficients

As shown in Table F.5, each statistics area for AC coding consists of a contiguous set of 245 statistics bins. Three bins areused for each value of the zig-zag index K, and two sets of 28 additional bins X2,...,X15,M2,...,M15 are used for coding
the magnitude category and magnitude bits.
The value of SE (and also S0, SP and SN) is determined by the zig-zag index K. Since K is in the range 1 to 63, thelowest value for SE is 0 and the largest value for SP is 188. SS is not assigned a value in AC coefficient coding, as thesigns of the coefficients are coded with a fixed probability value of approximately 0.5 (Qe = X’5A1D’, MPS = 0).
The value of X2 is given by AC_Context(K). This gives X2 = 189 when K ≤ Kx and X2 = 217 when K > Kx, where Kx isdefined using the DAC marker segment (see B.2.4.3).
Note that a X1 statistics bin is not used in this sequence. Instead, the 63 × 1 array of statistics bins for the magnitudecategory is used for two decisions. Once the magnitude bound has been determined – at statistics bin Xn, for example – asingle statistics bin, Mn, is used to code the magnitude bit sequence for that bound.
F.1.4.4.2.1

Default conditioning for AC coefficient coding

The default value of Kx is 5. This may be modified using the DAC marker segment, as described in Annex B.
F.1.4.4.2.2

Initial conditions for AC statistical model

At the start of a scan and at each restart, all statistics bins are re-initialized to the standard default value described in
Annex D.

CCITT Rec. T.81 (1992 E)

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ISO/IEC 10918-1 : 1993(E)Table F.5 – Statistical model for AC coefficient coding

Context-index

Value
3 × (K – 1)
SE + 1
Fixed estimate
S0 + 1S0 + 1
AC_Context(K)X2 + 1.
.
X2 + 13
X2 + 14
X3 + 14.
.
X15 + 14

SE
S0
SS
SN,SP
X1
X2
X3
.
.
X15
M2
M3
.
.
M15

F.1.5

Coding decision
K = EOB
V=0
Sign of V
Sz < 1
Sz < 2
Sz < 4
Sz < 8.
.
Sz < 215
Magnitude bits if Sz < 4
Magnitude bits if Sz < 8.
.
Magnitude bits if Sz < 215

Extended sequential DCT-based Huffman encoding process for 12-bit sample precisionThis process is identical to the sequential DCT process for 8-bit precision extended to four Huffman table destinations as
documented in F.1.3, with the following changes.
F.1.5.1

Structure of DC code table for 12-bit sample precision

The two’s complement difference magnitudes are grouped into 16 categories, SSSS, and a Huffman code is created foreach of the 16 difference magnitude categories.
The Huffman table for DC coding (see Table F.1) is extended as shown in Table F.6.
Table F.6 – Difference magnitude categories for DC coding

F.1.5.2

SSSS

Difference values

12–4 095..–2 048,2 048..4 095

13–8 191..–4 096,4 096..8 191

14–16 383..–8 192,8 192..16 383

15–32 767..–16 384,16 384..32 767

Structure of AC code table for 12-bit sample precision

The general structure of the code table is extended as illustrated in Figure F.11. The Huffman table for AC coding is
extended as shown in Table F.7.

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ISO/IEC 10918-1 : 1993(E)
0

RRRR

0
.
.
.
15

1

2

EOB
N/A
N/A
N/A
ZRL

SSSS
.
.

.

14

13

COMPOSITE VALUESTISO1430-93/d081

Figure F.11 – Two-dimensional value array for Huffman coding
Figure F.11 {D81] = 4.5 cm = 176 %Table F.7 – Values assigned to coefficient amplitude ranges

F.1.6

SSSS

AC coefficients11–2 047..–1 024,1 024..2 047

12–4 095..–2 048,2 048..4 095

13–8 191..–4 096,4 096..8 191

14–16 383..–8 192,8 192..16 383

Extended sequential DCT-based arithmetic encoding process for 12-bit sample precision

The process is identical to the sequential DCT process for 8-bit precision except for changes in the precision of the FDCT
computation.
The structure of the encoding procedure is identical to that specified in F.1.4 which was already defined for a 12-bit
sample precision.

F.2

Sequential DCT-based decoding processes

F.2.1

Sequential DCT-based control procedures and coding models

F.2.1.1

Control procedures for sequential DCT-based decoders

The control procedures for decoding compressed image data and its constituent parts – the frame, scan, restart interval and
MCU – are given in Figures E.6 to E.10. The procedure for decoding a MCU (Figure E.10) repetitively calls theprocedure for decoding a data unit. For DCT-based decoders the data unit is an 8 × 8 block of samples.
F.2.1.2

Procedure for decoding an 8 × 8 block data unit

In the sequential DCT-based decoding process, decoding an 8 × 8 block data unit consists of the following procedures:F.2.1.3a)decode DC coefficient for 8 × 8 block using the DC table destination specified in the scan header;b)

decode AC coefficients for 8 × 8 block using the AC table destination specified in the scan header;c)dequantize using table destination specified in the frame header and calculate the inverse 8 × 8 DCT.

Decoding models for the sequential DCT procedures

Two decoding procedures are used, one for the DC coefficient ZZ(0) and the other for the AC coefficients ZZ(1)...ZZ(63).
The coefficients are decoded in the order in which they occur in the zig-zag sequence order, starting with the DC
coefficient. The coefficients are represented as two’s complement integers.

CCITT Rec. T.81 (1992 E)

103

ISO/IEC 10918-1 : 1993(E)F.2.1.3.1

Decoding model for DC coefficients

The decoded difference, DIFF, is added to PRED, the DC value from the most recently decoded 8 × 8 block from thesame component. Thus ZZ(0) = PRED + DIFF.
At the beginning of the scan and at the beginning of each restart interval, the prediction for the DC coefficient isinitialized to zero.
F.2.1.3.2

Decoding model for AC coefficients

The AC coefficients are decoded in the order in which they occur in ZZ. When the EOB is decoded, all remaining
coefficients in ZZ are initialized to zero.
F.2.1.4

Dequantization of the quantized DCT coefficients

The dequantization of the quantized DCT coefficients as described in Annex A, is accomplished by multiplying eachquantized coefficient value by the quantization table value for that coefficient. The decoder shall be able to use up to four
quantization table destinations.
F.2.1.5

Inverse DCT (IDCT)The mathematical definition of the IDCT is given in A.3.3.
After computation of the IDCT, the signed output samples are level-shifted, as described in Annex A, converting theoutput to an unsigned representation. For 8-bit precision the level shift is performed by adding 128. For 12-bit precision
the level shift is performed by adding 2 048. If necessary, the output samples shall be clamped to stay within the range
appropriate for the precision (0 to 255 for 8-bit precision and 0 to 4 095 for 12-bit precision).

F.2.2

Baseline Huffman Decoding procedures

The baseline decoding procedure is for 8-bit sample precision. The decoder shall be capable of using up to two DC and
two AC Huffman tables within one scan.
F.2.2.1

Huffman decoding of DC coefficients

The decoding procedure for the DC difference, DIFF, is:T = DECODE
DIFF = RECEIVE(T)DIFF = EXTEND(DIFF,T)
where DECODE is a procedure which returns the 8-bit value associated with the next Huffman code in the compressed
image data (see F.2.2.3) and RECEIVE(T) is a procedure which places the next T bits of the serial bit string into the loworder bits of DIFF, MSB first. If T is zero, DIFF is set to zero. EXTEND is a procedure which converts the partiallydecoded DIFF value of precision T to the full precision difference. EXTEND is shown in Figure F.12.

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ISO/IEC 10918-1 : 1993(E)

EXTEND(V,T)

V t = 2 T –1

V < Vt?

YesNo
V t = (SLL –1 T) + 1
V = V + Vt

Return V
TISO1440-93/d082

Figure F.12 – Extending the sign bit of a decoded value in V
Figure F.12 [D82] = 11 cm = 430 %F.2.2.2

Decoding procedure for AC coefficients

The decoding procedure for AC coefficients is shown in Figures F.13 and F.14.

CCITT Rec. T.81 (1992 E)

105

ISO/IEC 10918-1 : 1993(E)Decode_AC_
coefficients

K=1
ZZ(1,...,63) = 0

K=K+1

K = K + 16

RS = DECODE

SSSS = RS modulo 16
RRRR = SRL RS 4
R = RRRR

SSSS = 0
?

Yes

No
K=K+R

Decode_ZZ(K)No

K = 63?
Yes

R = 15
?

Yes

No

Done
TISO1450-93/d083

Figure F.13 – Huffman decoding procedure for AC coefficients

Figure F.13 [D83] = 21 cm = 821 %106

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Decode_ZZ(K)ZZ(K) = RECEIVE(SSSS)ZZ(K) = EXTEND(ZZ(K),SSSS)Done

TISO1460-93/d084

Figure F.14 – Decoding a non-zero AC coefficient

Figure F.14 [D84] = 7 cm = 273 %The decoding of the amplitude and sign of the non-zero coefficient is done in the procedure “Decode_ZZ(K)”, shown in
Figure F.14.
DECODE is a procedure which returns the value, RS, associated with the next Huffman code in the code stream(see F.2.2.3). The values SSSS and R are derived from RS. The value of SSSS is the four low order bits of the composite
value and R contains the value of RRRR (the four high order bits of the composite value). The interpretation of thesevalues is described in F.1.2.2. EXTEND is shown in Figure F.12.

F.2.2.3

The DECODE procedure

The DECODE procedure decodes an 8-bit value which, for the DC coefficient, determines the difference magnitudecategory. For the AC coefficient this 8-bit value determines the zero run length and non-zero coefficient category.
Three tables, HUFFVAL, HUFFCODE, and HUFFSIZE, have been defined in Annex C. This particular implementationof DECODE makes use of the ordering of the Huffman codes in HUFFCODE according to both value and code size.
Many other implementations of DECODE are possible.
NOTE – The values in HUFFVAL are assigned to each code in HUFFCODE and HUFFSIZE in sequence. There are noordering requirements for the values in HUFFVAL which have assigned codes of the same length.

The implementation of DECODE described in this subclause uses three tables, MINCODE, MAXCODE and VALPTR,
to decode a pointer to the HUFFVAL table. MINCODE, MAXCODE and VALPTR each have 16 entries, one for eachpossible code size. MINCODE(I) contains the smallest code value for a given length I, MAXCODE(I) contains the largest
code value for a given length I, and VALPTR(I) contains the index to the start of the list of values in HUFFVAL which
are decoded by code words of length I. The values in MINCODE and MAXCODE are signed 16-bit integers; therefore, avalue of –1 sets all of the bits.
The procedure for generating these tables is shown in Figure F.15. The procedure for DECODE is shown in Figure F.16.
Note that the 8-bit “VALUE” is returned to the procedure which invokes DECODE.

CCITT Rec. T.81 (1992 E)

107

ISO/IEC 10918-1 : 1993(E)Decoder_tables

I=0
J=0

MAXCODE(I) = –1

I=I+1

I > 16
?

Yes

No
Yes

BITS(I) = 0
?

Done

No
VALPTR(I) = J
MINCODE(I) = HUFFCODE(J)J = J + BITS(I) – 1
MAXCODE(I) = HUFFCODE(J)
J=J+1
TISO1470-93/d085

Figure F.15 – Decoder table generation

Figure F.15 [D85] = 14.5 cm = 567 %108

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)

DECODE

I=1
CODE = NEXTBIT

I=I+1
CODE = (SLL CODE 1) + NEXTBITYes

CODE > MAXCODE(I)?
No
J = VALPTR(I)J = J + CODE – MINCODE(I)VALUE = HUFFVAL(J)

Return VALUE

TISO1480-93/d086

Figure F.16 – Procedure for DECODE

Figure F.16 [D86] = 14 cm = 547 %CCITT Rec. T.81 (1992 E)

109

ISO/IEC 10918-1 : 1993(E)F.2.2.4

The RECEIVE procedure

RECEIVE(SSSS) is a procedure which places the next SSSS bits of the entropy-coded segment into the low order bits of
DIFF, MSB first. It calls NEXTBIT and it returns the value of DIFF to the calling procedure (see Figure F.17).

RECEIVE(SSSS)

I=0
V=0

I= I+ 1V = (SLL V 1) + NEXTBITNo

I = SSSS?
Yes

Return V

TISO1490-93/d087

F igu r e F .17 – Pr oced u r e for R E C E I V E (SSSS)

Figure F.17 [D87] = 11.5 cm = 449 %F.2.2.5

The NEXTBIT procedure

NEXTBIT reads the next bit of compressed data and passes it to higher level routines. It also intercepts and removes stuff
bytes and detects markers. NEXTBIT reads the bits of a byte starting with the MSB (see Figure F.18).
Before starting the decoding of a scan, and after processing a RST marker, CNT is cleared. The compressed data are readone byte at a time, using the procedure NEXTBYTE. Each time a byte, B, is read, CNT is set to 8.
The only valid marker which may occur within the Huffman coded data is the RSTm marker. Other than the EOI or
markers which may occur at or before the start of a scan, the only marker which can occur at the end of the scan is the
DNL (define-number-of-lines).
Normally, the decoder will terminate the decoding at the end of the final restart interval before the terminating marker isintercepted. If the DNL marker is encountered, the current line count is set to the value specified by that marker. Since the
DNL marker can only be used at the end of the first scan, the scan decode procedure must be terminated when it isencountered.

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ISO/IEC 10918-1 : 1993(E)

NEXTBITYes

CNT = 0?

No
B = NEXTBYTE
CNT = 8No

B = X’FF’?
Yes
B2 = NEXTBYTE

Yes

B2 = 0?
No

BIT = SRL B 7
CNT = CNT – 1
B = SLL B 1

B2 = DNL?

Yes

Process DNL marker

No

Return BIT

Error

Terminate scan
TISO1500-93/d088

Figure F.18 – Procedure for fetching the next bit of compressed data
Figure F.18 [D88] = 17 cm = 665 %F.2.3

Sequential DCT decoding process with 8-bit precision extended to four sets of Huffman tables

This process is identical to the Baseline decoding process described in F.2.2, with the exception that the decoder shall becapable of using up to four DC and four AC Huffman tables within one scan. Four DC and four AC Huffman tables is the
maximum allowed by this Specification.
F.2.4

Sequential DCT decoding process with arithmetic codingThis subclause describes the sequential DCT decoding process with arithmetic decoding.
The arithmetic decoding procedures for decoding binary decisions, initializing the statistical model, initializing thedecoder, and resynchronizing the decoder are listed in Table D.4 of Annex D.
Some of the procedures in Table D.4 are used in the higher level control structure for scans and restart intervals describedin F.2. At the beginning of scans and restart intervals, the probability estimates used in the arithmetic decoder are reset tothe standard initial value as part of the Initdec procedure which restarts the arithmetic coder.

CCITT Rec. T.81 (1992 E)

111

ISO/IEC 10918-1 : 1993(E)The statistical models defined in F.1.4.4 also apply to this decoding process.
The decoder shall be capable of using up to four DC and four AC conditioning tables and associated statistics areas within
one scan.
F.2.4.1

Arithmetic decoding of DC coefficients

The basic structure of the decision sequence for decoding a DC difference value, DIFF, is shown in Figure F.19. The
equivalent structure for the encoder is found in Figure F.4.

Decode_DC_DIFF

D = Decode(S0)

No

D=0
?

Decode_V(S0)Yes

DIFF = 0

DIFF = V

Done
TISO1510-93/d089

Figure F.19 – Arithmetic decoding of DC difference
Figure F.19 [D89] = 13 cm = 508 %The context-indices used in the DC decoding procedures are defined in Table F.4 (see F.1.4.4.1.3).
The “Decode” procedure returns the value “D” of the binary decision. If the value is not zero, the sign and magnitude of
the non-zero DIFF must be decoded by the procedure “Decode_V(S0)”.
F.2.4.2

Arithmetic Decoding of AC coefficients

The AC coefficients are decoded in the order that they occur in ZZ(1,...,63). The encoder procedure for the coding process
is found in Figure F.5. Figure F.20 illustrates the decoding sequence.

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ISO/IEC 10918-1 : 1993(E)Decode_AC_
coefficients

K = Kmin

D = Decode(SE)

D=1
?

Yes

No
K=K+1

K=K+1

D = Decode(S0)

D=0
?

Yes

No
Decode_V(S0)ZZ(K) = VNo

K = Se
?

Yes

Done

TISO1520-93/d090

Figure F.20 – Procedure for decoding the AC coefficients
Figure F.20 [D90] = 21 cm = 821 % presque pleine...

The context-indices used in the AC decoding procedures are defined in Table F.5 (see F.1.4.4.2).
CCITT Rec. T.81 (1992 E)

113

ISO/IEC 10918-1 : 1993(E)In Figure F.20, K is the index to the zig-zag sequence position. For the sequential scan, Kmin = 1 and Se = 63. The
decision at the top of the loop is the EOB decision. If the EOB occurs (D = 1), the remaining coefficients in the block are
set to zero. The inner loop just below the EOB decoding decodes runs of zero coefficients. Whenever the coefficient is
non-zero, “Decode_V” decodes the sign and magnitude of the coefficient. After each non-zero coefficient is decoded, theEOB decision is again decoded unless K = Se.
F.2.4.3

Decoding the binary decision sequence for non-zero DC differences and AC coefficients

Both the DC difference and the AC coefficients are represented as signed two’s complement 16-bit integer values. The
decoding decision tree for these signed integer values is the same for both the DC and AC coding models. Note, however,that the statistical models are not the same.
F.2.4.3.1

Arithmetic decoding of non-zero values

Denoting either DC differences or AC coefficients as V, the non-zero signed integer value of V is decoded by thesequence shown in Figure F.21. This sequence first decodes the sign of V. It then decodes the magnitude category of V
(Decode_log2_Sz), and then decodes the low order magnitude bits (Decode_Sz_bits). Note that the value decoded for Sz
must be incremented by 1 to get the actual coefficient magnitude.

Decode_V(S)Decode_sign_of_V

Decode_log2_Sz

Decode_Sz_bits

V = Sz + 1

SIGN = 1?

Yes

V = –V

No

Done
TISO1530-93/d091

Figure F.21 – Sequence of procedures in decoding non-zero values of V
Figure F.21 [D91] = 15.5 cm = 606 %114

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)F.2.4.3.1.1

Decoding the sign

The sign is decoded by the procedure shown in Figure F.22.
The context-indices are defined for DC decoding in Table F.4 and AC decoding in Table F.5.
If SIGN = 0, the sign of the coefficient is positive; if SIGN = 1, the sign of the coefficient is negative.

Decode_sign_of_V

SIGN = Decode(SS)

Yes

SIGN = 1?

S = SNNo

S = SP

Done
TISO1540-93/d092

Figure F.22 – Decoding the sign of V

Figure F.22 [D92] = 11 cm = 430 %F.2.4.3.1.2

Decoding the magnitude category

The context-index S is set in Decode_sign_of_V and the context-index values X1 and X2 are defined for DC coding in
Table F.4 and for AC coding in Table F.5.
In Figure F.23, M is set to the upper bound for the magnitude and shifted left until the decoded decision is zero. It is thenshifted right by 1 to become the leading bit of the magnitude of Sz.

CCITT Rec. T.81 (1992 E)

115

ISO/IEC 10918-1 : 1993(E)Decode_log2_Sz

M=1

D = Decode(S)

D=0
?

Yes

No
M=2
S = X1

D = Decode(S)

D=0
?

Yes

No
M=4
S = X2

D = Decode(S)

D=0
?

Yes

No
M = SLL M 1
S=S+1

M = SRL M 1
Sz = M

Done

TISO1550-93/d093

Figure F.23 – Decoding procedure to establish the magnitude category

116

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)F.2.4.3.1.3

Decoding the exact value of the magnitude

After the magnitude category is decoded, the low order magnitude bits are decoded. These bits are decoded in order ofdecreasing bit significance. The procedure is shown in Figure F.24.
The context-index S is set in Decode_log2_Sz.

Decode_Sz_bits

S = S + 14

M = SRL M 1

M=0
?

Yes

No
D = Decode(S)

Yes

Done

D=0
?
No

Sz = M OR Sz
TISO1560-93/d094

Figure F.24 – Decision sequence to decode the magnitude bit patternFigure F.24 [D94] = 16 cm = 625 %F.2.4.4

Decoder restart

The RSTm markers which are added to the compressed data between each restart interval have a two byte value whichcannot be generated by the coding procedures. These two byte sequences can be located without decoding, and cantherefore be used to resynchronize the decoder. RSTm markers can therefore be used for error recovery.

CCITT Rec. T.81 (1992 E)

117

ISO/IEC 10918-1 : 1993(E)Before error recovery procedures can be invoked, the error condition must first be detected. Errors during decoding canshow up in two places:a)

The decoder fails to find the expected marker at the point where it is expecting resynchronization.

b)

Physically impossible data are decoded. For example, decoding a magnitude beyond the range of values
allowed by the model is quite likely when the compressed data are corrupted by errors. For arithmetic
decoders this error condition is extremely important to detect, as otherwise the decoder may reach acondition where it uses the compressed data very slowly.
NOTE – Some errors will not cause the decoder to lose synchronization. In addition, recovery is notpossible for all errors; for example, errors in the headers are likely to be catastrophic. The two error
conditions listed above, however, almost always cause the decoder to lose synchronization in a way which
permits recovery.

In regaining synchronization, the decoder can make use of the modulo 8 coding restart interval number in the low order
bits of the RSTm marker. By comparing the expected restart interval number to the value in the next RSTm marker in thecompressed image data, the decoder can usually recover synchronization. It then fills in missing lines in the output data by
replication or some other suitable procedure, and continues decoding. Of course, the reconstructed image will usually behighly corrupted for at least a part of the restart interval where the error occurred.

F.2.5

Sequential DCT decoding process with Huffman coding and 12-bit precisionThis process is identical to the sequential DCT process defined for 8-bit sample precision and extended to four Huffman
tables, as documented in F.2.3, but with the following changes.
F.2.5.1

Structure of DC Huffman decode table

The general structure of the DC Huffman decode table is extended as described in F.1.5.1.
F.2.5.2

Structure of AC Huffman decode table

The general structure of the AC Huffman decode table is extended as described in F.1.5.2.

F.2.6

Sequential DCT decoding process with arithmetic coding and 12-bit precision

The process is identical to the sequential DCT process for 8-bit precision except for changes in the precision of the IDCT
computation.
The structure of the decoding procedure in F.2.4 is already defined for a 12-bit input precision.

118

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Annex G
Progressive DCT-based mode of operation(This annex forms an integral part of this Recommendation | International Standard)This annex provides a functional specification of the following coding processes for the progressive DCT-based modeof operation:1)

spectral selection only, Huffman coding, 8-bit sample precision;2)

spectral selection only, arithmetic coding, 8-bit sample precision;

3)

full progression, Huffman coding, 8-bit sample precision;

4)

full progression, arithmetic coding, 8-bit sample precision;

5)

spectral selection only, Huffman coding, 12-bit sample precision;

6)

spectral selection only, arithmetic coding, 12-bit sample precision;

7)

full progression, Huffman coding, 12-bit sample precision;

8)

full progression, arithmetic coding, 12-bit sample precision.

For each of these, the encoding process is specified in G.1, and the decoding process is specified in G.2. The functional
specification is presented by means of specific flow charts for the various procedures which comprise these coding
processes.
NOTE – There is no requirement in this Specification that any encoder or decoder which embodies one of the above-named
processes shall implement the procedures in precisely the manner specified by the flow charts in this annex. It is necessary only that an
encoder or decoder implement the function specified in this annex. The sole criterion for an encoder or decoder to be considered incompliance with this Specification is that it satisfy the requirements given in clause 6 (for encoders) or clause 7 (for decoders), as
determined by the compliance tests specified in Part 2.

The number of Huffman or arithmetic conditioning tables which may be used within the same scan is four.
Two complementary progressive procedures are defined, spectral selection and successive approximation.
In spectral selection the DCT coefficients of each block are segmented into frequency bands. The bands are coded inseparate scans.
In successive approximation the DCT coefficients are divided by a power of two before coding. In the decoder thecoefficients are multiplied by that same power of two before computing the IDCT. In the succeeding scans the precision of
the coefficients is increased by one bit in each scan until full precision is reached.
An encoder or decoder implementing a full progression uses spectral selection within successive approximation. An
allowed subset is spectral selection alone.
Figure G.1 illustrates the spectral selection and successive approximation progressive processes.

G.1

Progressive DCT-based encoding processes

G.1.1

Control procedures and coding models for progressive DCT-based procedures

G.1.1.1 Control procedures for progressive DCT-based encoders
The control procedures for encoding an image and its constituent parts – the frame, scan, restart interval and MCU – aregiven in Figures E.1 through E.5.
The control structure for encoding a frame is the same as for the sequential procedures. However, it is convenient tocalculate the FDCT for the entire set of components in a frame before starting the scans. A buffer which is large enough tostore all of the DCT coefficients may be used for this progressive mode of operation.
The number of scans is determined by the progression defined; the number of scans may be much larger than the numberof components in the frame.

CCITT Rec. T.81 (1992 E)

119ISO/IEC 10918-1 : 1993(E)BlocksDCT
coefficients

1
0
1

2

Sendinga) Image componenta) as quantizeda) DCT coefficients

62
63
7 6
MSB

10
LSB

b) Sequential encoding

Sending00

7

1st scanSending

1st scan

0

1
2

1
2

Sending

62
63

2nd scan7654
MSB
2nd scanSending3
4
5

Sending

3rd scan3
3rd scanSending61
62
63

Sending

nth scanTISO1570-93/d0950(LSB)
6th scanc) Progressive encoding –a) Spectral selectiond) Progressive encoding –a) Successive approximation

Figure G.1 – Spectral selection and successive approximation progressive processes

120

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)The procedure for encoding a MCU (see Figure E.5) repetitively invokes the procedure for coding a data unit. For
DCT-based encoders the data unit is an 8 × 8 block of samples.
Only a portion of each 8 × 8 block is coded in each scan, the portion being determined by the scan header parameters Ss,
Se, Ah, and Al (see B.2.3). The procedures used to code portions of each 8 × 8 block are described in this annex. Note,however, that where these procedures are identical to those used in the sequential DCT-based mode of operation, thesequential procedures are simply referenced.
G.1.1.1.1

Spectral selection control

In spectral selection the zig-zag sequence of DCT coefficients is segmented into bands. A band is defined in the scan
header by specifying the starting and ending indices in the zig-zag sequence. One band is coded in a given scan of the
progression. DC coefficients are always coded separately from AC coefficients, and only scans which code DC
coefficients may have interleaved blocks from more than one component. All other scans shall have only one component.
With the exception of the first DC scans for the components, the sequence of bands defined in the scans need not follow
the zig-zag ordering. For each component, a first DC scan shall precede any AC scans.
G.1.1.1.2

Successive approximation control

If successive approximation is used, the DCT coefficients are reduced in precision by the point transform (see A.4)
defined in the scan header (see B.2.3). The successive approximation bit position parameter Al specifies the actual pointtransform, and the high four bits (Ah) – if there are preceding scans for the band – contain the value of the point transform
used in those preceding scans. If there are no preceding scans for the band, Ah is zero.
Each scan which follows the first scan for a given band progressively improves the precision of the coefficients by one bit,until full precision is reached.
G.1.1.2 Coding models for progressive DCT-based encoders
If successive approximation is used, the DCT coefficients are reduced in precision by the point transform (see A.4)
defined in the scan header (see B.2.3). These models also apply to the progressive DCT-based encoders, but with thefollowing changes.
G.1.1.2.1

Progressive encoding model for DC coefficients

If Al is not zero, the point transform for DC coefficients shall be used to reduce the precision of the DC coefficients. If Ah
is zero, the coefficient values (as modified by the point transform) shall be coded, using the procedure described in Annex
F. If Ah is not zero, the least significant bit of the point transformed DC coefficients shall be coded, using the procedures
described in this annex.
G.1.1.2.2

Progressive encoding model for AC coefficients

If Al is not zero, the point transform for AC coefficients shall be used to reduce the precision of the AC coefficients. If Ah
is zero, the coefficient values (as modified by the point transform) shall be coded using modifications of the procedures
described in Annex F. These modifications are described in this annex. If Ah is not zero, the precision of the coefficientsshall be improved using the procedures described in this annex.
G.1.2

Progressive encoding procedures with Huffman coding

G.1.2.1 Progressive encoding of DC coefficients with Huffman coding
The first scan for a given component shall encode the DC coefficient values using the procedures described in F.1.2.1. If
the successive approximation bit position parameter Al is not zero, the coefficient values shall be reduced in precision by
the point transform described in Annex A before coding.
In subsequent scans using successive approximation the least significant bits are appended to the compressed bit stream
without compression or modification (see G.1.2.3), except for byte stuffing.
G.1.2.2 Progressive encoding of AC coefficients with Huffman coding
In spectral selection and in the first scan of successive approximation for a component, the AC coefficient coding model issimilar to that used by the sequential procedures. However, the Huffman code tables are extended to include coding ofruns of End-Of-Bands (EOBs). See Table G.1.

CCITT Rec. T.81 (1992 E)

121

ISO/IEC 10918-1 : 1993(E)Table G.1 – EOBn code run length extensions
EOBn code

Run length

EOB0

1

EOB1

2,3

EOB2

4..7

EOB3

8..15

EOB4

16..31

EOB5

32..63EOB664..127

EOB7

128..255

EOB8

256..511

EOB9

512..1 023

EOB10

1 024..2 047

EOB11

2 048..4 095

EOB12

4 096..8 191

EOB13

8 192..16 383

EOB14

16 384..32 767

The end-of-band run structure allows efficient coding of blocks which have only zero coefficients. An EOB run of length
5 means that the current block and the next four blocks have an end-of-band with no intervening non-zero coefficients.
The EOB run length is limited only by the restart interval.
The extension of the code table is illustrated in Figure G.2.

SSSS
0

RRRR

0
1
.
.
.
14
15

EOB0
EOB1
.
.
.
EOB14
ZRL

1

2

.

.

.

13

14

COMPOSITE VALUESTISO1580-93/d096

Figure G.2 – Two-dimensional value array for Huffman coding

Figure G.2 [D96] = 4.5 cm = 176 %The EOBn code sequence is defined as follows. Each EOBn code is followed by an extension field similar to theextension field for the coefficient amplitudes (but with positive numbers only). The number of bits appended to the EOBn
code is the minimum number required to specify the run length.
If an EOB run is greater than 32 767, it is coded as a sequence of EOB runs of length 32 767 followed by a final EOB run
sufficient to complete the run.
At the beginning of each restart interval the EOB run count, EOBRUN, is set to zero. At the end of each restart interval
any remaining EOB run is coded.
The Huffman encoding procedure for AC coefficients in spectral selection and in the first scan of successive
approximation is illustrated in Figures G.3, G.4, G.5, and G.6.
122

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Encode_AC_
coefficients_SS

K = Ss – 1
R=0

K=K+1

No

ZZ(K) = 0?

Encode_EOBRUN

Yes

Yes

R=R+1

K = Se?

R < 16
?

No

Yes
No
EOBRUN =EOBRUN + 1
Encode_ZRL

EOBRUN = X’7FFF’
?

No

Yes
Encode_R_ZZ(K)
Encode_EOBRUNNo

K = Se?

Yes

Done
TISO1590-93/d097

Figure G.3 – Procedure for progressive encoding of AC coefficients with Huffman coding

Figure G.3[D97] = Pleine page

CCITT Rec. T.81 (1992 E)

123ISO/IEC 10918-1 : 1993(E)In Figure G.3, Ss is the start of spectral selection, Se is the end of spectral selection, K is the index into the list ofcoefficients stored in the zig-zag sequence ZZ, R is the run length of zero coefficients, and EOBRUN is the run length of
EOBs. EOBRUN is set to zero at the start of each restart interval.
If the scan header parameter Al (successive approximation bit position low) is not zero, the DCT coefficient values ZZ(K)in Figure G.3 and figures which follow in this annex, including those in the arithmetic coding section, shall be replacedby the point transformed values ZZ’(K), where ZZ’(K) is defined by:
ZZ’(K) =ZZ(K)x2 Al

EOBSIZE is a procedure which returns the size of the EOB extension field given the EOB run length as input. CSIZE is aprocedure which maps an AC coefficient to the SSSS value defined in the subclauses on sequential encoding (see F.1.1
and F.1.3).

Encode_EOBRUNYes

EOBRUN = 0?
No
SSSS = EOBSIZE(EOBRUN)
I = SSSS × 16
Append EHUFSI(I)
bits of EHUFCO(I)
Append SSSS low order
bits of EOBRUNEOBRUN = 0

Done
TISO1600-93/d098

Figure G.4 – Progressive encoding of a non-zero AC coefficient
Figure G.4 [98] = 11 cm = 430 %Encode_ZRL

Append EHUFSI(X’F0’)
bits of EHUFCO(X’F0’)
R = R – 16

Done

TISO1610-93/d099

Figure G.5 – Encoding of the run of zero coefficients
124

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Encode_R_ZZ(K)SSSS = CSIZE(ZZ(K))
I = (16 × R) + SSSS
Append EHUFSI(I)
bits of EHUFCO(I)

ZZ(K) < 0
?

No

Yes

ZZ(K) = ZZ(K) – 1

Append SSSS low order
bits of ZZ(K)
R=0

Done
TISO1620-93/d100

Figure G.5 [99] = 7 cm = 273 % Figure G.6 – Encoding of the zero run and non-zero coefficient
Figure G.6 [D100] = 12.5 cm = 489 %G.1.2.3 Coding model for subsequent scans of successive approximation
The Huffman coding structure of the subsequent scans of successive approximation for a given component is similar to thecoding structure of the first scan of that component.
The structure of the AC code table is identical to the structure described in G.1.2.2. Each non-zero point transformed
coefficient that has a zero history (i.e. that has a value ± 1, and therefore has not been coded in a previous scan) is definedby a composite 8-bit run length-magnitude value of the form:RRRRSSSS
The four most significant bits, RRRR, give the number of zero coefficients that are between the current coefficient and thepreviously coded coefficient (or the start of band). Coefficients with non-zero history (a non-zero value coded in aprevious scan) are skipped over when counting the zero coefficients. The four least significant bits, SSSS, provide themagnitude category of the non-zero coefficient; for a given component the value of SSSS can only be one.
The run length-magnitude composite value is Huffman coded and each Huffman code is followed by additional bits:a)

One bit codes the sign of the newly non-zero coefficient. A 0-bit codes a negative sign; a 1-bit codes a
positive sign.

b)

For each coefficient with a non-zero history, one bit is used to code the correction. A 0-bit means nocorrection and a 1-bit means that one shall be added to the (scaled) decoded magnitude of the coefficient.

CCITT Rec. T.81 (1992 E)

125

ISO/IEC 10918-1 : 1993(E)Non-zero coefficients with zero history are coded with a composite code of the form:
HUFFCO(RRRRSSSS) + additional bit (rule a) + correction bits (rule b)
In addition whenever zero runs are coded with ZRL or EOBn codes, correction bits for those coefficients with non-zero
history contained within the zero run are appended according to rule b above.
For the Huffman coding version of Encode_AC_Coefficients_SA the EOB is defined to be the position of the last pointtransformed coefficient of magnitude 1 in the band. If there are no coefficients of magnitude 1, the EOB is defined to be
zero.
NOTE – The definition of EOB is different for Huffman and arithmetic coding procedures.

In Figures G.7 and G.8 BE is the count of buffered correction bits at the start of coding of the block. BE is initialized tozero at the start of each restart interval. At the end of each restart interval any remaining buffered bits are appended to the
bit stream following the last EOBn Huffman code and associated appended bits.
In Figures G.7 and G.9, BR is the count of buffered correction bits which are appended to the bit stream according to ruleb. BR is set to zero at the beginning of each Encode_AC_Coefficients_SA. At the end of each restart interval any
remaining buffered bits are appended to the bit stream following the last Huffman code and associated appended bits.

G.1.3

Progressive encoding procedures with arithmetic coding

G.1.3.1 Progressive encoding of DC coefficients with arithmetic coding
The first scan for a given component shall encode the DC coefficient values using the procedures described in F.1.4.1. If
the successive approximation bit position parameter is not zero, the coefficient values shall be reduced in precision by the
point transform described in Annex A before coding.
In subsequent scans using successive approximation the least significant bits shall be coded as binary decisions using afixed probability estimate of 0.5 (Qe = X’5A1D’, MPS = 0).
G.1.3.2 Progressive encoding of AC coefficients with arithmetic coding
Except for the point transform scaling of the DCT coefficients and the grouping of the coefficients into bands, the firstscan(s) of successive approximation is identical to the sequential encoding procedure described in F.1.4. If Kmin isequated to Ss, the index of the first AC coefficient index in the band, the flow chart shown in Figure F.5 applies. The
EOB decision in that figure refers to the “end-of-band” rather than the “end-of-block”. For the arithmetic coding version
of Encode_AC_Coefficients_SA (and all other AC coefficient coding procedures) the EOB is defined to be the position
following the last non-zero coefficient in the band.
NOTE - The definition of EOB is different for Huffman and arithmetic coding procedures.

The statistical model described in F.1.4 also holds. For this model the default value of Kx is 5. Other values of Kx may be
specified using the DAC marker code (Annex B). The following calculation for Kx has proven to give good results for 8bit precision samples:
Kx = Kmin + SRL (8 + Se – Kmin) 4
This expression reduces to the default of Kx = 5 when the band is from index 1 to index 63.

126

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Encode_AC_
coefficients_SA

K = Ss – 1
R=0
BR = 0

K=K+1

No

Yes

Yes

R > 15?

K ≥ EOB?

NoNo|ZZ(K)| = 1?
Yes
Encode_EOBRUN
Append_BE_bits
Encode_R_ZZ(K)Append_BR_bits

No

ZZ(K) = 0?

Yes

Append LSB of ZZ(K)to buffered bits
BR = BR + 1

K = Se?

K = Se?

Encode_EOBRUN
Append_BE_bits
Encode_ZRL
Append_BR_bits

No

R=R+1

No

Yes
EOBRUN =EOBRUN + 1
BE = BE + BRYes

EOBRUN = X’7FFF’
?

No

Yes
Encode_EOBRUN
Append_BE_bits

TISO1630-93/d101

Done

Figure G.7 – Successive approximation coding of AC coefficients using Huffman coding

CCITT Rec. T.81 (1992 E)

127

ISO/IEC 10918-1 : 1993(E)Append_BE_bits

Yes

BE = 0?
No
Append BE buffered bits
to bit stream
BE = 0Done

TISO1640-93/d102

Figure G.8 – Transferring BE buffered bits from buffer to bit stream

Figure G.8 [D102] = 9.5 cm = 371 %Append_BR_bits

Yes

BR = 0?
No
Append BR buffered bits
to bit stream
BR = 0Done

TISO1650-93/d103

Figure G.9 – Transferring BR buffered bits from buffer to bit stream

Figaure G.9 [D103] = 9.5 cm = 371 %128

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)G.1.3.3 Coding model for subsequent scans of successive approximation
The procedure “Encode_AC_Coefficient_SA” shown in Figure G.10 increases the precision of the AC coefficient values
in the band by one bit.
As in the first scan of successive approximation for a component, an EOB decision is coded at the start of the band andafter each non-zero coefficient.
However, since the end-of-band index of the previous successive approximation scan for a given component, EOBx, isknown from the data coded in the prior scan of that component, this decision is bypassed whenever the current index, K,
is less than EOBx. As in the first scan(s), the EOB decision is also bypassed whenever the last coefficient in the band is
not zero. The decision ZZ(K) = 0 decodes runs of zero coefficients. If the decoder is at this step of the procedure, at least
one non-zero coefficient remains in the band of the block being coded. If ZZ(K) is not zero, the procedure in Figure G.11
is followed to code the value.
The context-indices in Figures G.10 and G.11 are defined in Table G.2 (see G.1.3.3.1). The signs of coefficients withmagnitude of one are coded with a fixed probability value of approximately 0.5 (Qe = X’5A1D’, MPS = 0).
G.1.3.3.1

Statistical model for subsequent successive approximation scans

As shown in Table G.2, each statistics area for subsequent successive approximation scans of AC coefficients consists of acontiguous set of 189 statistics bins. The signs of coefficients with magnitude of one are coded with a fixed probability
value of approximately 0.5 (Qe = X’5A1D’, MPS = 0).

G.2

Progressive decoding of the DCT

The description of the computation of the IDCT and the dequantization procedure contained in A.3.3 and A.3.4 apply tothe progressive operation.
Progressive decoding processes must be able to decompress compressed image data which requires up to four sets ofHuffman or arithmetic coder conditioning tables within a scan.
In order to avoid repetition, detailed flow diagrams of progressive decoder operation are not included. Decoder operation
is defined by reversing the function of each step described in the encoder flow charts, and performing the steps in reverse
order.

CCITT Rec. T.81 (1992 E)

129

ISO/IEC 10918-1 : 1993(E)Encode_AC_
coefficients_SA

K = KminYes

K < EOBx?
No
K = EOB?

Yes

Code_1(SE)No
Code_0(SE)

K=K+1

K=K+1

ZZ(K) = 0?

Yes

Code_0(S0)No
CodeSA_ZZ(K)No

K = Se
?

Yes

Done

TISO1660-93/d104

Figure G.10 – Subsequent successive approximation scans for codingof AC coefficients using arithmetic coding

Figure G.10 [D104] = PLEINE130

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)

CodeSA_ZZ(K)T = LSB ZZ(K)

No

T=1
?

Code_0(SC)Yes| ZZ(K) | > 1
?

Yes

No

Code_1(S0)No

Code_1(SC)ZZ(K) > 0?

Code_1(SS)

Yes

Code_0(SS)

TISO1670-93/d105

Done

Figure G.11 – Coding non-zero coefficients for subsequent successive approximation scans

Figure G.11 [D105] = 11 cm = 430 %Table G.2 – Statistical model for subsequent scans of successive
approximation coding of AC coefficient

Context-index

AC coding

Coding decisionSE

3 × (K–1)

K = EOB

S0

SE + 1

V=0

SS

Fixed estimate

Sign

SC

S0 + 1LSB ZZ(K) = 1

CCITT Rec. T.81 (1992 E)

131

ISO/IEC 10918-1 : 1993(E)Annex H
Lossless mode of operation(This annex forms an integral part of this Recommendation | International Standard)
ISO/IEC 10918-1 : 1993(E)
CCITT Rec. T.81 (1992 E)

This annex provides a functional specification of the following coding processes for the lossless mode of operation:
1)

lossless processes with Huffman coding;2)

lossless processes with arithmetic coding.

For each of these, the encoding process is specified in H.1, and the decoding process is specified in H.2. The functional
specification is presented by means of specific procedures which comprise these coding processes.
NOTE – There is no requirement in this Specification that any encoder or decoder which embodies one of the above-named
processes shall implement the procedures in precisely the manner specified in this annex. It is necessary only that an encoder or decoder
implement the function specified in this annex. The sole criterion for an encoder or decoder to be considered in compliance with thisSpecification is that it satisfy the requirements given in clause 6 (for encoders) or clause 7 (for decoders), as determined by thecompliance tests specified in Part 2.

The processes which provide for sequential lossless encoding and decoding are not based on the DCT. The processes used
are spatial processes based on the coding model developed for the DC coefficients of the DCT. However, the model isextended by incorporating a set of selectable one- and two-dimensional predictors, and for interleaved data the ordering ofsamples for the one-dimensional predictor can be different from that used in the DCT-based processes.
Either Huffman coding or arithmetic coding entropy coding may be employed for these lossless encoding and decoding
processes. The Huffman code table structure is extended to allow up to 16-bit precision for the input data. The arithmetic
coder statistical model is extended to a two-dimensional form.

H.1

Lossless encoder processes

H.1.1

Lossless encoder control procedures

Subclause E.1 contains the encoder control procedures. In applying these procedures to the lossless encoder, the data unit
is one sample.
Input data precision may be from 2 to 16 bits/sample. If the input data path has different precision from the input data, thedata shall be aligned with the least significant bits of the input data path. Input data is represented as unsigned integers
and is not level shifted prior to coding.
When the encoder is reset in the restart interval control procedure (see E.1.4), the prediction is reset to a default value. Ifarithmetic coding is used, the statistics are also reset.
For the lossless processes the restart interval shall be an integer multiple of the number of MCU in an MCU-row.
H.1.2

Coding model for lossless encoding

The coding model developed for encoding the DC coefficients of the DCT is extended to allow a selection from a set ofseven one-dimensional and two-dimensional predictors. The predictor is selected in the scan header (see Annex B). The
same predictor is used for all components of the scan. Each component in the scan is modeled independently, using
predictions derived from neighbouring samples of that component.
H.1.2.1 Prediction
Figure H.1 shows the relationship between the positions (a, b, c) of the reconstructed neighboring samples used forprediction and the position of x, the sample being coded.

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ISO/IEC 10918-1 : 1993(E)

c

b

a

x

TISO1680-93/d106

Figure H.1 – Relationship between sample and prediction samples

Figure H.1 [D106] = 4.5 cm = 176 %Define Px to be the prediction and Ra, Rb, and Rc to be the reconstructed samples immediately to the left, immediately
above, and diagonally to the left of the current sample. The allowed predictors, one of which is selected in the scan
header, are listed in Table H.1.

Table H.1 – Predictors for lossless coding

Selection-valuea)Prediction

0

No prediction (See Annex J)

1

Px = Ra2

Px = Rb

3

Px = Rc

4

Px = Ra + Rb – Rc

5

Px = Ra + ((Rb – Rc)/2)a)6

Px = Rb + ((Ra – Rc)/2)a)7

Px = (Ra + Rb)/2

Shift right arithmetic operation

Selection-value 0 shall only be used for differential coding in the hierarchical mode of operation. Selections 1, 2 and 3 are
one-dimensional predictors and selections 4, 5, 6, and 7 are two-dimensional predictors.
The one-dimensional horizontal predictor (prediction sample Ra) is used for the first line of samples at the start of the scan
and at the beginning of each restart interval. The selected predictor is used for all other lines. The sample from the line
above (prediction sample Rb) is used at the start of each line, except for the first line. At the beginning of the first line andat the beginning of each restart interval the prediction value of 2P – 1 is used, where P is the input precision.
If the point transformation parameter (see A.4) is non-zero, the prediction value at the beginning of the first lines and the
beginning of each restart interval is 2P – Pt – 1, where Pt is the value of the point transformation parameter.
Each prediction is calculated with full integer arithmetic precision, and without clamping of either underflow or overflow
beyond the input precision bounds. For example, if Ra and Rb are both 16-bit integers, the sum is a 17-bit integer. After
dividing the sum by 2 (predictor 7), the prediction is a 16-bit integer.

CCITT Rec. T.81 (1992 E)

133

ISO/IEC 10918-1 : 1993(E)For simplicity of implementation, the divide by 2 in the prediction selections 5 and 6 of Table H.1 is done by anarithmetic-right-shift of the integer values.
The difference between the prediction value and the input is calculated modulo 216. In the decoder the difference isdecoded and added, modulo 216, to the prediction.
H.1.2.2 Huffman coding of the modulo difference
The Huffman coding procedures defined in Annex F for coding the DC coefficients are used to code the modulo 216
differences. The table for DC coding contained in Tables F.1 and F.6 is extended by one additional entry. No extra bits
are appended after SSSS = 16 is encoded. See Table H.2.
Table H.2 – Difference categories for lossless Huffman coding
SSSS

Difference values

10

0

11

–1,1

12

–3,–2,2,3

13–7..–4,4..7

14–15..–8,8..15

15–31..–16,16..31

16–63..–32,32..6317–127..–64,64..12718–255..–128,128..255

19–511..–256,256..511

10–1 023..–512,512..1 023

11–2 047..–1 024,1 024..2 047

12–4 095..–2 048,2 048..4 095

13–8 191..–4 096,4 096..8 191

14–16 383..–8 192,8 192..16 383

15–32 767..–16 384,16 384..32 767

16

32 768H.1.2.3 Arithmetic coding of the modulo difference
The statistical model defined for the DC coefficient arithmetic coding model (see F.1.4.4.1) is generalized to a twodimensional form in which differences coded for the sample to the left and for the line above are used for conditioning.
H.1.2.3.1

Two-dimensional statistical model

The binary decisions are conditioned on the differences coded for the neighbouring samples immediately above andimmediately to the left from the same component. As in the coding of the DC coefficients, the differences are classified
into 5 categories: zero(0), small positive (+S), small negative (–S), large positive (+L), and large negative (–L). The two
independent difference categories combine to give 25 different conditioning states. Figure H.2 shows the two-dimensional
array of conditioning indices. For each of the 25 conditioning states probability estimates for four binary decisions are
kept.
At the beginning of the scan and each restart interval the conditioning derived from the line above is set to zero for the
first line of each component. At the start of each line, the difference to the left is set to zero for the purposes of calculating
the conditioning.

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ISO/IEC 10918-1 : 1993(E)Difference above (position b)

Difference to left
(position a)

0

+S

–S

+L

–L

0

0

4

8

12

16

+S

20

24

28

32

36

–S

40

44

48

52

56

+L

60

64

68

72

76

–L

80

84

88

92

96

TISO1690-93/d107

Figure H.2 – 5 × 5 Conditioning array for two-dimensional statistical model
Figure H.2 [D107] = 7 cm = 273 %H.1.2.3.2

Assignment of statistical bins to the DC binary decision tree

Each statistics area for lossless coding consists of a contiguous set of 158 statistics bins. The first 100 bins consist of
25 sets of four bins selected by a context-index S0. The value of S0 is given by L_Context(Da,Db), which provides avalue of 0, 4,..., 92 or 96, depending on the difference classifications of Da and Db (see H.1.2.3.1). The value for S0
provided by L_Context(Da,Db) is from the array in Figure H.2.
The remaining 58 bins consist of two sets of 29 bins, X1, ..., X15, M2, ..., M15, which are used to code magnitudecategory decisions and magnitude bits. The value of X1 is given by X1_Context(Db), which provides a value of 100 when
Db is in the zero, small positive or small negative categories and a value of 129 when Db is in the large positive or large
negative categories.
The assignment of statistical bins to the binary decision tree used for coding the difference is given in Table H.3.
Table H.3 – Statistical model for lossless coding
Context-index
S0
SS
SP
SN
X1
X2
X3
.
.
X15
M2
M3
.
.
M15

Value
L_Context(Da,Db)
S0 + 1S0 + 2S0 + 3
X1_Context(Db)
X1 + 1X1 + 2.
.
X1 + 14
X2 + 14
X3 + 14.
.
X15 + 14

Coding decision
V=0
Sign
Sz < 1 if V > 0
Sz < 1 if V < 0
Sz < 2
Sz < 4
Sz < 8.
.
Sz < 215
Magnitude bits if Sz < 4
Magnitude bits if Sz < 8.
.
Magnitude bits if Sz < 215

CCITT Rec. T.81 (1992 E)

135

ISO/IEC 10918-1 : 1993(E)H.1.2.3.3

Default conditioning bounds

The bounds, L and U, for determining the conditioning category have the default values L = 0 and U = 1. Other bounds
may be set using the DAC (Define-Arithmetic-Conditioning) marker segment, as described in Annex B.
H.1.2.3.4

Initial conditions for statistical model

At the start of a scan and at each restart, all statistics bins are re-initialized to the standard default value described in
Annex D.

H.2

Lossless decoder processes

Lossless decoders may employ either Huffman decoding or arithmetic decoding. They shall be capable of using up to four
tables in a scan. Lossless decoders shall be able to decode encoded image source data with any input precision from 2 to
16 bits per sample.
H.2.1

Lossless decoder control procedures

Subclause E.2 contains the decoder control procedures. In applying these procedures to the lossless decoder the data unit
is one sample.
When the decoder is reset in the restart interval control procedure (see E.2.4) the prediction is reset to the same value
used in the encoder (see H.1.2.1). If arithmetic coding is used, the statistics are also reset.
Restrictions on the restart interval are specified in H.1.1.
H.2.2

Coding model for lossless decoding

The predictor calculations defined in H.1.2 also apply to the lossless decoder processes.
The lossless decoders, decode the differences and add them, modulo 216, to the predictions to create the output. The
lossless decoders shall be able to interpret the point transform parameter, and if non-zero, multiply the output of thelossless decoder by 2Pt.
In order to avoid repetition, detailed flow charts of the lossless decoding procedures are omitted.

136

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Annex J
Hierarchical mode of operation(This annex forms an integral part of this Recommendation | International Standard)This annex provides a functional specification of the coding processes for the hierarchical mode of operation.
In the hierarchical mode of operation each component is encoded or decoded in a non-differential frame. Such frames may
be followed by a sequence of differential frames. A non-differential frame shall be encoded or decoded using theprocedures defined in Annexes F, G and H. Differential frame procedures are defined in this annex.
The coding process for a hierarchical encoding containing DCT-based processes is defined as the highest numberedprocess listed in Table J.1 which is used to code any non-differential DCT-based or differential DCT-based frame in thecompressed image data format. The coding process for a hierarchical encoding containing only lossless processes isdefined to be the process used for the non-differential frames.
Table J.1 – Coding processes for hierarchical mode
Process
11
12
13
14
15
16
17
18
19
10
11
12
13
14

Non-differential frame specification
Extended sequential DCT, Huffman, 8-bit
Extended sequential DCT, arithmetic, 8-bit
Extended sequential DCT, Huffman, 12-bit
Extended sequential DCT, arithmetic, 12-bit
Spectral selection only, Huffman, 8-bit
Spectral selection only, arithmetic, 8-bit
Full progression, Huffman, 8-bit
Full progression, arithmetic, 8-bit
Spectral selection only, Huffman, 12-bit
Spectral selection only, arithmetic, 12-bit
Full progression, Huffman, 12-bit
Full progression, arithmetic, 12-bit
Lossless, Huffman, 2 through 16 bits
Lossless, arithmetic, 2 through 16 bits

Annex F, process 2
Annex F, process 3
Annex F, process 4
Annex F, process 5
Annex G, process 1
Annex G, process 2
Annex G, process 3
Annex G, process 4
Annex G, process 5
Annex G, process 6
Annex G, process 7
Annex G, process 8
Annex H, process 1
Annex H, process 2

Hierarchical mode syntax requires a DHP marker segment that appears before the non-differential frame or frames. It may
include EXP marker segments and differential frames which shall follow the initial non-differential frame. The frame
structure in hierarchical mode is identical to the frame structure in non-hierarchical mode.
Either all non-differential frames within an image shall be coded with DCT-based processes, or all non-differential frames
shall be coded with lossless processes. All frames within an image must use the same entropy coding procedure, either
Huffman or arithmetic, with the exception that non-differential frames coded with the baseline process may occur in thesame image with frames coded with arithmetic coding processes.
If the non-differential frames use DCT-based processes, all differential frames except the final frame for a component shalluse DCT-based processes. The final differential frame for each component may use a differential lossless process.
If the non-differential frames use lossless processes, all differential frames shall use differential lossless processes.
For each of the processes listed in Table J.1, the encoding processes are specified in J.1, and decoding processes are
specified in J.2.
NOTE – There is no requirement in this Specification that any encoder or decoder which embodies one of theabove-named processes shall implement the procedures in precisely the manner specified by the flow charts in this annex. It isnecessary only that an encoder or decoder implement the function specified in this annex. The sole criterion for an encoder or decoder
to be considered in compliance with this Specification is that it satisfy the requirements given in clause 6 (for encoders) or clause 7 (fordecoders), as determined by the compliance tests specified in Part 2.

CCITT Rec. T.81 (1992 E)

137

ISO/IEC 10918-1 : 1993(E)In the hierarchical mode of operation each component is encoded or decoded in a non-differential frame followed by asequence of differential frames. A non-differential frame shall use the procedures defined in Annexes F, G, and H.
Differential frame procedures are defined in this annex.

J.1

Hierarchical encoding

J.1.1

Hierarchical control procedure for encoding an image

The control structure for encoding of an image using the hierarchical mode is given in Figure J.1.

Encode_image[Generate down-sampled images]
Append SOI marker[Append tables/miscellaneous]
Append DHP marker segment

No

Differential frame?

Yes[Upsample reference components andappend EXP marker segment]
Generate differential components
Encode_differential_frame
Reconstruct differential components
Reconstruct components

Encode_frame

Reconstruct components
using matching
decoder process

Yes

More frames?
No
Append EOI marker

Done
TISO1700-93/d108

Figure J.1 – Hierarchical control procedure for encoding an image
Figure J.1 [D108] = 18 cm = 704 %In Figure J.1 procedures in brackets shall be performed whenever the particular hierarchical encoding sequence being
followed requires them.

138

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)In the hierarchical mode the define-hierarchical-progression (DHP) marker segment shall be placed in the compressed
image data before the first start-of-frame. The DHP segment is used to signal the size of the image components of thecompleted image. The syntax of the DHP segment is specified in Annex B.
The first frame for each component or group of components in a hierarchical process shall be encoded by anon-differential frame. Differential frames shall then be used to encode the two’s complement differences between source
input components (possibly downsampled) and the reference components (possibly upsampled). The referencecomponents are reconstructed components created by previous frames in the hierarchical process. For either differential or
non-differential frames, reconstructions of the components shall be generated if needed as reference components for asubsequent frame in the hierarchical process.
Resolution changes may occur between hierarchical frames in a hierarchical process. These changes occur if
downsampling filters are used to reduce the spatial resolution of some or all of the components of the source image. Whenthe resolution of a reference component does not match the resolution of the component input to a differential frame, anupsampling filter shall be used to increase the spatial resolution of the reference component. The EXP marker segment
shall be added to the compressed image data before the start-of-frame whenever upsampling of a reference component isrequired. No more than one EXP marker segment shall precede a given frame.
Any of the marker segments allowed before a start-of-frame for the encoding process selected may be used before either
non-differential or differential frames.
For 16-bit input precision (lossless encoder), the differential components which are input to a differential frame arecalculated modulo 216. The reconstructed components calculated from the reconstructed differential components are also
calculated modulo 216.
If a hierarchical encoding process uses a DCT encoding process for the first frame, all frames in the hierarchical process
except for the final frame for each component shall use the DCT encoding processes defined in either Annex F or Annex
G, or the modified DCT encoding processes defined in this annex. The final frame may use a modified lossless process
defined in this annex.
If a hierarchical encoding process uses a lossless encoding process for the first frame, all frames in the hierarchical process
shall use a lossless encoding process defined in Annex H, or a modified lossless process defined in this annex.
J.1.1.1

Downsampling filter

The downsampled components are generated using a downsampling filter that is not specified in this Specification. Thisfilter should, however, be consistent with the upsampling filter. An example of a downsampling filter is provided in K.5.
J.1.1.2

Upsampling filter

The upsampling filter increases the spatial resolution by a factor of two horizontally, vertically, or both. Bi-linear
interpolation is used for the upsampling filter, as illustrated in Figure J.2.

a

x

b

a
x
b
TISO1710-93/d109

Figure J.2 – Diagram of sample positions for upsampling rules
Figure J.2 [D109] = 4 cm = 156 %CCITT Rec. T.81 (1992 E)

139

ISO/IEC 10918-1 : 1993(E)The rule for calculating the interpolated value is:Px = (Ra + Rb) / 2
where Ra and Rb are sample values from adjacent positions a and b of the lower resolution image and Px is theinterpolated value. The division indicates truncation, not rounding. The left-most column of the upsampled image matches
the left-most column of the lower resolution image. The top line of the upsampled image matches the top line of the lower
resolution image. The right column and the bottom line of the lower resolution image are replicated to provide the values
required for the right column edge and bottom line interpolations. The upsampling process always doubles the line length
or the number of lines.
If both horizontal and vertical expansions are signalled, they are done in sequence – first the horizontal expansion andthen the vertical.
J.1.2

Control procedure for encoding a differential frame

The control procedures in Annex E for frames, scans, restart intervals, and MCU also apply to the encoding of differential
frames, and the scans, restart intervals, and MCU from which the differential frame is constructed. The differential framesdiffer from the frames of Annexes F, G, and H only at the coding model level.
J.1.3

Encoder coding models for differential frames

The coding models defined in Annexes F, G, and H are modified to allow them to be used for coding of two’s complement
differences.
J.1.3.1

Modifications to encoder DCT encoding models for differential frames

Two modifications are made to the DCT coding models to allow them to be used in differential frames. First, the FDCT ofthe differential input is calculated without the level shift. Second, the DC coefficient of the DCT is coded directly –without prediction.
J.1.3.2

Modifications to lossless encoding models for differential frames

One modification is made to the lossless coding models. The difference is coded directly – without prediction. The
prediction selection parameter in the scan header shall be set to zero. The point transform which may be applied to thedifferential inputs is defined in Annex A.
J.1.4

Modifications to the entropy encoders for differential frames

The coding of two’s complement differences requires one extra bit of precision for the Huffman coding of AC coefficients.
The extension to Tables F.1 and F.7 is given in Table J.2.
Table J.2 – Modifications to tableof AC coefficient amplitude ranges

SSSS

AC coefficients15–32 767..–16 384, 16 384..32 767

The arithmetic coding models are already defined for the precision needed in differential frames.

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ISO/IEC 10918-1 : 1993(E)

J.2

Hierarchical decoding

J.2.1

Hierarchical control procedure for decoding an image

The control structure for decoding an image using the hierarchical mode is given in Figure J.3.

Decode_image

SOI marker
?

No

Yes

Interpret markers

EOI marker
?

Error

Yes

No

Hierarchical
?

Done

No

Non-Hierarchical mode

Yes

No

Decode_frame

Differential frame?

Yes[Upsample reference components]
Decode_differential_frame
Reconstruct_components
TISO1720-93/d110

Figure J.3 – Hierarchical control procedure for decoding an image
Figure J.3 [D110] = 18 cm = 704 %CCITT Rec. T.81 (1992 E)

141

ISO/IEC 10918-1 : 1993(E)The Interpret markers procedure shall decode the markers which may precede the SOF marker, continuing this decoding
until either a SOF or EOI marker is found. If the DHP marker is encountered before the first frame, a flag is set which
selects the hierarchical decoder at the “hierarchical?” decision point. In addition to the DHP marker (which shall precede
any SOF) and the EXP marker (which shall precede any differential SOF requiring resolution changes in the referencecomponents), any other markers which may precede a SOF shall be interpreted to the extent required for decoding of thecompressed image data.
If a differential SOF marker is found, the differential frame path is followed. If the EXP was encountered in the Interpretmarkers procedure, the reference components for the frame shall be upsampled as required by the parameters in the EXP
segment. The upsampling procedure described in J.1.1.2 shall be followed.
The Decode_differential_frame procedure generates a set of differential components. These differential components shallbe added, modulo 216, to the upsampled reference components in the Reconstruct_components procedure. This creates a
new set of reference components which shall be used when required in subsequent frames of the hierarchical process.
J.2.2

Control procedure for decoding a differential frame

The control procedures in Annex E for frames, scans, restart intervals, and MCU also apply to the decoding of differential
frames and the scans, restart intervals, and MCU from which the differential frame is constructed. The differential frame
differs from the frames of Annexes F, G, and H only at the decoder coding model level.
J.2.3

Decoder coding models for differential frames

The decoding models described in Annexes F, G, and H are modified to allow them to be used for decoding of two’s
complement differential components.
J.2.3.1

Modifications to the differential frame decoder DCT coding model

Two modifications are made to the decoder DCT coding models to allow them to code differential frames. First, the IDCTof the differential output is calculated without the level shift. Second, the DC coefficient of the DCT is decoded directly –without prediction.
J.2.3.2

Modifications to the differential frame decoder lossless coding model

One modification is made to the lossless decoder coding model. The difference is decoded directly – without prediction. If
the point transformation parameter in the scan header is not zero, the point transform, defined in Annex A, shall beapplied to the differential output.
J.2.4

Modifications to the entropy decoders for differential frames

The decoding of two’s complement differences requires one extra bit of precision in the Huffman code table. This is
described in J.1.4. The arithmetic coding models are already defined for the precision needed in differential frames.

142

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ISO/IEC 10918-1 : 1993(E)Annex K
Examples and guidelines(This annex does not form an integral part of this Recommendation | International Standard)This annex provides examples of various tables, procedures, and other guidelines.

K.1

Quantization tables for luminance and chrominance components

Two examples of quantization tables are given in Tables K.1 and K.2. These are based on psychovisual thresholding andare derived empirically using luminance and chrominance and 2:1 horizontal subsampling. These tables are provided as
examples only and are not necessarily suitable for any particular application. These quantization values have been usedwith good results on 8-bit per sample luminance and chrominance images of the format illustrated in Figure 13. Note thatthese quantization values are appropriate for the DCT normalization defined in A.3.3.
If these quantization values are divided by 2, the resulting reconstructed image is usually nearly indistinguishable from thesource image.
Table K.1 – Luminance quantization table
16

11

10

16

124

140

151

161

12

12

14

19

126

158

160

155

14

13

16

24

140

157

169

156

14

17

22

29

151

187

180

162

18

22

37

56

168

109

103

177

24

35

55

64

181

104

113

192

49

64

78

87

103

121

120

101

72

92

95

98

112

100

103

199

Table K.2 – Chrominance quantization table
17

18

24

47

99

99

99

99

18

21

26

66

99

99

99

99

24

26

56

99

99

99

99

99

47

66

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

99

CCITT Rec. T.81 (1992 E)

143

ISO/IEC 10918-1 : 1993(E)K.2

A procedure for generating the lists which specify a Huffman code table

A Huffman table is generated from a collection of statistics in two steps. The first step is the generation of the list oflengths and values which are in accord with the rules for generating the Huffman code tables. The second step is thegeneration of the Huffman code table from the list of lengths and values.
The first step, the topic of this section, is needed only for custom Huffman table generation and is done only in theencoder. In this step the statistics are used to create a table associating each value to be coded with the size (in bits) of thecorresponding Huffman code. This table is sorted by code size.
A procedure for creating a Huffman table for a set of up to 256 symbols is shown in Figure K.1. Three vectors are definedfor this procedure:
FREQ(V)CODESIZE(V)OTHERS(V)

Frequency of occurrence of symbol V
Code size of symbol V
Index to next symbol in chain of all symbols in current branch of code tree

where V goes from 0 to 256.
Before starting the procedure, the values of FREQ are collected for V = 0 to 255 and the FREQ value for V = 256 is set to
1 to reserve one code point. FREQ values for unused symbols are defined to be zero. In addition, the entries in
CODESIZE are all set to 0, and the indices in OTHERS are set to –1, the value which terminates a chain of indices.
Reserving one code point guarantees that no code word can ever be all “1” bits.
The search for the entry with the least value of FREQ(V) selects the largest value of V with the least value of FREQ(V)greater than zero.
The procedure “Find V1 for least value of FREQ(V1) > 0” always selects the value with the largest value of V1 whenmore than one V1 with the same frequency occurs. The reserved code point is then guaranteed to be in the longest code
word category.

144

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ISO/IEC 10918-1 : 1993(E)

Code_size

Find V1 for least value of
FREQ(V1) > 0
Find V2 for next least valueof FREQ(V2) > 0No

V2 exists
?

Yes
Done

FREQ(V1) =FREQ(V1) +FREQ(V2)
FREQ(V2) = 0

CODESIZE(V1) =CODESIZE(V1) + 1

V1 = OTHERS(V1)No

OTHERS(V1) = –1?
Yes
OTHERS(V1) = V2

CODESIZE(V2) =CODESIZE(V2) + 1

V2 = OTHERS(V2)No

OTHERS(V2) = –1?

Yes

TISO1730-93/d111

Figure K.1 – Procedure to find Huffman code sizes

Figure K.1 [D111] = 21 cm = 821 % (PAGE PLEINE)CCITT Rec. T.81 (1992 E)

145

ISO/IEC 10918-1 : 1993(E)Once the code lengths for each symbol have been obtained, the number of codes of each length is obtained using theprocedure in Figure K.2. The count for each size is contained in the list, BITS. The counts in BITS are zero at the start ofthe procedure. The procedure assumes that the probabilities are large enough that code lengths greater than 32 bits neveroccur. Note that until the final Adjust_BITS procedure is complete, BITS may have more than the 16 entries required in
the table specification (see Annex C).

Count_BITS

I= 0

CODESIZE(I) = 0?

No BITS(CODESIZE(I)) =BITS(CODESIZE(I)) + 1

Yes

I=I+1

No

I = 257

Yes
Adjust_BITS

Done
TISO1740-93/d112

Figure K.2 – Procedure to find the number of codes of each size

Figure K.2 [D112] = 16 cm = 625 %146

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Figure K.3 gives the procedure for adjusting the BITS list so that no code is longer than 16 bits. Since symbols are paired
for the longest Huffman code, the symbols are removed from this length category two at a time. The prefix for the pair(which is one bit shorter) is allocated to one of the pair; then (skipping the BITS entry for that prefix length) a code wordfrom the next shortest non-zero BITS entry is converted into a prefix for two code words one bit longer. After the BITS
list is reduced to a maximum code length of 16 bits, the last step removes the reserved code point from the code lengthcount.

Adjust_BITS

I = 32

Yes

BITS(I) > 0
?

J=I–1

No

I=I–1

No

I = 16
?
J=J–1
Yes

No

BITS(J) > 0
?

I=I–1

Yes
BITS(I) = BITS(I) – 2
BITS(I – 1) = BITS(I – 1) + 1
BITS(J + 1) = BITS(J + 1) + 2
BITS(J) = BITS (J) – 1

Yes

BITS(I) = 0?
No
BITS(I) = BITS(I) – 1

Done
TISO1750-93/d113

Figure K.3 – Procedure for limiting code lengths to 16 bits

Figure K.3 [D113] = 20 cm = 782 %CCITT Rec. T.81 (1992 E)

147

ISO/IEC 10918-1 : 1993(E)The input values are sorted according to code size as shown in Figure K.4. HUFFVAL is the list containing the input
values associated with each code word, in order of increasing code length.
At this point, the list of code lengths (BITS) and the list of values (HUFFVAL) can be used to generate the code tables.
These procedures are described in Annex C.

Sort_input

I= 1
K=0

J=0

CODESIZE(J) = I?

Yes

HUFFVAL(K) = J
K=K+1

No

J=J+1

No

J > 255
?
Yes
I=I+1

No

I > 32?
Yes
Done
TISO1760-93/d114

Figure K.4 – Sorting of input values according to code size
Figure K.4 [D114] = 20.5 cm = 801 %K.3

Typical Huffman tables for 8-bit precision luminance and chrominance

Huffman table-specification syntax is specified in B.2.4.2.
148

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)K.3.1

Typical Huffman tables for the DC coefficient differences

Tables K.3 and K.4 give Huffman tables for the DC coefficient differences which have been developed from the average
statistics of a large set of video images with 8-bit precision. Table K.3 is appropriate for luminance components and Table
K.4 is appropriate for chrominance components. Although there are no default tables, these tables may prove to be usefulfor many applications.
Table K.3 – Table for luminance DC coefficient differences
Category

Code length

Code word

10

2

000

11

3

010

12

3

011

13

3

100

14

3

101

15

3

110

16

4

1110

17

5

11110

18

6

11111019

7111111010

81111111011

9111111110

Table K.4 – Table for chrominance DC coefficient differences

K.3.2

Category

Code length

Code word

10

12

000

11

12

01

12

12

10

13

13

110

14

14

1110

15

15

11110

16

16

1111101717111111018

181111111019

19111111110

10101111111110

11

1111111111110

Typical Huffman tables for the AC coefficients

Tables K.5 and K.6 give Huffman tables for the AC coefficients which have been developed from the average statistics ofa large set of images with 8-bit precision. Table K.5 is appropriate for luminance components and Table K.6 is appropriate
for chrominance components. Although there are no default tables, these tables may prove to be useful for many
applications.

CCITT Rec. T.81 (1992 E)

149

ISO/IEC 10918-1 : 1993(E)Table K.5 – Table for luminance AC coefficients (sheet 1 of 4)
Run/Size
0/0 (EOB)
0/1
0/2
0/3
0/4
0/5
0/6
0/7
0/8
0/9
0/A
1/1
1/2
1/3
1/4
1/5
1/6
1/7
1/8
1/9
1/A
2/1
2/2
2/3
2/4
2/5
2/6
2/7
2/8
2/9
2/A
3/1
3/2
3/3
3/4
3/5
3/6
3/7
3/8
3/9
3/A

150

CCITT Rec. T.81 (1992 E)

Code length
14
12
12
13
14
15
17
18
10
16
16
14
15
17
19
11
16
16
16
16
16
15
18
10
12
16
16
16
16
16
16
16
19
12
16
16
16
16
16
16
16

Code word
1010
00
01
100
1011
11010
1111000
11111000
1111110110
1111111110000010
1111111110000011
1100
11011
1111001
111110110
11111110110
1111111110000100
1111111110000101
1111111110000110
1111111110000111
1111111110001000
11100
11111001
1111110111
111111110100
1111111110001001
1111111110001010
1111111110001011
1111111110001100
1111111110001101
1111111110001110
111010111110111
111111110101
1111111110001111
1111111110010000
1111111110010001
1111111110010010
1111111110010011
1111111110010100
1111111110010101

ISO/IEC 10918-1 : 1993(E)Table K.5 (sheet 2 of 4)
Run/Size
4/1
4/2
4/3
4/4
4/5
4/6
4/7
4/8
4/9
4/A
5/1
5/2
5/3
5/4
5/5
5/6
5/7
5/8
5/9
5/A
6/1
6/2
6/3
6/4
6/5
6/6
6/7
6/8
6/9
6/A
7/1
7/2
7/3
7/4
7/5
7/6
7/7
7/8
7/9
7/A
8/1
8/2

Code length
16
10
16
16
16
16
16
16
16
16
17
11
16
16
16
16
16
16
16
16
17
12
16
16
16
16
16
16
16
16
18
12
16
16
16
16
16
16
16
16
19
15

Code word
1110111111111000
1111111110010110
1111111110010111
1111111110011000
1111111110011001
1111111110011010
1111111110011011
1111111110011100
1111111110011101
111101011111110111
1111111110011110
1111111110011111
1111111110100000
1111111110100001
1111111110100010
1111111110100011
1111111110100100
1111111110100101
1111011111111110110
1111111110100110
1111111110100111
1111111110101000
1111111110101001
1111111110101010
1111111110101011
1111111110101100
1111111110101101
11111010
111111110111
1111111110101110
1111111110101111
1111111110110000
1111111110110001
1111111110110010
1111111110110011
1111111110110100
1111111110110101
111111000
111111111000000

CCITT Rec. T.81 (1992 E)

151

ISO/IEC 10918-1 : 1993(E)Table K.5 (sheet 3 of 4)
Run/Size
8/3
8/4
8/5
8/6
8/7
8/8
8/9
8/A
9/1
9/2
9/3
9/4
9/5
9/6
9/7
9/8
9/9
9/A
A/1
A/2
A/3
A/4
A/5
A/6
A/7
A/8
A/9
A/A
B/1
B/2
B/3
B/4
B/5
B/6
B/7
B/8
B/9
B/A
C/1
C/2
C/3
C/4

152

CCITT Rec. T.81 (1992 E)

Code length
16
16
16
16
16
16
16
16
19
16
16
16
16
16
16
16
16
16
19
16
16
16
16
16
16
16
16
16
10
16
16
16
16
16
16
16
16
16
10
16
16
16

Code word
1111111110110110
1111111110110111
1111111110111000
1111111110111001
1111111110111010
1111111110111011
1111111110111100
1111111110111101
111111001
1111111110111110
1111111110111111
1111111111000000
1111111111000001
1111111111000010
1111111111000011
1111111111000100
1111111111000101
1111111111000110
111111010
1111111111000111
1111111111001000
1111111111001001
1111111111001010
1111111111001011
1111111111001100
1111111111001101
1111111111001110
1111111111001111
1111111001
1111111111010000
1111111111010001
1111111111010010
1111111111010011
1111111111010100
1111111111010101
1111111111010110
1111111111010111
1111111111011000
1111111010
1111111111011001
1111111111011010
1111111111011011

ISO/IEC 10918-1 : 1993(E)Table K.5 (sheet 4 of 4)

Run/Size
C/5
C/6
C/7
C/8
C/9
C/A
D/1
D/2
D/3
D/4
D/5
D/6
D/7
D/8
D/9
D/A
E/1
E/2
E/3
E/4
E/5
E/6
E/7
E/8
E/9
E/A
F/0 (ZRL)
F/1
F/2
F/3
F/4
F/5
F/6
F/7
F/8
F/9
F/A

Code length
16
16
16
16
16
16
11
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
11
16
16
16
16
16
16
16
16
16
16

Code word
1111111111011100
1111111111011101
1111111111011110
1111111111011111
1111111111100000
1111111111100001
11111111000
1111111111100010
1111111111100011
1111111111100100
1111111111100101
1111111111100110
1111111111100111
1111111111101000
1111111111101001
1111111111101010
1111111111101011
1111111111101100
1111111111101101
1111111111101110
1111111111101111
1111111111110000
1111111111110001
1111111111110010
1111111111110011
1111111111110100
11111111001
1111111111110101
1111111111110110
1111111111110111
1111111111111000
1111111111111001
1111111111111010
1111111111111011
1111111111111100
1111111111111101
1111111111111110

CCITT Rec. T.81 (1992 E)

153

ISO/IEC 10918-1 : 1993(E)Table K.6 – Table for chrominance AC coefficients (sheet 1 of 4)
Run/Size
0/0 (EOB)
0/1
0/2
0/3
0/4
0/5
0/6
0/7
0/8
0/9
0/A
1/1
1/2
1/3
1/4
1/5
1/6
1/7
1/8
1/9
1/A
2/1
2/2
2/3
2/4
2/5
2/6
2/7
2/8
2/9
2/A
3/1
3/2
3/3
3/4
3/5
3/6
3/7
3/8
3/9
3/A
4/1

154

CCITT Rec. T.81 (1992 E)

Code length
12
12
13
14
15
15
16
17
19
10
12
14
16
18
19
11
12
16
16
16
16
15
18
10
12
15
16
16
16
16
16
15
18
10
12
16
16
16
16
16
16
16

Code word
00
01
100
1010
11000
11001
1110001111000
111110100
1111110110
111111110100
1011
11100111110110111110101
11111110110
111111110101
1111111110001000
1111111110001001
1111111110001010
1111111110001011
11010
11110111
1111110111
111111110110
111111111000010
1111111110001100
1111111110001101
1111111110001110
1111111110001111
1111111110010000
11011
11111000
1111111000
111111110111
1111111110010001
1111111110010010
1111111110010011
1111111110010100
1111111110010101
1111111110010110
111010ISO/IEC 10918-1 : 1993(E)Table K.6 (sheet 2 of 4)
Run/Size
4/2
4/3
4/4
4/5
4/6
4/7
4/8
4/9
4/A
5/1
5/2
5/3
5/4
5/5
5/6
5/7
5/8
5/9
5/A
6/1
6/2
6/3
6/4
6/5
6/6
6/7
6/8
6/9
6/A
7/1
7/2
7/3
7/4
7/5
7/6
7/7
7/8
7/9
7/A
8/1
8/2
8/3

Code length
19
16
16
16
16
16
16
16
16
16
10
16
16
16
16
16
16
16
16
17
11
16
16
16
16
16
16
16
16
17
11
16
16
16
16
16
16
16
16
18
16
16

Code word
111110110
1111111110010111
1111111110011000
1111111110011001
1111111110011010
1111111110011011
1111111110011100
1111111110011101
1111111110011110
1110111111111001
1111111110011111
1111111110100000
1111111110100001
1111111110100010
1111111110100011
1111111110100100
1111111110100101
1111111110100110
1111001
11111110111
1111111110100111
1111111110101000
1111111110101001
1111111110101010
1111111110101011
1111111110101100
1111111110101101
1111111110101110
111101011111111000
1111111110101111
1111111110110000
1111111110110001
1111111110110010
1111111110110011
1111111110110100
1111111110110101
1111111110110110
11111001
1111111110110111
1111111110111000

CCITT Rec. T.81 (1992 E)

155

ISO/IEC 10918-1 : 1993(E)Table K.6 (sheet 3 of 4)
Run/Size
8/4
8/5
8/6
8/7
8/8
8/9
8/A
9/1
9/2
9/3
9/4
9/5
9/6
9/7
9/8
9/9
9/A
A/1
A/2
A/3
A/4
A/5
A/6
A/7
A/8
A/9
A/A
B/1
B/2
B/3
B/4
B/5
B/6
B/7
B/8
B/9
B/A
C/1
C/2
C/3
C/4
C/5

156

CCITT Rec. T.81 (1992 E)

Code length
16
16
16
16
16
16
16
19
16
16
16
16
16
16
16
16
16
19
16
16
16
16
16
16
16
16
16
19
16
16
16
16
16
16
16
16
16
19
16
16
16
16

Code word
1111111110111001
1111111110111010
1111111110111011
1111111110111100
1111111110111101
1111111110111110
1111111110111111
111110111
1111111111000000
1111111111000001
1111111111000010
1111111111000011
1111111111000100
1111111111000101
1111111111000110
1111111111000111
1111111111001000
111111000
1111111111001001
1111111111001010
1111111111001011
1111111111001100
1111111111001101
1111111111001110
1111111111001111
1111111111010000
1111111111010001
111111001
1111111111010010
1111111111010011
1111111111010100
1111111111010101
1111111111010110
1111111111010111
1111111111011000
1111111111011001
1111111111011010
111111010
1111111111011011
1111111111011100
1111111111011101
1111111111011110

ISO/IEC 10918-1 : 1993(E)Table K.6 (sheet 4 of 4)
Run/Size
C/6
C/7
C/8
C/9
C/A
D/1
D/2
D/3
D/4
D/5
D/6
D/7
D/8
D/9
D/A
E/1
E/2
E/3
E/4
E/5
E/6
E/7
E/8
E/9
E/A
F/0 (ZRL)
F/1
F/2
F/3
F/4
F/5
F/6
F/7
F/8
F/9
F/A

Code length
16
16
16
16
16
11
16
16
16
16
16
16
16
16
16
14
16
16
16
16
16
16
16
16
16
10
15
16
16
16
16
16
16
16
16
16

Code word
1111111111011111
1111111111100000
1111111111100001
1111111111100010
1111111111100011
11111111001
1111111111100100
1111111111100101
1111111111100110
1111111111100111
1111111111101000
1111111111101001
1111111111101010
1111111111101011
1111111111101100
11111111100000
1111111111101101
1111111111101110
1111111111101111
1111111111110000
1111111111110001
1111111111110010
1111111111110011
1111111111110100
1111111111110101
1111111010
111111111000011
1111111111110110
1111111111110111
1111111111111000
1111111111111001
1111111111111010
1111111111111011
1111111111111100
1111111111111101
1111111111111110

CCITT Rec. T.81 (1992 E)

157

ISO/IEC 10918-1 : 1993(E)K.3.3

Huffman table-specification examples

K.3.3.1 Specification of typical tables for DC difference coding
A set of typical tables for DC component coding is given in K.3.1. The specification of these tables is as follows:

For Table K.3 (for luminance DC coefficients), the 16 bytes which specify the list of code lengths for the table are
X’00

01

05

01

01

01

01

01

01

00

00

00

04

05

06

07

08

09

0A

0B’

00

00

00

00’

The set of values following this list is
X’00

01

02

03

For Table K.4 (for chrominance DC coefficients), the 16 bytes which specify the list of code lengths for the table are
X’00

03

01

01

01

01

01

01

01

01

01

00

04

05

06

07

08

09

0A

0B’

00

00

00

00’

The set of values following this list is
X’00

01

02

03

K.3.3.2 Specification of typical tables for AC coefficient coding
A set of typical tables for AC component coding is given in K.3.2. The specification of these tables is as follows:

For Table K.5 (for luminance AC coefficients), the 16 bytes which specify the list of code lengths for the table are
X’00

02

01

03

03

02

04

03

05

05

04

04

00

00

01

7D’

The set of values which follows this list is
X’01

02

03

00

04

11

05

12

21

31

41

06

13

51

61

07

X’22

71

14

32

81

91

A1

08

23

42

B1

C1

15

52

D1

F0

X’24

33

62

72

82

09

0A

16

17

18

19

1A

25

26

27

28

X’29

2A

34

35

36

37

38

39

3A

43

44

45

46

47

48

49

X’4A

53

54

55

56

57

58

59

5A

63

64

65

66

67

68

69

X’6A

73

74

75

76

77

78

79

7A

83

84

85

86

87

88

89

X’8A

92

93

94

95

96

97

98

99

9A

A2

A3

A4

A5

A6

A7

X’A8

A9

AA

B2

B3

B4

B5

B6

B7

B8

B9

BA

C2

C3

C4

C5

X’C6

C7

C8

C9

CA

D2

D3

D4

D5

D6

D7

D8

D9

DA

E1

E2

X’E3

E4

E5

E6

E7

E8

E9

EA

F1

F2

F3

F4

F5

F6

F7

F8

X’F9

FA’

158

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)For Table K.6 (for chrominance AC coefficients), the 16 bytes which specify the list of code lengths for the table are
X’00

02

01

02

04

04

03

04

07

05

04

04

00

01

02

77’

The set of values which follows this list is:
X’00

01

02

03

11

04

05

21

31

06

12

41

51

07

61

71

X’13

22

32

81

08

14

42

91

A1

B1

C1

09

23

33

52

F0

X'15

62

72

D1

0A

16

24

34

E1

25

F1

17

18

19

1A

26

X'27

28

29

2A

35

36

37

38

39

3A

43

44

45

46

47

48

X'49

4A

53

54

55

56

57

58

59

5A

63

64

65

66

67

68

X'69

6A

73

74

75

76

77

78

79

7A

82

83

84

85

86

87

X'88

89

8A

92

93

94

95

96

97

98

99

9A

A2

A3

A4

A5

X'A6

A7

A8

A9

AA

B2

B3

B4

B5

B6

B7

B8

B9

BA

C2

C3

X'C4

C5

C6

C7

C8

C9

CA

D2

D3

D4

D5

D6

D7

D8

D9

DA

X'E2

E3

E4

E5

E6

E7

E8

E9

EA

F2

F3

F4

F5

F6

F7

F8

X'F9

FA’

K.4

Additional information on arithmetic coding

K.4.1

Test sequence for a small data set for the arithmetic coder

The following 256-bit test sequence (in hexadecimal form) is structured to test many of the encoder and decoder paths:
X’00020051

000000C00352872AAAAAAAAA

82C02000

FCD79EF6

74EAABF7

697EE74C’

Tables K.7 and K.8 provide a symbol-by-symbol list of the arithmetic encoder and decoder operation. In these tables theevent count, EC, is listed first, followed by the value of Qe used in encoding and decoding that event. The decision D to
be encoded (and decoded) is listed next. The column labeled MPS contains the sense of the MPS, and if it is followed bya CE (in the “CX” column), the conditional MPS/LPS exchange occurs when encoding and decoding the decision (seeFigures D.3, D.4 and D.17). The contents of the A and C registers are the values before the event is encoded and decoded.
ST is the number of X’FF’ bytes stacked in the encoder waiting for a resolution of the carry-over. Note that the A register
is always greater than X’7FFF’. (The starting value has an implied value of X’10000’.)
In the encoder test, the code bytes (B) are listed if they were completed during the coding of the preceding event. If
additional bytes follow, they were also completed during the coding of the preceding event. If a byte is listed in the
Bx column, the preceding byte in column B was modified by a carry-over.
In the decoder the code bytes are listed if they were placed in the code register just prior to the event EC.
For this file the coded bit count is 240, including the overhead to flush the final data from the C register. When themarker X’FFD9’ is appended, a total of 256 bits are output. The actual compressed data sequence for the encoder is (inhexadecimal form)
X’655B5144

F7969D51

7855BFFF

00FC5184

C7CEF939

00287D46

708ECBC0F6FFD900’

CCITT Rec. T.81 (1992 E)

159

ISO/IEC 10918-1 : 1993(E)Table K.7 – Encoder test sequence (sheet 1 of 7)

160

EC

D

MPS

11
12
13
14
15
16
17
18
19
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36

0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

CX

CE

CCITT Rec. T.81 (1992 E)

Qe(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

ST

5A1D
5A1D
2586
2586
1114
1114
1114
1114
1114
080B
080B
080B
080B
080B
080B
17B9
1182
1182
1182
1182
1182
0CEF
0CEF
0CEF
0CEF
0CEF
1518
1518
1AA9
1AA9
174E
174E
1AA9
1AA9
1AA9
174E

0000
A5E3
B43A
8EB4
D25C
C148
B034
9F20
8E0C
F9F0
F1E5
E9DA
E1CF
D9C4
D1B9
80B0
D1EE
C06C
AEEA
9D68
8BE6
F4C8
E7D9
DAEA
CDFB
C10C
CEF0
B9D8
A8C0
8E17
E6DC
CF8E
BA70
9FC7
851E
D4EA

00000000
00000000
0000978C
0000978C
00012F18
00012F18
00012F18
00012F18
00012F1800025E30
00025E30
00025E30
00025E30
00025E30
00025E30
00327DE00064FBC00064FBC00064FBC00064FBC00064FBC000C9F780
00C9F780
00C9F780
00C9F780
00C9F780
000AB9D0000AB9D0005AF480
005AF480
00B5E900
00B5E900
00050A00
00050A00
00050A00
000A1400

11
11
10
10
19
19
19
19
19
18
18
18
18
18
18
14
13
13
13
13
13
12
12
12
12
12
16
16
13
13
12
12
17
17
17
16

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Bx

B

65

5B

ISO/IEC 10918-1 : 1993(E)Table K.7 – Encoder test sequence (sheet 2 of 7)

EC

D

MPS

37
38

0
0

39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0

CX

Qe
(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

ST

0
0

174E
174E

BD9C
A64E

000A1400
000A1400

16
16

0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

174E
1424
1424
1424
1424
1424
1424
119C
119C
119C
119C
119C
119C
119C
0F6B
0F6B
0F6B
0F6B
0F6B
1424
1AA9
1AA9
174E
174E
174E
174E
1424
1424
1424
1424
1424
1424
119C
1424
1AA9

8F00
EF64
DB40
C71C
B2F8
9ED4
8AB0
ED18
DB7C
C9E0
B844
A6A8
950C
8370
E3A8
D43D
C4D2
B567
A5FC
F6B0
A120
8677
D79C
C04E
A900
91B2
F4C8
E0A4
CC80
B85C
A438
9014
F7E0
8CE0
A120

000A1400
00142800
00142800
00142800
00142800
00142800
00142800
00285000
00285000
00285000
00285000
00285000
00285000
00285000
0050A000
0050A000
0050A000
0050A000
0050A000
00036910
00225CE000225CE00044B9C00044B9C00044B9C00044B9C000897380
00897380
00897380
00897380
00897380
00897380
0112E700
001E6A20
00F716E0

16
15
5
5
5
5
5
4
4
4
4
4
4
4
3
3
3
3
3
7
4
4
3
3
3
3
2
2
2
2
2
2
1
6
3

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Bx

CCITT Rec. T.81 (1992 E)

B

51

44

161

ISO/IEC 10918-1 : 1993(E)Table K.7 – Encoder test sequence (sheet 3 of 7)

162

EC

D

MPS

174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
100
101
102
103
104
105
106
107
108
109
110

1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

CX

CE
CE
CE
CE
CE
CE
CE

CCITT Rec. T.81 (1992 E)

Qe(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

ST

1AA9
2516
2516
299A
2516
2516
299A
2516
299A
2516
2516
2516
1EDF
2516
299A
32B4
2E17
2E17
32B4
32B4
3C3D
3C3D
415E
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639

8677
D548
B032
9458
D57C
B066
9458
D57C
9458
D57C
B066
8B50
CC74
F6F8
9458
A668
E768
B951
B85C
85A8
CAD0
8E93
F0F4
AF96
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC

00F716E0
00041570
00041570
00128230
00250460
00250460
00963EC0012C7D80
0004B798
00096F30
00096F30
00096F30
0012DE60
009C5FA80274C628
0004C398
00098730
00098730
002849A8002849A800A27270
00A27270
00031318
00031318
000702A0
000E7E46
001D92B4003B9E6E
0077D304
00F01F0E
01E0D444
0002218E
0004D944
000A2B8E
0014ED44
002A538E
00553D44

3
8
8
6
5
5
3
2
8
7
7
7
6
3
1
7
6
6
4
4
2
2
8
8
7
6
5
4
3
2
1
8
7
6
5
4
3

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Bx

B

F7

96

9D

51

78

ISO/IEC 10918-1 : 1993(E)Table K.7 – Encoder test sequence (sheet 4 of 7)

EC

D

MPS

111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146

1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

CX

CE
CE
CE
CE
CE
CE
CE
CE
CE
CE

CE

Qe
(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

ST

415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
3C3D
375E
32B4
32B4
3C3D
3C3D
415E
4639
415E
3C3D
375E
32B4
32B4
32B4
2E17

8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
9628
B3D6
F8F0
C63C
CAD0
8E93
F0F4
82BC
8C72
9628
B3D6
F8F0
C63C
9388
C1A8

00AAF38E
01567D440005738E
000B7D440017738E
002F7D44
005F738E
00BF7D44
017F738E
02FF7D440007738E
000F7D44001F738E
003F7D44
007F738E
00FF7D44
01FF738E
03FF7D440007738E
000F7D44001F738E
003EE71C
007DCE38
00FB9C7000FB9C70
03F0BFE0
03F0BFE0000448D80009F0DC
00145ABE
0028B57C
00516AF800A2D5F0
00A2D5F0
00A2D5F00145ABE0

2
1
8
7
6
5
4
3
2
1
8
7
6
5
4
3
2
1
8
7
6
5
4
3
3
1
1
7
6
5
4
3
2
2
2
1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0

Bx

CCITT Rec. T.81 (1992 E)

B

55

BF

FF00FC163

ISO/IEC 10918-1 : 1993(E)Table K.7 – Encoder test sequence (sheet 5 of 7)

164

EC

D

MPS

147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183

1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

CX

CE

CE
CE
CE
CE
CE

CE
CE

CCITT Rec. T.81 (1992 E)

Qe(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

ST

2E17
32B4
32B4
2E17
299A
299A
299A
2516
2516
2516
1EDF
1EDF
1EDF
1EDF
1AA9
2516
299A
32B4
3C3D
415E
4639
415E
3C3D
415E
4639
415E
4639
415E
4639
4B85
504F
5522
504F
4B85
504F
5522
59EB

9391
B85C
85A8
A5E8
EFA2
C608
9C6E
E5A8
C092
9B7C
ECCC
CDED
AF0E
902F
E2A0
D548
9458
A668
CAD0
F0F4
82BC
8C72
9628
F0F4
82BC
8C72
82BC
8C72
82BC
F20C
970A
8D76
AA44
B3EA
970A
8D76
E150

0145ABE000084568
00084568
00108AD0002115A0002115A0002115A000422B40
00422B40
00422B40
00845680
00845680
00845680
00845680
0108AD00
000BA7B800315FA8
00C72998
031E7530
000C0F0C
00197D440033738E
0066E71C
019D041C
033B6764
000747CE
000F25C4001EC48E
003E1F44
00F87D10
01F2472E
03E48E5C
00018D60
00031AC00007064A
000E0C94
00383250

1
7
7
6
5
5
5
4
4
4
3
3
3
3
2
7
5
3
1
7
6
5
4
2
1
8
7
6
5
3
2
1
8
7
6
5
3

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Bx

B

51

84

C7

CE

F9

ISO/IEC 10918-1 : 1993(E)Table K.7 – Encoder test sequence (sheet 6 of 7)

EC

D

MPS

184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220

0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1

1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

CX

CE

CE
CE

CE
CE

CE
CE
CE
CE
CE
CE

Qe
(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

ST

59EB
59EB
59EB
5522
504F
4B85
504F
4B85
4639
4B85
504F
4B85
4639
415E
4639
415E
4639
4B85
4B85
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
3C3D
375E
32B4
32B4

B3D6
B3D6
B3D6
B3D6
BD68
DA32
970A
A09E
AA32
8C72
81DA
A09E
AA32
C7F2
82BC
8C72
82BC
F20C
A687
B604
DF96
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
9628
B3D6
F8F0
C63C

0071736A
00E39AAA
0007E92A
000FD254
001FA4A8003F4950
007FAFFA
00FFED6A
01FFDAD4
04007D9A
0000FB34
0002597E
0004B2FC
000965F80013D918
00282B36
0050EC94
0003B250
0003B250
000764A0000EC940
001ECEF0003E16E6007CC3F400FA00EE
01F49804
0001A90E
0003E844
0008498E
00112944
0022CB8E
00462D44008CD38E
0119A71C
00034E38
00069C7000069C70

2
1
8
7
6
5
4
3
2
1
8
7
6
5
4
3
2
8
8
7
6
5
4
3
2
1
8
7
6
5
4
3
2
1
8
7
7

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Bx

B

38

39

CCITT Rec. T.81 (1992 E)

00

28

7D

46

165

ISO/IEC 10918-1 : 1993(E)Table K.7 – Encoder test sequence (sheet 7 of 7)
EC

D

MPS

221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
Flush:

0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

CX

CE
CE

CE

CE

Qe
(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

ST

32B4
3C3D
3C3D
375E
32B4
3C3D
3C3D
375E
3C3D
3C3D
415E
4639
415E
4639
415E
3C3D
375E
32B4
32B4
32B4
3C3D
3C3D
375E
32B4
3C3D
415E
415E
3C3D
3C3D
415E
415E
4639
4B85
4B85
4639
4B85

9388
CAD0
8E93
A4AC
DA9C
CAD0
8E93
A4AC
DD78
A13B
F0F4
82BC
8C72
82BC
8C72
9628
B3D6
F8F0
C63C
9388
CAD0
8E93
A4AC
DA9C
CAD0
F0F4
AF96
DC70
A033
F0F4
AF96
82BC
F20C
A687
B604
8C72
81DA

00069C70
001BF510
001BF510
0037EA20006FD440
01C1F0A0
01C1F0A0
0003E140
00113A38
00113A38
00467CD8008E58DC
011D2ABE
023AEBA4
0006504E
000CA09C
0019413800328270003282700032827000CB8D10
00CB8D1001971A20
032E3440
000B70A0
002FFCCC
002FFCCC
005FF998
005FF998
01817638
01817638
0303C8E0
000F2380
000F2380
001E4700003D6D96
007ADB2C

7
5
5
4
3
1
1
8
6
6
4
3
2
1
8
7
6
5
5
5
3
3
2
1
7
5
5
4
4
2
2
1
7
7
6
5
4

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Bx

B

70

8E

CB

C0

F6
FFD9

166

CCITT Rec. T.81 (1992 E)

ISO/IEC 10918-1 : 1993(E)Table K.8 – Decoder test sequence (sheet 1 of 7)

EC

D

MPS

11
12
13
14
15
16
17
18
19
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40

0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

CX

CE

Qe
(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

B

5A1D
5A1D
2586
2586
1114
1114
1114
1114
1114
080B
080B
080B
080B
080B
080B
17B9
1182
1182
1182
1182
1182
0CEF
0CEF
0CEF
0CEF
0CEF
1518
1518
1AA9
1AA9
174E
174E
1AA9
1AA9
1AA9
174E
174E
174E
174E
1424

0000
A5E3
B43A
8EB4
D25C
C148
B034
9F20
8E0C
F9F0
F1E5
E9DA
E1CF
D9C4
D1B9
80B0
D1EE
C06C
AEEA
9D68
8BE6
F4C8
E7D9
DAEA
CDFB
C10C
CEF0
B9D8
A8C0
8E17
E6DC
CF8E
BA70
9FC7
851E
D4EA
BD9C
A64E
8F00
EF64

655B0000
655B0000
332AA200
332AA20066554400
66554400
66554400
66554400
66554400
CCAA8800
CCAA8800
CCAA8800
CCAA8800
CCAA8800
CCAA8800
2FC88000
5F910000
5F910000
5F910000
5F910000
5F910000
BF228800
BF228800
BF228800
BF228800
BF228800
B0588000
B0588000
5CC40000
5CC40000
B989EE00
B989EE00
0A4F7000
0A4F7000
0A4F7000
149EE000
149EE000
149EE000
149EE000
293DC000

0
0
7
7
6
6
6
6
6
5
5
5
5
5
5
1
0
0
0
0
0
7
7
7
7
7
3
3
0
0
7
7
4
4
4
3
3
3
3
2

65 5B
51

44

F7

CCITT Rec. T.81 (1992 E)

167

ISO/IEC 10918-1 : 1993(E)Table K.8 – Decoder test sequence (sheet 2 of 7)

168

EC

D

MPS

41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

CX

CCITT Rec. T.81 (1992 E)

Qe(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

1424
1424
1424
1424
1424
119C
119C
119C
119C
119C
119C
119C
0F6B
0F6B
0F6B
0F6B
0F6B
1424
1AA9
1AA9
174E
174E
174E
174E
1424
1424
1424
1424
1424
1424
119C
1424
1AA9
1AA9
2516
2516
299A
2516
2516
299A

DB40
C71C
B2F8
9ED4
8AB0
ED18
DB7C
C9E0
B844
A6A8
950C
8370
E3A8
D43D
C4D2
B567
A5FC
F6B0
A120
8677
D79C
C04E
A900
91B2
F4C8
E0A4
CC80
B85C
A438
9014
F7E0
8CE0
A120
8677
D548
B032
9458
D57C
B066
9458

293DC000
293DC000
293DC000
293DC000
293DC000
527B8000
527B8000
527B8000
527B8000
527B8000
527B8000
527B8000
A4F70000
A4F70000
A4F70000
A4F70000
A4F70000
E6696000
1EEB0000
1EEB0000
3DD60000
3DD60000
3DD60000
3DD60000
7BAD3A00
7BAD3A00
7BAD3A00
7BAD3A00
7BAD3A00
7BAD3A00
F75A7400
88B3A000
7FBD0000
7FBD0000
9F7A8800
9F7A8800
517A2000
A2F44000
A2F44000
5E910000

2
2
2
2
2
1
1
1
1
1
1
1
0
0
0
0
0
4
1
1
0
0
0
0
7
7
7
7
7
7
6
3
0
0
5
5
3
2
2
0

B

96

9D

51

ISO/IEC 10918-1 : 1993(E)Table K.8 – Decoder test sequence (sheet 3 of 7)

EC

D

MPS

181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119

1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

120

CX

CE
CE
CE
CE
CE
CE
CE
CE
CE
CE
CE
CE

Qe
(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

B

2516
299A
2516
2516
2516
1EDF
2516
299A
32B4
2E17
2E17
32B4
32B4
3C3D
3C3D
415E
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639

D57C
9458
D57C
B066
8B50
CC74
F6F8
9458
A668
E768
B951
B85C
85A8
CAD0
8E93
F0F4
AF96
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC

BD22F000
32F3C000
65E78000
65E78000
65E78000
CBCF0000
F1D00000
7FB95400
53ED5000
A7DAA000
A7DAA000
72828000
72828000
7E3B7E00
7E3B7E00
AF95F800
AF95F800
82BBF000
8C71E000
82BBC000
8C718000
82BB0000
8C71FE00
82BBFC00
8C71F800
82BBF000
8C71E000
82BBC000
8C718000
82BB0000
8C71F800
82BBF000
8C71E000
82BBC000
8C718000
82BB0000
8C700000
82B80000
8C6AA200
82AD4400

7
5
4
4
4
3
0
6
4
3
3
1
1
7
7
5
5
4
3
2
1
0
7
6
5
4
3
2
1
0
7
6
5
4
3
2
1
0
7
6

78

55

BF

FF 00

FC

51

CCITT Rec. T.81 (1992 E)

169

ISO/IEC 10918-1 : 1993(E)Table K.8 – Decoder test sequence (sheet 4 of 7)

170

EC

D

MPS

121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160

1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

CX

CE
CE
CE
CE
CE

CE

CCITT Rec. T.81 (1992 E)

Qe(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
3C3D
375E
32B4
32B4
3C3D
3C3D
415E
4639
415E
3C3D
375E
32B4
32B4
32B4
2E17
2E17
32B4
32B4
2E17
299A
299A
299A
2516
2516
2516
1EDF
1EDF
1EDF
1EDF

8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
9628
B3D6
F8F0
C63C
CAD0
8E93
F0F4
82BC
8C72
9628
B3D6
F8F0
C63C
9388
C1A8
9391
B85C
85A8
A5E8
EFA2
C608
9C6E
E5A8
C092
9B7C
ECCC
CDED
AF0E
902F

8C548800
82811000
8BFC2000
81D04000
8A9A8000
7F0D0000
85150800
74021000
6EFE2000
47D44000
16A28000
2D450000
5A8A0000
B5140000
B5140000
86331C00
86331C00
CF747000
3FBCE000
0673C000
0CE78000
19CF0000
339F9C00
339F9C00
339F9C00
673F3800
673F3800
0714E000
0714E000
0E29C000
1C538000
1C538000
1C538000
38A70000
38A70000
38A70000
714E0000
714E0000
714E0000
714E0000

5
4
3
2
1
0
7
6
5
4
3
2
1
0
0
6
6
4
3
2
1
0
7
7
7
6
6
4
4
3
2
2
2
1
1
1
0
0
0
0

B

84

C7

CE

ISO/IEC 10918-1 : 1993(E)Table K.8 – Decoder test sequence (sheet 5 of 7)

EC

D

MPS

161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200

1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

CX

CE

CE
CE
CE
CE
CE

CE
CE

CE

CE
CE

CE
CE

Qe
(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

B

1AA9
2516
299A
32B4
3C3D
415E
4639
415E
3C3D
415E
4639
415E
4639
415E
4639
4B85
504F
5522
504F
4B85
504F
5522
59EB
59EB
59EB
59EB
5522
504F
4B85
504F
4B85
4639
4B85
504F
4B85
4639
415E
4639
415E
4639

E2A0
D548
9458
A668
CAD0
F0F4
82BC
8C72
9628
F0F4
82BC
8C72
82BC
8C72
82BC
F20C
970A
8D76
AA44
B3EA
970A
8D76
E150
B3D6
B3D6
B3D6
B3D6
BD68
DA32
970A
A09E
AA32
8C72
81DA
A09E
AA32
C7F2
82BC
8C72
82BC

E29DF200
D5379000
94164000
A5610000
C6B4E400
E0879000
61E32000
4AC04000
95808000
EE560000
7D800000
81FA0000
6DCC0000
62920000
2EFC0000
BBF00000
2AD25000
55A4A000
3AA14000
75428000
19BB0000
33760000
CDD80000
8CE6FA00
65F7F400
1819E800
3033D000
6067A000
C0CF4000
64448000
3B130000
76268C00
245B1800
48B63000
2E566000
5CACC000
B9598000
658B0000
52100000
0DF8E000

7
4
2
0
6
4
3
2
1
7
6
5
4
3
2
0
7
6
5
4
3
2
0
7
6
5
4
3
2
1
0
7
6
5
4
3
2
1
0
7

F9

39

00

28

7D

46

70

CCITT Rec. T.81 (1992 E)

171

ISO/IEC 10918-1 : 1993(E)Table K.8 – Decoder test sequence (sheet 6 of 7)

172

EC

D

MPS

201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240

1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

CX

CE
CE
CE
CE
CE
CE

CE
CE

CCITT Rec. T.81 (1992 E)

Qe(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

4B85
4B85
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
4639
415E
3C3D
375E
32B4
32B4
32B4
3C3D
3C3D
375E
32B4
3C3D
3C3D
375E
3C3D
3C3D
415E
4639
415E
4639
415E
3C3D
375E
32B4
32B4
32B4

F20C
A687
B604
DF96
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
82BC
8C72
9628
B3D6
F8F0
C63C
9388
CAD0
8E93
A4AC
DA9C
CAD0
8E93
A4AC
DD78
A13B
F0F4
82BC
8C72
82BC
8C72
9628
B3D6
F8F0
C63C
9388

37E38000
37E38000
6FC70000
DF8E0000
82AC0000
8C520000
827C0000
8BF31C00
81BE3800
8A767000
7EC4E000
8483C000
72DF8000
6CB90000
434A0000
0D8F9600
1B1F2C00
363E5800
6C7CB000
6C7CB000
6C7CB000
2EA2C000
2EA2C000
5D458000
BA8B0000
4A8F0000
4A8F0000
951E0000
9F400000
9F400000
E9080000
72E40000
6CC3EC00
435FD800
0DB9B000
1B736000
36E6C000
6DCD8000
6DCD8000
6DCD8000

5
5
4
3
2
1
0
7
6
5
4
3
2
1
0
7
6
5
4
4
4
2
2
1
0
6
6
5
3
3
1
0
7
6
5
4
3
2
2
2

B

8E

CB

C0

F6

ISO/IEC 10918-1 : 1993(E)Table K.8 – Decoder test sequence (sheet 7 of 7)
EC

D

MPS

CX

241
1
1
242
1
1
Marker detected: zero byte fed to decoder
243
1
1
244
0
1
245
0
1
246
1
1
247
1
1
248
1
1
249
0
1
Marker detected: zero byte fed to decoder
250
1
1
251
0
1
252
0
1
CE
253
1
1
254
1
1
255
0
1
256
0
1
CE

K.5

Qe
(hexadecimal)A(hexadecimal)C(hexadecimal)

CT

3C3D
3C3D

CAD0
8E93

33E60000
33E60000

0
0

375E
32B4
3C3D
415E
415E
3C3D
3C3D

A4AC
DA9C
CAD0
F0F4
AF96
DC70
A033

67CC0000
CF980000
9EC00000
40B40000
40B40000
81680000
81680000

7
6
4
2
2
1
1

415E
415E
4639
4B85
4B85
4639
4B85

F0F4
AF96
82BC
F20C
A687
B604
8C72

75C80000
75C80000
0F200000
3C800000
3C800000
79000000
126A0000

7
7
6
4
4
3
2

B

Low-pass downsampling filters for hierarchical coding

In this section simple examples are given of downsampling filters which are compatible with the upsampling filter definedin J.1.1.2.
Figure K.5 shows the weighting of neighbouring samples for simple one-dimensional horizontal and vertical low-passfilters. The output of the filter must be normalized by the sum of the neighbourhood weights.

1

2

1

1
2
1
TISO1770-93/d115

Figure K.5 – Low-pass filter example
Figure K.5 [D115] = 4 cm = 156 %The centre sample in Figure K.5 should be aligned with the left column or top line of the high resolution image whencalculating the left column or top line of the low resolution image. Sample values which are situated outside of the image
boundary are replicated from the sample values at the boundary to provide missing edge values.
If the image being downsampled has an odd width or length, the odd dimension is increased by 1 by sample replication on
the right edge or bottom line before downsampling.

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ISO/IEC 10918-1 : 1993(E)K.6

Domain of applicability of DCT and spatial coding techniques

The DCT coder is intended for lossy coding in a range from quite visible loss to distortion well below the threshold forvisibility. However in general, DCT-based processes cannot be used for true lossless coding.
The lossless coder is intended for completely lossless coding. The lossless coding process is significantly less effective
than the DCT-based processes for distortions near and above the threshold of visibility.
The point transform of the input to the lossless coder permits a very restricted form of lossy coding with the “lossless”
coder. (The coder is still lossless after the input point transform.) Since the DCT is intended for lossy coding, there may
be some confusion about when this alternative lossy technique should be used.
Lossless coding with a point transformed input is intended for applications which cannot be addressed by DCT coding
techniques. Among these are–true lossless coding to a specified precision;–

lossy coding with precisely defined error bounds;–

hierarchical progression to a truly lossless final stage.

If lossless coding with a point transformed input is used in applications which can be met effectively by DCT coding, theresults will be significantly less satisfactory. For example, distortion in the form of visible contours usually appears when
precision of the luminance component is reduced to about six bits. For normal image data, this occurs at bit rates well
above those for which the DCT gives outputs which are visually indistinguishable from the source.

K.7

Domain of applicability of the progressive coding modes of operation

Two very different progressive coding modes of operation have been defined, progressive coding of the DCT coefficientsand hierarchical progression. Progressive coding of the DCT coefficients has two complementary procedures, spectral
selection and successive approximation. Because of this diversity of choices, there may be some confusion as to which
method of progression to use for a given application.
K.7.1

Progressive coding of the DCT

In progressive coding of the DCT coefficients two complementary procedures are defined for decomposing the 8 × 8 DCT
coefficient array, spectral selection and successive approximation. Spectral selection partitions zig-zag array of DCT
coefficients into “bands”, one band being coded in each scan. Successive approximation codes the coefficients with
reduced precision in the first scan; in each subsequent scan the precision is increased by one bit.
A single forward DCT is calculated for these procedures. When all coefficients are coded to full precision, the DCT is thesame as in the sequential mode. Therefore, like the sequential DCT coding, progressive coding of DCT coefficients is
intended for applications which need very good compression for a given level of visual distortion.
The simplest progressive coding technique is spectral selection; indeed, because of this simplicity, some applications may
choose – despite the limited progression that can be achieved – to use only spectral selection. Note, however, that theabsence of high frequency bands typically leads – for a given bit rate – to a significantly lower image quality in theintermediate stages than can be achieved with the more general progressions. The net coding efficiency at the completionof the final stage is typically comparable to or slightly less than that achieved with the sequential DCT.
A much more flexible progressive system is attained at some increase in complexity when successive approximation isadded to the spectral selection progression. For a given bit rate, this system typically provides significantly better image
quality than spectral selection alone. The net coding efficiency at the completion of the final stage is typically comparable
to or slightly better than that achieved with the sequential DCT.
K.7.2

Hierarchical progression

Hierarchical progression permits a sequence of outputs of increasing spatial resolution, and also allows refinement ofimage quality at a given spatial resolution. Both DCT and spatial versions of the hierarchical progression are allowed, andprogressive coding of DCT coefficients may be used in a frame of the DCT hierarchical progression.
The DCT hierarchical progression is intended for applications which need very good compression for a given level ofvisual distortion; the spatial hierarchical progression is intended for applications which need a simple progression with atruly lossless final stage. Figure K.6 illustrates examples of these two basic hierarchical progressions.

174

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ISO/IEC 10918-1 : 1993(E)DCT path

Lossless path

DCT (dif)

Predicted (dif)DCT (dif)

Predicted (dif)Lossless (dif)+Point transform

Predicted (dif)Bounded error onreconstructed image

No error onreconstructed image
TISO1780-93/d116

Figure K.6 – Sketch of the basic operations of the hierarchical mode
Figure K.6 [D116] = 14 cm = 547 %K.7.2.1 DCT Hierarchical progression
If a DCT hierarchical progression uses reduced spatial resolution, the early stages of the progression can have better image
quality for a given bit rate than the early stages of non-hierarchical progressive coding of the DCT coefficients. However,at the point where the distortion between source and output becomes indistinguishable, the coding efficiency achieved
with a DCT hierarchical progression is typically significantly lower than the coding efficiency achieved with a nonhierarchical progressive coding of the DCT coefficients.
While the hierarchical DCT progression is intended for lossy progressive coding, a final spatial differential coding stage
can be used. When this final stage is used, the output can be almost lossless, limited only by the difference between theencoder and decoder IDCT implementations. Since IDCT implementations can differ significantly, truly lossless coding
after a DCT hierarchical progression cannot be guaranteed. An important alternative, therefore, is to use the input pointtransform of the final lossless differential coding stage to reduce the precision of the differential input. This allows abounding of the difference between source and output at a significantly lower cost in coded bits than coding of the full
precision spatial difference would require.
K.7.2.2 Spatial hierarchical progression
If lossless progression is required, a very simple hierarchical progression may be used in which the spatial lossless coderwith point transformed input is used as a first stage. This first stage is followed by one or more spatial differential coding
stages. The first stage should be nearly lossless, such that the low order bits which are truncated by the point transform areessentially random – otherwise the compression efficiency will be degraded relative to non-progressive lossless coding.

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ISO/IEC 10918-1 : 1993(E)K.8

Suppression of block-to-block discontinuities in decoded images

A simple technique is available for suppressing the block-to-block discontinuities which can occur in images compressedby DCT techniques.
The first few (five in this example) low frequency DCT coefficients are predicted from the nine DC values of the blockand the eight nearest-neighbour blocks, and the predicted values are used to suppress blocking artifacts in smooth areas of
the image.
The prediction equations for the first five AC coefficients in the zig-zag sequence are obtained as follows:
K.8.1

AC prediction

The sample field in a 3 by 3 array of blocks (each block containing an 8 × 8 array of samples) is modeled by a
two-dimensional second degree polynomial of the form:
P(x,y) = A1(x2y2) + A2(x2y) + A3(xy2) + A4(x2) + A5(xy) + A6(y2) + A7(x) + A8(y) + A9
The nine coefficients A1 through A9 are uniquely determined by imposing the constraint that the mean of P(x,y) overeach of the nine blocks must yield the correct DC-values.
Applying the DCT to the quadratic field predicting the samples in the central block gives a prediction of the low
frequency AC coefficients depicted in Figure K.7.

DC

x

x

x

x

x

TISO1790-93/d117

Figure K.7 – DCT array positions of predicted AC coefficients
Figure K.7 [D.117] = 8 cm = 313 %The prediction equations derived in this manner are as follows:
For the two dimensional array of DC values shown
DC1
DC4
DC7

DC2
DC5
DC8

DC3
DC6
DC9

The unquantized prediction equations are
AC01 = 1,13885 (DC4 – DC6)
AC10 = 1,13885 (DC2 – DC8)
AC20 = 0,27881 (DC2 + DC8 – 2 × DC5)
AC11 = 0,16213 ((DC1 – DC3) – (DC7 – DC9))AC02 = 0,27881 (DC4 + DC6 – 2 × DC5)
The scaling of the predicted AC coefficients is consistent with the DCT normalization defined in A.3.3.
176

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ISO/IEC 10918-1 : 1993(E)K.8.2

Quantized AC prediction

The prediction equations can be mapped to a form which uses quantized values of the DC coefficients and which
computes quantized AC coefficients using integer arithmetic. The quantized DC coefficients need to be scaled, however,such that the predicted coefficients have fractional bit precision.
First, the prediction equation coefficients are scaled by 32 and rounded to the nearest integer. Thus,
1,13885 × 32 = 36
0,27881 × 32 = 39
0,16213 × 32 = 35
The multiplicative factors are then scaled by the ratio of the DC and AC quantization factors and rounded appropriately.
The normalization defined for the DCT introduces another factor of 8 in the unquantized DC values. Therefore, in termsof the quantized DC values, the predicted quantized AC coefficients are given by the equations below. Note that if (forexample) the DC values are scaled by a factor of 4, the AC predictions will have 2 fractional bits of precision relative tothe quantized DCT coefficients.
QAC01 = ( (Rd × Q01) + (36 × Q00 × (QDC4 – QDC6)))/(256 × Q01)
QAC10 = ( (Rd × Q10) + (36 × Q00 × (QDC2 – QDC8)))/(256 × Q10)
QAC20 = ( (Rd × Q20) + ( 9 × Q00 × (QDC2 + QDC8 – 2 × QDC5)))/(256 × Q20)
QAC11 = ( (Rd × Q11) + ( 5 × Q00 × ((QDC1 – QDC3) – (QDC7 – QDC9))))/(256 × Q11)
QAC02 = ( (Rd × Q02) + ( 9 × Q00 × (QDC4 + QDC6 – 2 × QDC5)))/(256 × Q02)
where QDCx and QACxy are the quantized and scaled DC and AC coefficient values. The constant Rd is added to get acorrect rounding in the division. Rd is 128 for positive numerators, and –128 for negative numerators.
Predicted values should not override coded values. Therefore, predicted values for coefficients which are already non-zeroshould be set to zero. Predictions should be clamped if they exceed a value which would be quantized to a non-zero value
for the current precision in the successive approximation.

K.9

Modification of dequantization to improve displayed image quality

For a progression where the first stage successive approximation bit, Al, is set to 3, uniform quantization of the DCT gives
the following quantization and dequantization levels for a sequence of successive approximation scans, as shown in
Figure K.8:

Al
3

r¯ t

2

r¯ t

1

r¯ t

0

r¯ t¯ r¯ t¯ r¯ t¯ r¯ t¯ r¯ t¯ r¯ t¯ r¯ t¯ r¯ t _r_t¯ r¯ t¯ r¯ t¯ r¯ t¯ r¯ t¯ r¯ t¯ r¯ t¯ r¯ t¯ r
–8rxx¯ r¯ t

–7

–6

r¯ t

r

x¯ r¯ t

–5

–4

t¯ r

x¯ r¯ t

–3

–2

r

–1

0

t¯ r¯ x

+1

+2

+3

t¯ r

x

t¯ r

t¯ r¯ xt¯ r¯ x

t¯ r

+4

+5

+6

+7

+8

T0812990-93/d118

Quantized DCT coefficient value

F i gur e K .8 – I l l ust r at i on of t w o r econst r uct i on st r at egi es

Figure K.8 [D118] = 6 cm = 234 %The column to the left labelled “Al” gives the bit position specified in the scan header. The quantized DCT coefficientmagnitudes are therefore divided by 2Al during that scan.

CCITT Rec. T.81 (1992 E)

177

ISO/IEC 10918-1 : 1993(E)Referring to the final scan (Al = 0), the points marked with “t” are the threshold values, while the points marked with “r”
are the reconstruction values. The unquantized output is obtained by multiplying the horizontal scale in Figure K.8 by thequantization value.
The quantization interval for a coefficient value of zero is indicated by the depressed interval of the line. As the bit
position Al is increased, a “fat zero” quantization interval develops around the zero DCT coefficient value. In the limit
where the scaling factor is very large, the zero interval is twice as large as the rest of the quantization intervals.
Two different reconstruction strategies are shown. The points marked “r” are the reconstruction obtained using the normal
rounding rules for the DCT for the complete full precision output. This rule seems to give better image quality when highbandwidth displays are used. The points marked “x” are an alternative reconstruction which tends to give better images onlower bandwidth displays. “x” and “r” are the same for slice 0. The system designer must determine which strategy is bestfor the display system being used.

K.10

Example of point transform

The difference between the arithmetic-shift-right by Pt and divide by 2Pt can be seen from the following:
After the level shift the DC has values from +127 to –128. Consider values near zero (after the level shift), and the casewhere Pt = 1:

BeforeBefore

After

After

level shift

point transform

divide by 2

shift-right-arithmetic 1

131

+3

+1

+1

130

+2

+1

+1

129

+1

+0

+0

128

+0

+0

+0

127

–1

+0

–1

126

–2

–1

–1

125

–3

–1

–2

124

–4

–2

–2

123

–5

–2

–3

The key difference is in the truncation of precision. The divide truncates the magnitude; the arithmetic shift truncates the
LSB. With a divide by 2 we would get non-uniform quantization of the DC values; therefore we use the shift-rightarithmetic operation.
For positive values, the divide by 2 and the shift-right-arithmetic by 1 operations are the same. Therefore, the shift-rightarithmetic by 1 operation effectively is a divide by 2 when the point transform is done before the level shift.

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ISO/IEC 10918-1 : 1993(E)Annex L
Patents(This annex does not form an integral part of this Recommendation | International Standard)

L.1

Introductory remarks

The user’s attention is called to the possibility that – for some of the coding processes specified in Annexes F, G, H, and J– compliance with this Specification may require use of an invention covered by patent rights.
By publication of this Specification, no position is taken with respect to the validity of this claim or of any patent rights inconnection therewith. However, for each patent listed in this annex, the patent holder has filed with the Information
Technology Task Force (ITTF) and the Telecommunication Standardization Bureau (TSB) a statement of willingness togrant a license under these rights on reasonable and non-discriminatory terms and conditions to applicants desiring toobtain such a license.
The criteria for including patents in this annex are:a)the patent has been identified by someone who is familiar with the technical fields relevant to thisSpecification, and who believes use of the invention covered by the patent is required for implementationof one or more of the coding processes specified in Annexes F, G, H, or J;b)

the patent-holder has written a letter to the ITTF and TSB, stating willingness to grant a license to an
unlimited number of applicants throughout the world under reasonable terms and conditions that aredemonstrably free of any unfair discrimination.

This list of patents shall be updated, if necessary, upon publication of any revisions to the Recommendation | International
Standard.

L.2

List of patents

The following patents may be required for implementation of any one of the processes specified in Annexes F, G, H, and J
which uses arithmetic coding:US 4,633,490, December 30, 1986, IBM, MITCHELL (J.L.) and GOERTZEL (G.): Symmetrical Adaptive Data
Compression/Decompression System.
US 4,652,856, February 4, 1986, IBM, MOHIUDDIN (K.M.) and RISSANEN (J.J.): A Multiplication-free
Multi-Alphabet Arithmetic Code.
US 4,369,463, January 18, 1983, IBM, ANASTASSIOU (D.) and MITCHELL (J.L.): Grey Scale Image
Compression with Code Words a Function of Image History.
US 4,749,983, June 7, 1988, IBM, LANGDON (G.): Compression of Multilevel Signals.
US 4,935,882, June 19, 1990, IBM, PENNEBAKER (W.B.) and MITCHELL (J.L.): Probability Adaptation
for Arithmetic Coders.
US 4,905,297, February 27, 1990, IBM, LANGDON (G.G.), Jr., MITCHELL (J.L.), PENNEBAKER (W.B.),
and RISSANEN (J.J.): Arithmetic Coding Encoder and Decoder System.
US 4,973,961, November 27, 1990, AT&T, CHAMZAS (C.), DUTTWEILER (D.L.): Method and Apparatus
for Carry-over Control in Arithmetic Entropy Coding.
US 5,025,258, June 18, 1991, AT&T, DUTTWEILER (D.L): Adaptive Probability Estimator for Entropy
Encoding/Decoding.
US 5,099,440, March 24, 1992, IBM, PENNEBAKER (W.B.) and MITCHELL (J.L.): Probability Adaptation
for Arithmetic Coders.
Japanese Patent Application 2-46275, February 26, 1990, MEL ONO (F.), KIMURA (T.), YOSHIDA (M.), andKINO (S.): Coding System.
The following patent may be required for implementation of any one of the hierarchical processes specified in Annex H
when used with a lossless final frame:
US 4,665,436, May 12, 1987, EI OSBORNE (J.A.) and SEIFFERT (C.): Narrow Bandwidth Signal
Transmission.
CCITT Rec. T.81 (1992 E)

179

ISO/IEC 10918-1 : 1993(E)No other patents required for implementation of any of the other processes specified in Annexes F, G, H, or J had been
identified at the time of publication of this Specification.

L.3

Contact addresses for patent information
Director, Telecommunication Standardization Bureau (formerly CCITT)International Telecommunication Union
Place des Nations
CH-1211 Genève 20, Switzerland
Tel. +41 (22) 730 5111
Fax: +41 (22) 730 5853
Information Technology Task Force
International Organization for Standardization
1, rue de Varembé
CH-1211 Genève 20, Switzerland
Tel: +41 (22) 734 0150
Fax: +41 (22) 733 3843
Program Manager, LicensingIntellectual Property and Licensing Services
IBM Corporation
208 Harbor Drive
P.O. Box 10501
Stamford, Connecticut 08904-2501, USA
Tel: +1 (203) 973 7935
Fax: +1 (203) 973 7981 or +1 (203) 973 7982
Mitsubishi Electric Corp.
Intellectual Property License Department
1-2-3 Morunouchi, Chiyoda-ku
Tokyo 100, Japan
Tel: +81 (3) 3218 3465
Fax: +81 (3) 3215 3842
AT&T Intellectual Property Division Manager
Room 3A21
10 Independence Blvd.
Warren, NJ 07059, USA
Tel: +1 (908) 580 5392
Fax: +1 (908) 580 6355
Senior General Manager
Corporate Intellectual Property and Legal Headquarters
Canon Inc.
30-2 Shimomaruko 3-chome
Ohta-ku Tokyo 146 Japan
Tel: +81 (3) 3758 2111
Fax: +81 (3) 3756 0947
Chief Executive Officer
Electronic Imagery, Inc.
1100 Park Central Boulevard South
Suite 3400
Pompano Beach, FL 33064, USA
Tel: +1 (305) 968 7100
Fax: +1 (305) 968 7319

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ISO/IEC 10918-1 : 1993(E)Annex M
Bibliography(This annex does not form an integral part of this Recommendation | International Standard)

M.1

General references

LEGER (A.), OMACHI (T.), and WALLACE (G.K.): JPEG Still Picture Compression Algorithm, Optical Engineering,Vol. 30, No. 7, pp. 947-954, 1991.
RABBANI (M.) and JONES (P.): Digital Image Compression Techniques, Tutorial Texts in Optical Engineering,Vol. TT7, SPIE Press, 1991.
HUDSON (G.), YASUDA (H.) and SEBESTYEN (I.): The International Standardization of a Still Picture Compression
Technique, Proc. of IEEE Global Telecommunications Conference, pp. 1016-1021, 1988.
LEGER (A.), MITCHELL (J.) and YAMAZAKI (Y.): Still Picture Compression Algorithm Evaluated for International
Standardization, Proc. of the IEEE Global Telecommunications Conference, pp. 1028-1032, 1988.
WALLACE (G.), VIVIAN (R.) and POULSEN (H.): Subjective Testing Results for Still Picture Compression Algorithms
for International Standardization, Proc. of the IEEE Global Telecommunications Conference, pp. 1022-1027, 1988.
MITCHELL (J.L.) and PENNEBAKER (W.B.): Evolving JPEG Colour Data Compression Standard, Standards forElectronic Imaging Systems, M. Nier, M.E. Courtot, Editors, SPIE, Vol. CR37, pp. 68-97, 1991.
WALLACE (G.K.): The JPEG Still Picture Compression Standard, Communications of the ACM, Vol. 34, No. 4, pp. 3144, 1991.
NETRAVALI (A.N.) and HASKELL (B.G.): Digital Pictures: Representation and Compression, Plenum
New York 1988.

Press,PENNEBAKER (W.B.) and MITCHELL (J.L.): JPEG: Still Image Data Compression Standard, Van Nostrand
Reinhold, New York 1993.

M.2

DCT references

CHEN (W.), SMITH (C.H.) and FRALICK (S.C.): A Fast Computational Algorithm for the Discrete Cosine Transform,
IEEE Trans. on Communications, Vol. COM-25, pp. 1004-1009, 1977.
AHMED (N.), NATARAJAN (T.) and RAO (K.R.): Discrete Cosine Transform, IEEE Trans. on Computers, Vol. C-23,
pp. 90-93, 1974.
NARASINHA (N.J.) and PETERSON (A.M.): On the Computation of the Discrete Cosine Transform, IEEE Trans. on
Communications, Vol. COM-26, No. 6, pp. 966-968, 1978.
DUHAMEL (P.) and GUILLEMOT (C.): Polynomial Transform Computation of the 2-D DCT, Proc. IEEE ICASSP-90,
pp. 1515-1518, Albuquerque, New Mexico 1990.
FEIG (E.): A Fast Scaled DCT Algorithm, in Image Processing Algorithms and Techniques, Proc. SPIE, Vol. 1244, K.S.
Pennington and R. J. Moorhead II, Editors, pp. 2-13, Santa Clara, California, 1990.
HOU (H.S.): A Fast Recursive Algorithm for Computing the Discrete Cosine Transform, IEEE Trans. Acoust. Speech andSignal Processing, Vol. ASSP-35, No. 10, pp. 1455-1461.
LEE (B.G.): A New Algorithm to Compute the Discrete Cosine Transform, IEEE Trans. on Acoust., Speech and Signal
Processing, Vol. ASSP-32, No. 6, pp. 1243-1245, 1984.
LINZER (E.N.) and FEIG (E.): New DCT and Scaled DCT Algorithms for Fused Multiply/Add Architectures, Proc.
IEEE ICASSP-91, pp. 2201-2204, Toronto, Canada, 1991.
VETTERLI (M.) and NUSSBAUMER (H.J.): Simple FFT and DCT Algorithms with Reduced Number of Operations,
Signal Processing, 1984.

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ISO/IEC 10918-1 : 1993(E)
VETTERLI (M.): Fast 2-D Discrete Cosine Transform, Proc. IEEE ICASSP-85, pp. 1538-1541, Tampa, Florida, 1985.
ARAI (Y.), AGUI (T.), and NAKAJIMA (M.): A Fast DCT-SQ Scheme for Images, Trans. of IEICE, Vol. E.71, No. 11,
pp. 1095-1097, 1988.
SUEHIRO (N.) and HATORI (M.): Fast Algorithms for the DFT and other Sinusoidal Transforms, IEEE Trans. on
Acoust., Speech and Signal Processing, Vol ASSP-34, No. 3, pp. 642-644, 1986.

M.3

Quantization and human visual model references

CHEN (W.H.) and PRATT (W.K.): Scene adaptive coder, IEEE Trans. on Communications, Vol. COM-32, pp. 225-232,
1984.
GRANRATH (D.J.): The role of human visual models in image processing, Proceedings of the IEEE, Vol. 67,
pp. 552-561, 1981.
LOHSCHELLER (H.): Vision adapted progressive image transmission, Proceedings of EUSIPCO, Vol. 83, pp. 191-194,
1983.
LOHSCHELLER (H.) and FRANKE (U.): Colour picture coding – Algorithm optimization and technical realization,
Frequenze, Vol. 41, pp. 291-299, 1987.
LOHSCHELLER (H.): A subjectively adapted image communication system, IEEE Trans. on Communications,Vol. COM-32, pp. 1316-1322, 1984.
PETERSON (H.A.) et al: Quantization of colour image components in the DCT domain, SPIE/IS&T 1991 Symposium on
Electronic Imaging Science and Technology, 1991.

M.4

Arithmetic coding references

LANGDON (G.): An Introduction to Arithmetic Coding, IBM J. Res. Develop., Vol. 28, pp. 135-149, 1984.
PENNEBAKER (W.B.), MITCHELL (J.L.), LANGDON (G.) Jr., and ARPS (R.B.): An Overview of the Basic Principlesof the Q-Coder Binary Arithmetic Coder, IBM J. Res. Develop., Vol. 32, No. 6, pp. 717-726, 1988.
MITCHELL (J.L.) and PENNEBAKER (W.B.): Optimal Hardware and Software Arithmetic Coding Procedures for the
Q-Coder Binary Arithmetic Coder, IBM J. Res. Develop., Vol. 32, No. 6, pp. 727-736, 1988.
PENNEBAKER (W.B.) and MITCHELL (J.L.): Probability Estimation for the Q-Coder, IBM J. Res. Develop., Vol. 32,
No. 6, pp. 737-752, 1988.
MITCHELL (J.L.) and PENNEBAKER (W.B.): Software Implementations of the Q-Coder, IBM J. Res. Develop.,Vol. 32, No. 6, pp. 753-774, 1988.
ARPS (R.B.), TRUONG (T.K.), LU (D.J.), PASCO (R.C.) and FRIEDMAN (T.D.): A Multi-Purpose VLSI Chip for
Adaptive Data Compression of Bilevel Images, IBM J. Res. Develop., Vol. 32, No. 6, pp. 775-795, 1988.
ONO (F.), YOSHIDA (M.), KIMURA (T.) and KINO (S.): Subtraction-type Arithmetic Coding with
Conditional Exchange, Annual Spring Conference of IECED, Japan, D-288, 1990.

MPS/LPSDUTTWEILER (D.) and CHAMZAS (C.): Probability Estimation in Arithmetic and Adaptive-Huffman Entropy Coders,
submitted to IEEE Trans. on Image Processing.
JONES (C.B.): An Efficient Coding System for Long Source Sequences, IEEE Trans. Inf. Theory,Vol. IT-27,
pp. 280-291, 1981.
LANGDON (G.): Method for Carry-over Control in a Fifo Arithmetic Code String, IBM Technical Disclosure Bulletin,Vol. 23, No.1, pp. 310-312, 1980.

M.5

Huffman coding references

HUFFMAN (D.A.): A Method for the Construction of Minimum Redundancy codes, Proc. IRE, Vol. 40, pp. 1098-1101,
1952.

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