NISTIR 7939

Effects of Decomposition Levels and Quality Layers

with JPEG 2000 Compression of 1000 ppi 

Fingerprint Images

John M. Libert

Shahram Orandi

Michael D. Garris

John D. Grantham
NISTIR 7939

Effects of Decomposition Levels and Quality Layers 

with JPEG 2000 Compression of

1000 ppi Fingerprint Images

John M. Libert

Shahram Orandi

Michael D. Garris

Information Access Division

Information Technology Laboratory

John D. Grantham

Systems Plus, Inc.

Rockville, MD

August 2013

U.S. Department of Commerce 

Penny Pritzker, Secretary

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director 
ii

Table of Contents

1. INTRODUCTION.........................................................................................................................................................1

2. INVESTIGATIVE GOALS......................................................................................................................................... 2

3. METHOD ..................................................................................................................................................................... 2

3.1. IMAGE DATA.............................................................................................................................................................. 2

3.2. IMAGE COMPRESSION............................................................................................................................................ 3

3.2.1. JPEG 2000 Image Compression – Part One ................................................................................................... 3

3.2.2. JPEG 2000 Image Compression – Part Two .................................................................................................. 3

3.3. FIDELITY METRICS................................................................................................................................................ 4

3.3.1. Count of Changed Pixels................................................................................................................................ 4

3.3.2. Image Mean Squared Error ............................................................................................................................ 4

3.3.3. Image Structural Metrics................................................................................................................................ 5

3.3.4. Latent Print Examiner Inspection...................................................................................................................8

3.4. HYPOTHESIS TESTING .......................................................................................................................................... 11

3.4.1. Friedman’s Procedure.................................................................................................................................... 11

3.4.2. Post Hoc Pairwise Multiple Comparisons Procedure....................................................................................12

3.4.3. Wilcoxon Signed Rank Test..........................................................................................................................13

3.5. UNCERTAINTY OF SAMPLE STATISTICS ................................................................................................................13

4. RESULTS – PART ONE: DECOMPOSITION LEVELS......................................................................................14

4.1. EXAMINER RATINGS..................................................................................................................................................14

4.2. COMPUTATIONAL IMAGE FIDELITY MEASURES .....................................................................................................14

4.2.1. Counts of Changed Pixels .............................................................................................................................14

4.2.2. Image Mean Squared Error .......................................................................................................................... 16

4.2.3. Structural Analysis Based Measures .............................................................................................................17

4.2.4. Conclusions: DWT Decomposition Levels ...................................................................................................21

5. RESULTS - PART TWO: QUALITY LAYERS.................................................................................................... 22

5.1. COMPUTATIONAL IMAGE FIDELITY MEASURES ........................................................................................................ 22

5.1.1. Counts of Changed Pixels ............................................................................................................................ 22

5.1.2. Image Mean Squared Error .......................................................................................................................... 24

5.1.3. Structural Analysis Based Measures ............................................................................................................ 25

5.2. COMPARISON OF RELATIVE ERROR: DECOMPOSITION LEVELS VS. QUALITY LAYERS ............................................ 29

6. CONCLUSIONS ........................................................................................................................................................ 30

6.1. WAVELET DECOMPOSITION LEVELS............................................................................................................. 30

6.1.1. To what extent does the number of decomposition levels affect computational measures of image fidelity 

with respect to source, non-compressed images? ......................................................................................................... 30

6.1.2. Are potential fidelity differences detected by trained latent fingerprint examiners? ....................................30

6.2. EFFECT OF MULTIPLE QUALITY LAYERS................................................................................................ 30

6.2.1. What is the effect on image fidelity of using more than a single quality layer? ........................................... 30

6.2.2. What is the effect on image fidelity of increasing numbers of quality layers? ............................................. 30

7. REFERENCES............................................................................................................................................................ 31
iii

List of Tables

Table 1 - Compression Profile – Part One ............................................................................................................. 3

Table 2 - Compression Profile – Part Two............................................................................................................. 3

Table 3 - Compression Ratio (Quality Layer) Specifications................................................................................4

Table 4 - Observation Codes for Compression Degradation Observation .............................................................9

Table 5 - Block Design Example ..........................................................................................................................11

Table 6 - Friedman’s Test With Post Hoc Analysis For Counts of Changed Pixels , SD27 (alpha = 0.05, 

n=2484, critical difference = 0.1513)..........................................................................................................15

Table 7 - Friedman’s Test With Post Hoc Analysis For Image MSE, FIXT Sample (alpha = 0.05, n=100, 

critical difference = 0.7540)....................................................................................................................... 16

Table 8 - Friedman’s Test With Post Hoc Analysis For Image MSE, SD27 (alpha = 0.05, n=2484, critical 

difference = 0.1513)................................................................................................................................... 16

Table 9 - Friedman’s Test with Post Hoc Multiple Comparisons – SIVV RMSE – FIXT (alpha = 0.05, n=100, 

critical difference = 0.7540)....................................................................................................................... 18

Table 10 - Friedman’s Test with Post Hoc Multiple Comparisons – SIVV RMSE – SD27, (alpha = 0.05, 

n=2484, critical difference = 0.1513)......................................................................................................... 18

Table 11 - Friedman’s Test with Post Hoc Multiple Comparisons – MSSIM ́ – FIXT Sample, (alpha = 0.05, 

n=100, critical difference = 0.7540)...........................................................................................................20

Table 12 - Friedman’s Test with Post Hoc Multiple Comparisons – MSSIM ́ – SD27, , (alpha = 0.05, n=2484, 

critical difference = 0.1513).......................................................................................................................20

Table 13 - Friedman’s Test with Post Hoc Multiple Comparisons – Counts of changed Pixels, FIXT Sample 

(alpha = 0.05, n=100, critical difference = 1.2013).................................................................................... 22

Table 14 - Friedman’s Test with Post Hoc Multiple Comparisons – Counts of changed Pixels, SD27 (alpha = 

0.05, n=2484, critical difference = 0.2410)................................................................................................ 22

Table 15 - Friedman’s Test with Post Hoc Multiple Comparisons – Image MSE, FIXT Sample (alpha = 0.05, 

n=100, critical difference = 1.2013)...........................................................................................................24

Table 16 - Friedman’s Test with Post Hoc Multiple Comparisons – Image MSE, SD27 (alpha = 0.05, n=2484, 

n=2484, critical difference = 0.2410).........................................................................................................24

Table 17 - Friedman’s Test with Post Hoc Multiple Comparisons – SIVV RMSE, FIXT Sample (alpha = 0.05, 

n=100, critical difference = 1.2013)...........................................................................................................26

Table 18 - Friedman’s Test with Post Hoc Multiple Comparisons – SIVV RMSE, SD27 (alpha = 0.05, n=2484, 

n=2484, critical difference = 0.2410).........................................................................................................26

Table 19 Friedman’s Test with Post Hoc Multiple Comparisons – MSSIM ́, FIXT Sample (alpha = 0.05, n=100, 

critical difference = 1.2013)....................................................................................................................... 27

Table 20 - Friedman’s Test with Post Hoc Multiple Comparisons – MSSIM ́, SD27 (alpha = 0.05, n=2484, 

n=2484, critical difference = 0.2410).........................................................................................................28

Table 21 - Wilcoxon Tests of Extreme Error of Decomposition Levels vs. that for Quality Layers (alpha = 0.05, 

n=2484) ......................................................................................................................................................29
iv

List of Figures

Figure 1 - NIST SIVV metric applied to non-compressed original image and to its corresponding decoded JPEG 

2000 compressed image. ..............................................................................................................................5

Figure 2 - Split-Screen Presentation of Image Pairs............................................................................................ 10

Figure 3 - Median number of changed pixel values with 95 % confidence intervals for each of six 

decomposition level specifications used in JPEG 2000 compression of SD27 1000 ppi source images. 

(Note Median Counts values on the axis are times 104

.).............................................................................15

Figure 4 - Median of image MSE with 95 % confidence intervals for each of six decomposition level 

specifications used in JPEG 2000 compression of SD27 1000 ppi source images. (CI = confidence 

interval) .......................................................................................................................................................17

Figure 5 - Median SIVV RMSE with 95 % confidence intervals for each of six decomposition level 

specifications used in JPEG 2000 compression of SD27 1000 ppi source images. (Note that median 

values on ordinate are multiplied by 10-3

.)................................................................................................. 19

Figure 6 - Median MSSIM ́ with 95 % confidence intervals for each of six decomposition level specifications 

used in JPEG 2000 compression of SD27 1000 ppi source images. ...........................................................21

Figure 7 - Median of counts of changed pixels with 95 % confidence intervals for each of nine quality layer 

specifications used in JPEG 2000 compression of SD27 1000 ppi source images..................................... 23

Figure 8 - Median of image MSE with 95 % confidence intervals for each of nine quality layer specifications 

used in JPEG 2000 compression of SD27 1000 ppi source images. .......................................................... 25

Figure 9 - Median of image SIVV RMSE with 95 % confidence intervals for each of nine quality layer 

specifications used in JPEG 2000 compression of SD27 1000 ppi source images..................................... 27

Figure 10 - Median of MSSIM ́ with 95% confidence intervals for each of nine quality layer specifications used 

in JPEG 2000 compression of SD27 1000 ppi source images....................................................................28
v

EXECUTIVE SUMMARY

The criminal justice communities throughout the world exchange fingerprint imagery data primarily in 8-

bit gray-scale and at 500 pixels per inch1 (ppi) or 19.7 pixels per millimeter (ppmm). The Wavelet Scalar 

Quantization (WSQ) fingerprint image compression algorithm is currently the standard algorithm for the 

compression of 500 ppi fingerprint imagery. WSQ is a “lossy” compression algorithm. Lossy compression 

algorithms employ data encoding methods which discard (lose) some of the information through the 

encoding process in order to achieve more aggressive reduction in the size of the data being compressed. 

While previous research [29] has shown trained fingerprint examiners tolerant to even extreme loss of 

image fidelity in performing identification tasks, it remains desirable to ensure that loss of fidelity is kept to 

a minimum with respect to current or anticipated extensions to identification applications. The WSQ 

algorithm allows for users of the algorithm to specify how much compression is to be applied to the 

fingerprint image at the cost of increasingly greater loss in fingerprint image fidelity as the effective 

compression ratio is increased. The WSQ Gray-Scale Fingerprint Image Compression Specification [1]

provides guidance based on an International Association for Identification (IAI) study [2] to determine the 

acceptable amount of fidelity loss due to compression in order for a WSQ encoder and decoder to meet 

FBI certifications. These certifications are designed to ensure adherence to the WSQ specification and 

thereby to ensure fidelity and admissibility in courts of law for images that have been processed by such 

encoders and decoders. 

NIST is in the process of creating a normative guidance on utilizing JPEG 2000 [4] for the compression of 

fingerprint imagery at 1000 ppi (39.4 ppmm). The normative guidance will provide a comprehensive 

compression profile for 1000 ppi fingerprint imagery using JPEG 2000, particularly in its specification of 

software parameters for control and structure of the JPEG 2000 code stream. This study explores and 

validates two of the recommended parameters for control of the JPEG 2000 code stream. Specifically, it

examines the effects of the number of discrete wavelet transform (DWT) decompositions and the use of 

multiple quality layers (compression rates) used in the encoding.

While investigating each of the two compression parameters separately in this study, fidelity losses are 

measured via ratings by certified latent fingerprint examiners and by a suite of computational fidelity 

metrics. Fidelity losses from either decomposition level or quality layer configuration are found to be 

statistically undetectable among ratings of trained fingerprint examiners. More sensitive tests, 

computational fidelity metrics, indicated minimum losses with either five or six Discrete Wavelet 

Transform (DWT) decomposition levels over the six tested in the range from three to eight levels. Fidelity 

loss due to encoding at multiple quality layers was statistically significant over that of a single compression 

rate, but such losses were determined to be below the threshold of visibility for trained fingerprint 

examiners. 

 

1Resolution values for fingerprint imagery are specified in pixels per inch (ppi) throughout this document. This 

is based on widely used specification guidelines for such imagery and is accepted as common nomenclature 

within the industry. SI units for these will be presented only once.
vi

Abstract

As part of NIST’s research efforts to support development of the FBI Next Generation Identification (NGI) 

systems, this study evaluates effects on image fidelity of wavelet transform decomposition and quality 

layer options for JPEG 2000 compression of 1000 ppi fingerprint images. First, a suite of 1000 ppi 

fingerprints are subjected to encoding specifying from three to eight levels of DWT decomposition. 

Decoded images are compared to non-compressed source images and fidelity loss is evaluated by certified 

latent fingerprint examiners as well as by several automated computational fidelity metrics. Fidelity losses 

among the six decomposition level options result in no statistically significant differences among 

assessments of image degradation by trained fingerprint examiners. Computational metrics find 

statistically significant fidelity differences, with lowest error for five and six DWT decompositions. In a 

second experiment JPEG 2000 encoding using version 1.4 of the openJPEG2000 CODEC is applied using 

from one to nine quality layers. Computational fidelity metrics find statistically significant increase in error 

with the addition of even a single additional compression rate beyond using only a single target 

compression ratio of 10:1. Moreover, fidelity loss increases with the addition of each additional quality 

layer. Hence, while the provision of JPEG 2000 for multiple compression rates within a single code stream

adds to the flexibility of these CODECs, the additional flexibility may not be without measurable loss in 

fidelity. However, maximum error rates measured among the various quality layer configurations are 

found to be below that detectable by certified fingerprint examiners. Hence, use of quality layers for JPEG 

2000 compression of 1000 ppi fingerprints should be limited in number and chosen for anticipated 

applications. 
1

1. Introduction

NIST is involved in developing a JPEG 2000 profile and recommendations for the compression of 1000 ppi 

fingerprint images. In support of the FBI’s Next Generation Identification (NGI) program a series of studies 

have been completed toward answering questions regarding compression rate for the 1000 ppi images 

and optimum method by which to downsample these images to maintain compatibility with legacy 500 ppi 

systems. 

JPEG 2000 [4][1][5][6][7] CODECs provide for the encoding of an image at multiple spatial resolution levels 

corresponding to the sub-bands of the discrete wavelet transform (DWT) applied to the image and 

encoding the image at multiple bit rates, i.e. quality layers, in the same code stream. Both of these 

provisions provide for scalability of both resolution and image quality within the same compressed code 

stream. 

Details of the manner in which JPEG 2000 provides for scalability are elaborated in [8]. Resolution 

scalability is provided for by the multi-level dyadic (pyramidal) wavelet transform. The (9,7) floating point 

wavelet [9] may be used for lossy compression or the (5,3) integer wavelet [10] for lossless compression. 

In either case, a single code stream compressed using an L-level wavelet transform enables reconstruction 

of images at L + 1 spatial resolutions, each half the dimensions of the preceding. For example, an image 

initially sampled at 1000 ppi may be compressed at 10:1 using six decomposition levels specified to the 

CODEC. Upon decompression the image may be reconstructed at the original spatial resolution of 1000 

ppi, but the same code stream can also yield an images at 500 ppi, 250 ppi, 125 ppi, approximately 62 ppi, 

and approximately 31 ppi.

Quality or bitrate scalability is available as an option at encoding. Nominally the JPEG 2000 encoder 

generates a code stream enabling reconstruction of the input image at some target bit rate or 

compression level. However, JPEG 2000 CODECs also provide for optional input of a list of bit rates to 

enable reconstruction from a single code stream images at any of the bit rates contained in the list 

provided to the encoder. This dimension of scalability together with resolution scalability enables the same 

code stream to support multiple applications and platforms of varying capability to extract image 

information at the most appropriate spatial scale and quality.
2

2. Investigative Goals

This study attempts to explore and validate two of the recommended parameters for control of the JPEG 

2000 code stream. Specifically, it examines the effects of the number of discrete wavelet transform (DWT)

decompositions and the use of multiple quality layers (compression rates) used in the encoding with the 

following specific investigative goals:

1a. Expert Examiner Subjective Assessment of Various Wavelet Decomposition Level Counts: 

Investigate expert examiner opinion to gauge perceived degradation of 1000 ppi fingerprint 

images as a result of employing different numbers of wavelet decomposition levels during 

compression.

1b. Signal Analysis and Assessment of Various Wavelet Decomposition Level Counts: Investigate the 

effects of employing different numbers of wavelet decomposition levels in compression of 1000 

ppi fingerprint images via various signal analysis methods.

2a. Expert Examiner Subjective Assessment of Employing Multiple Quality Layers: Investigate 

expert examiner opinion to gauge perceived degradation of 1000 ppi fingerprint images as a 

result of employing different numbers of wavelet decomposition levels during compression.

2b. Signal Analysis and Assessment of Employing Multiple Quality Layers: Investigate the effects of 

employing multiple quality layers in compression of 1000 ppi fingerprint images via various signal 

analysis methods.

3. Method

The study is divided into two parts. Part One examines the impact on image fidelity of the selection of 

various numbers of decomposition levels used in encoding the image. Part Two evaluates the effect on 

image fidelity of compressing images when specifying more than a single quality layer (compression rates) 

to be included in the codestream.

3.1. Image Data 

Two datasets were used for the investigations. One dataset consisted of fingerprint impressions 1 to 12 of 

the NIST Special Database SD27 [11]. This subset of the SD27 dataset consisted of 2484 images scanned 

from standard FBI fingerprint 10-print cards at 1000 ppi. These images consisted of 12 fingerprint 

impressions for each of 207 subjects. Prints 1 to 10 are rolled impressions of right and left hands. Prints 11 

and 12 are flat impressions of the right and left thumbs.

For visual rating by trained fingerprint examiners used in part of the study as will be detailed below, a 

random sample of 100 impressions was selected from the larger SD27 database including only rolled 

impressions, i.e. from among finger positions 1 to 10. This dataset is referred to as the “FIXT dataset” or 

“FIXT sample,” where FIXT refers to the Fingerprint Image eXamination Tool used in several other NIST 

studies [29][30] involving fingerprint comparisons by expert fingerprint examiners.

Compression via version 1.4 of the openJPEG2000 CODEC [12][13] was applied to source images of both 

the SD27 subset and FIXT sample fingerprint datasets using compression profiles to be detailed in sections 

3.2.1 and 3.2.2 for decomposition levels (Part One) and quality layers (Part Two) of the study. 

Computational fidelity metrics (see sections 3.3.1 - 3.3.3) were applied to all processed images for Parts 
3

One and Two of the study. Part One, decomposition level experiments, included comparison of source to 

processed images by expert fingerprint examiners as described in section 3.3.4.

3.2. Image Compression

3.2.1. JPEG 2000 Image Compression – Part One

All source images were compressed using version 1.4 of the openJPEG2000 [12] CODEC modified by NIST 

and included in its NIST Biometric Image Software (NBIS) [13]. The target compression rate for all images 

was 10:1 the profile shown in Table 1. Each source image is compressed using each of the six 

decomposition levels shown in Table 1.

Table 1 - Compression Profile – Part One 

Parameter Value

Progression Order RPCL

Code Block Size 64 x 64

Transformation Filter 9, 7 Irreversible

Subsampling Factors 1, 1 (no subsampling)

Tile Size Image width, image height (single tile for image)

Quality Layers {10,15,24,34,58,86,144,214}

Decomposition Levels Each of the set {3,4,5,6,7,8} DWT levels

3.2.2. JPEG 2000 Image Compression – Part Two

Images were encoded using the openJPEG2000 encoder [12] using the profile summarized in Table 2. Only 

a single decomposition level was used for this part of the study and target compression ratio was 10:1 as 

with Part One. However, each source image was compressed using each of the nine rate specifications 

shown in Table 3.

Table 2 - Compression Profile – Part Two

Parameter Value

Progression Order RPCL

Code Block Size 64 x 64

Transformation Filter 9, 7 Irreversible

Subsampling Factors 1, 1 (no subsampling)

Tile Size Image width, image height (single tile for image)

Quality Layers 1 to 9 layers as shown in Table 3

Decomposition Levels 6
4

Table 3 - Compression Ratio (Quality Layer) Specifications

Layers Compression Ratios (X:1) Approximate Bit Rate

9 10,15,24,34,58,86,144,214,324 0.8,0.53,0.33,0.245,0.14,0.09,0.06,0.04,0.03

8 10,15,24,34,58,86,144,214 0.8,0.53,0.33,0.245,0.14,0.09,0.06,0.04

7 10,15,24,34,58,86,144 0.8,0.53,0.33,0.245,0.14,0.09,0.06

6 10,15,24,34,58,86 0.8,0.53,0.33,0.245,0.14,0.09

5 10,15,24,34,58 0.8,0.53,0.33,0.245,0.14

4 10,15,24,34 0.8,0.53,0.33,0.245,

3 10,15,24 0.8,0.53,0.33

2 10,15 0.8,0.53

1 10 0.8

3.3. Fidelity Metrics

In all cases, image fidelity is measured as a comparison between the non-compressed source image and a 

decoded compressed code stream. Computational fidelity metrics were applied to the 2,484 images of the 

SD27 dataset paired with each of six compressed versions encoded using decomposition levels as 

described above. The metrics also were applied to the subset of the images subjected to inspection by

trained fingerprint examiners.

3.3.1. Count of Changed Pixels

This metric was slightly different between Parts One and Two of the study.

Counts of Changed Pixels – Part One

Given a source image X and a decoded compressed image Yd

, d = one of the decomposition levels {3, 4, 5, 

6, 7, 8} count the number of pixels that differ between the two images by one or more gray levels 

excluding those that have similarly changed for all six decomposition level specifications.

Counts of Changed Pixels – Part Two

As in Part One of the study we count the number of pixels found to have changed from the original 

(source image) value by one or more gray levels. In analysis of the effect of quality layers, we do no 

additional filtering of the total count. That is, we do not exclude pixels observed to have changed under all 

conditions. Hence, given a source image, X, and a reconstructed image Yd

, d = 1...9 designating one of the 

quality level specifications, count the number of pixels that differ between the two images by one or 

more gray levels.

3.3.2. Image Mean Squared Error

Given a source image, X, and a processed image, Yd

, a commonly used measure of image fidelity, the mean 

squared error is defined as

( )

2

, ,

1 1

N N d

ij ij

d i j MSE

NM

= =

−

=

∑∑ X Y

(1)
5

where d is the nominal designation of one of k processes or treatments (d= 1...k), i, j are indices to image 

pixels, and N and M are numbers of image rows and columns, respectively. Note that the source image and 

processed image must be equal in dimensions in order to apply this metric.

3.3.3. Image Structural Metrics

NIST Spectral Image Validation/Verification (SIVV) Measures

Developed initially as a method to screen fingerprint databases for non-fingerprint images, segmentation 

errors, or mislabeled sample rates, the Spectral Image Validation Verification (SIVV) metric [25] provides a 

comparatively straightforward method by which to assess the frequency structure of an image. Pairwise 

display of the SIVV signals of non-compressed and compressed images enables summary visualization of 

the effects of compression across the composition frequency spectrum of the image. As a 1-dimensional 

representation of a 2-dimensional Fourier spectrum, the SIVV metric applied to a fingerprint image exhibits 

a peak corresponding to the frequency of the ridge spacing. Also, as shown in Figure 1, comparison of SIVV 

signals of non-compressed and compressed images shows the loss or gain of power over various 

frequencies. 

The SIVV signals denoted as s1 and s2 are respectively vectors of SIVV signal values for images having 

undergone different processing methods under study. The frequency samples, f, in units of cycles per pixel 

correspond to image pixels or Fourier transform frequencies along the length of one half of the minimum 

dimension of the 2D Fourier transform of the image under examination. Frequency along this dimension is 

scaled to the interval [0, 0.5] cycles/pixel. Note that the power value at f = 0 is the “direct current” (DC) 

term, corresponding to the average intensity of the image and is used to normalize the power spectrum.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.4

0.5

0.6

0.7

0.8

0.9

1

 Normalized Log Power (db)

 Frequency (cycles/pixel)

Source Image

Compressed Image

Figure 1 - NIST SIVV metric applied to non-compressed original image and 

to its corresponding decoded JPEG 2000 compressed image.
6

RMS Error of SIVV Signals

Either differences or ratios of SIVV signals can provide quantitative measures for the comparison of 

compression methods. For the present study, we examine image differences between pairs of images, I1

and I2, with respect to the Root Mean Squared Error (RMSE) between their two SIVV signals, s1 and s2, over 

the entire frequency range 0 - 0.5 cycles/pixel.

2

, , 1

( ) ( )

n

i i i RMSE n

= − = ∑ 1 2

1 2

s s

s ,s (2)

where 1 2 n = = s s (i.e., the lengths of the signal vectors). 

The RMSE metric defined above can provide a measure of the overall difference between the SIVV spectra 

of the non-compressed source image and that compressed at one of the decomposition levels. In addition 

to global effects, the RMSE may be evaluated over smaller frequency intervals enabling the comparison of 

effects over frequency bands that may have particular relevance to fingerprint image quality or matching, 

as well as quantifying and isolating changes confined to bands that specifically impact either the machine 

matcher or expert examiners.

Mean Structural Similarity Index (MSSIM)

The Structural Similarity Index (SSIM) , detailed in [22] provides a means by which to compare two images, 

X and Y, with respect to structural features of the image without the effects of global changes in 

luminance or contrast. The SSIM is computed for each of some number of M rectangular subsamples of 

two images being compared. The SSIM combines measures of local luminance, contrast, and structure. 

Given corresponding patches or blocks, x and y, extracted from two images to be compared, compute the 

mean of x and mean of y as

1

1

1

1

N

i

i

N

i

i

x N

y N

μ

μ

=

=

=

=

∑

∑

x

y

(3)

Compute the standard deviation of each of the corresponding blocks, x and y, as

( )

( )

1

2 2

1

1

2 2

1

1

1

1

1

N

i

i

N

i

i

x

N

y N

σ μ

σ μ

=

=

  = −     −

  = −     −

∑

∑

x x

y y

(4)

Compute the variance between the corresponding image blocks as
7

( )( ) 1

1

1

N

i i

i

x y N σ μμ =

= −− − xy ∑ x y (5)

The SSIM for each block of the two images is defined as

( )( )

( )( )

1 2

22 22

1 2

2 2

( ) . C CSSIM

C C

μμ σ

μμ σσ

+ + = ++ ++

x y xy

xy xy

x,y (6)

where C1 and C2 are included to handle small values of the image means or standard deviations (which 

might otherwise result in divide by zero problems) and are computed as 

2

11 1

2

22 2

( ) , 0.01

( ) , 0.03

C KL K

C KL K

= =

= = (7)

and L corresponds to the dynamic range of pixel values, which for the 8 bit image L=255. The values for K1

and K2 may be adjusted, but the values given in (7) were used in the present investigation. Further 

discussion of the constants, C1 and C2 may be found in [22].

Images are processed using overlapping sampling windows. For the present investigation the images were 

processed using overlapping 11 x 11 pixel blocks, each block centered at a pixel location2. It may be 

appreciated that processing a pair of images in this fashion results in a mapping of the SSIM corresponding 

roughly to the original image dimensions minus some edge pixels where the sampling window extends 

beyond the edge of the images. In order to avoid “blocky” artifacts in the SSIM map, the authors of [22]

use an 11 x 11 circularly symmetric Gaussian weighting function, { | 1, 2,..., } w = = wi N i ,N = 121, with 

standard deviation of 1.5 pixels and normalized to unit sum. Thus, the estimates of local statistics become

1

1

N

i i

i

N

i i

i

w x

w y

μ

μ

=

=

=

=

∑

∑

x

y

(8)

( )

( )

1

2 2

1

1

2 2

1

N

ii x

i

N

ii y

i

w x

w y

σ μ

σ μ

=

=

  = −    

  = −    

∑

∑

x

y

(9)

 

2 In our application, SSIM outputs are smaller than image inputs, trimmed to dimensions allowing filtering 

without extending edges of input images.
8

( )( ) 1

N

ii x i y

i

σ μμ wx y

=

xy = −− ∑ (10)

If, as in the present investigation, one requires a single overall measure of fidelity for the entire image pair, 

the mean SSIM index (MSSIM) is computed as

( ) 1

1 ( ) ,

M

j j

j

MSSIM SSIM

M =

X, Y = ∑ x y (11)

where M is the number of samples in the SSIM map.

All other computational fidelity metrics detailed in this section indicate fidelity loss increasing from zero. 

The MSSIM shows increasing fidelity loss with decrease of the measure from 1.0. Hence, in order to 

maintain consistency in the statistical analysis we define a measure MSSIM ́ as

MSSIM ′( )1 ( ) X,Y = − MSSIM X,Y (12)

A MATLAB [23] implementation for the MSSIM is given in [24].

3.3.4. Latent Print Examiner Inspection

Direct visual examination and assessment of compression outputs was only performed for Part One of the 

study. For Part Two we evaluate effects of quality layers indirectly via comparison of maximum fidelity 

losses observed due to variation in wavelet decomposition levels with those due to inclusion of multiple 

quality layers.

Examiner Assessment – Part One

Each decoded image, compressed using one of the six decomposition specifications, was paired with its 

non-compressed source and presented to exactly three examiners. Each examiner was first asked to 

determine if the image pair being displayed constitutes a matched pair, i.e., if the two fingerprints could 

have come from the same finger of the same individual. Their responses could be one of three choices:

• The presented image pair is from the same individual ([positive] Identification decision);

• The presented image pair does not appear to be from the same individual (Non-Identification 

decision);

• Determination of identity cannot be made (Inconclusive).

In contrast to the application of this procedure in [29], the identification exercise was included in the 

present experiment mainly for control purposes, as all image pairs were either compressed or noncompressed versions of each source image and no non-mates were included in the pairings presented to 

the examiners.

Subsequent to their identity determination for the pair of images each examiner then evaluated the image 

pair on fidelity loss of one of the pair relative to the other. To aid in analysis and quantification of fidelity 

loss, the examiner’s evaluation was collected using a Likert-type response scale [26]. The choices that the 

examiners were allowed to make are provided in Table 4 below. Observation codes are ordered in 

ascending order indicating a progressively greater amount of degradation from 1 to 4. 
9

Table 4 - Observation Codes for Compression Degradation Observation

Observation Numeric 

Code

Description

1 No apparent image quality degradation and the quality of Level 23 and Level 3 

detail in either image should not cause any difficulty in reaching a conclusive 

decision of identification or exclusion.

2 A noticeable degradation in the quality of Level 2 or Level 3 detail in either 

image, but not enough to have a negative impact on reaching a conclusive 

decision of identification or exclusion, though the amount of time to reach a 

decision may increase.

3 Level 3 detail quality diminished in either image to the extent that a Level 3 

identification is questionable or not possible, and/or is significantly more 

difficult.

4 Level 2 detail quality diminished in either image to the extent that a Level 2 

identification becomes questionable or not possible, and/or is significantly 

more difficult.

Furthermore, the features summarized in observation code 3 are among those typically used for forensiclevel decisions while features summarized in observation code 4 are those used primarily by automatedmatchers in rendering a match decision.

Examiner responses were recorded by custom test apparatus consisting of a commodity computer and 

software designed and developed specifically for this and related NIST studies [29][30]. The examiners 

were not provided any time limits on their responses.

The 600 image pairs (100 images x 6 decomposition level specifications under test) were queued on each 

examiner’s workstation and their presentation order was shuffled randomly on each of the three 

workstations. Each pair consisted of a non-compressed source image and a version of the identical image 

decoded from the JPEG 2000 codestream encoded 10:1 using one of the six decomposition level 

specifications as described in section 3.2.1. Examiners were not informed as to which fingerprint image 

had been compressed, nor were they told the nature of any process applied to either of the two 

fingerprints.

The examiners were provided the basic ability to independently reposition, rotate, invert and zoom in and 

out of each of the two images from the pair being examined. This provided them with the basic tools that 

they typically employ in their standard operating environments in performing their duties. While they 

were provided with basic tools, more advanced assistive technologies normally available to some 

examiners, such as on-screen feature marking or pixel intensity adjustments such as brightness and 

contrast were not provided to them in the interest of experimental control. 

 

3 The commonly accepted nomenclature defines Level 1 fingerprint details as the overall friction ridge 

pattern and flow, Level 2 detail as classic Galton features [27] such as minutiae points, and Level 3 as 

pores, creases, line shapes, incipient ridges and other non Level 1 or 2 features [28].
10

The image pairs were presented on split-screen to the examiners in randomized order (see Figure 2), and 

with randomized screen position (left/right split screen placement) to mitigate potential ordering effects 

or positional bias. Scientists overseeing the tests were blind to the placement order of the images, as well 

as to the compression level or other processing parameters of image pairs. These factors were tracked by 

the test apparatus.

Figure 2 - Split-Screen Presentation of Image Pairs

Each of the 600 image pairs was guaranteed to be observed by 3 different examiners over the course of 

the study without repeating. Due to the physical limitations of even the best modern monitors, it is 

impossible to show a 1000 ppi image without zooming or interpolation. The software apparatus enabled 

the examiner to view images at approximately 10x to 50x of the original size (see [29], Appendix C for 

additional information).

Once the examiner made a determination for a given pair of images, that pair was marked clearly as 

complete. The examiner was allowed to return to a completed pair and re-examine that image pair 

without penalty. The examiner was also allowed to jump to any image pair in the queue regardless of that 

pair’s position in the examiner’s queue.

Examiners were provided basic verbal instructions and a demonstration on how to use the workstations,

and they were allowed a brief practice session using image pairings that were not part of the study to gain 

familiarity with the procedure, scoring, and workstation controls. Examiners were allowed to freely ask 

questions for clarification on the workstations or tasking. The examiners were located in the same room 

and were allowed to interact freely as they do in their normal professional practice. Finally, the examiners 

were advised that once they had selected one of the three workstations on which to process images, they 
11

continue to use that workstation exclusively. This was done in order to eliminate the possibility of an 

examiner processing an image pair more than once.

Examiner Assessment – Part Two

Part Two includes no direct examiner rating measurement. Instead, we use the comparative values of 

computational fidelity metrics for Part One to infer the likelihood that differences between noncompressed source and encoding using quality layers will be visible to trained fingerprint examiners. If we 

find, for example, that ratings of trained examiners find no significant difference among the various 

decomposition level specifications, we can use the fidelity measurements of these images as thresholds 

below which trained examiners are unlikely to detect differences. 

3.4. Hypothesis Testing

3.4.1. Friedman’s Procedure

The Friedman test [14][15][16][17] is a non-parametric test for analyzing randomized complete block 

designs and is an extension of the sign test when there may be more than two treatments of interest. The 

Friedman test assumes that there are two or more experimental treatments (k). The observations are 

arranged in b blocks as in the example shown in Table 5.

Table 5 - Block Design Example

Block Treatment

1 2 ... k

1 X11 X12 ... X1k

2 X21 X22 ... X2k

3 X31 X32 ... X3k

... ... ... ... ...

b Xb1 Xb2 ... Xbk

Let R(Xij) be the rank assigned to Xij within block i, and in the case of ties the average rank is used.

The ranks are summed to obtain

( ) 1

b

j ij

i

R RX == ∑ (6)

for j = 1, 2, ..., k, i = 1, 2, ..., b.

Then the Friedman test is

H0: Null hypothesis, the treatment effects, τ, have identical effects, i.e. [τ1 = , ..., = τk]

Ha: Alternative hypothesis, at least one treatment is different from at least one other 

treatment, [ τ1 , ..., τk not all equal].

Test Statistic:

(( ( )) )

2

1

1

12 1 /2

( 1)

k

i

i

T R bk

bk k =

= − +

+ ∑ (7)

If there are ties, then
12

( ) ( ) 2

1

1 1

1

1

2 1

k b k

k Ri i T

A C

  + − − ∑   =   = − (8)

where

( ( ))

2

1

1 1

b k

ij

i j

A RX = == ∑∑ (9)

( )

2

1

1

4

bk k

C

+ = (10)

Note that Conover [16] recommends the statistic

( )

( )

1

2

1

1

1

b T

T

bk T

− = − − (11)

since it has a more accurate approximate distribution. The T2 statistic is the two-way analysis of variance 

statistic computed on the ranks R(Xij).

The significance level, or the accepted probability of incorrectly rejecting the null hypothesis (i.e., making a 

Type I error) for the Friedman’s test is set at 0.05.

For the T2 test statistic, the critical region for rejection of the null hypothesis at a chosen type I error rate, 

α, is 

( ( )( )) 2 , 1, 1 1 kbk T F α −− − > (12)

where ( , 1, 1 1 kbk ( )( )) F α −− − is the percent point function of the F distribution.

For the T1 test statistic, the critical region is given as

( )

2

1 , 1 k T α − = Χ (13)

where 2 Χ is the percent point function of the chi-square distribution.

The T2 approximation is typically preferred as more accurate than T1.

3.4.2. Post Hoc Pairwise Multiple Comparisons Procedure

A statistically significant Friedman’s test tells us only that at least one of the treatments (in this case either 

number of DWT decomposition levels or the number of quality layers used for encoding) differs from at 

least one other treatment. If the Friedman’s test yields a probability greater than or equal to the selected 

Type I error threshold, the alpha rate, we accept the null hypothesis that there are no differences among 

the treatments. If the Friedman’s test results in a probability value less than the selected alpha rate, we 

reject the null hypothesis and accept the alternative hypothesis that at least one of the treatments groups 

has been sampled from a different population. In order to determine which treatments are different, we 

must perform a post hoc analysis of the pairwise differences between the treatments.

We use the Nemenyi test [19][20][32] for post hoc multiple pairwise comparisons of treatments with 

paired observations. This test compares the mean ranks determined by the Friedman’s test against critical 

values of mean rank differences indicative of statistical significance at the selected Type I error rate. Our 
13

use of the Nemenyi test is conservative in that we test all possible comparisons rather than simply each 

treatment against a control. The Nemenyi test controls the experiment-wise error rate for the multiple 

comparisons, hence does not require additional adjustment of the alpha level criterion for rejection of the 

null hypothesis.

We apply the Nemenyi test to the set of mean ranks resulting from the Friedman’s test using the following 

procedure:

1. Order the treatments according to ascending mean rank

2. Given the chosen type I error rate, alpha (α=0.05), number of blocks, b, and number of 

treatments, k, decide that treatment, τu ≠ τv if 1/2 ( 1)

12 u v

k k RR q b α

  +

− ≥     (13)

otherwise conclude τu = τv, where u = 1...k, v = 1...k, and v ≠ u.

Critical values of qα,ν,k are based on the Studentized range statistic, Q. Tabled critical values of this statistic 

may be found in tables such as that shown in [32] given alpha (α), degrees of freedom (ν), and number of 

treatments (k). Degrees of freedom for large samples (e.g., b > 240) is typically taken as infinite, but may 

be computed as ν = −b k , where b is the number of blocks and k is the number of treatments.

Alternately, values of qα,ν,k may be computed via algorithmic implementations for computation of the 

cumulative distribution function of the Studentized range statistic and its inverse as was done in the 

current investigation.

3.4.3. Wilcoxon Signed Rank Test

For one of our analyses we employ the Wilcoxon Signed Rank Test [31][32] [33] to examine the differences 

between paired observations. This test ranks both positive and negative differences between paired 

observations. In addition to providing a probability that the two sets of observations cold have come from 

the same population, the test also reports the number of positive and negative differences that may 

indicate the direction of differences. Where this test is used in the present study, this information enables 

us to determine relative effect of one treatment in comparison to another.

3.5. Uncertainty Of Sample Statistics

Where provided, uncertainty of sample statistics, such as the median, is evaluated using a bootstrap 

procedure. The computation of the sample median is repeated for each of 10,000 replicates of the 

measurement data drawn randomly with replacement. The standard error, SE, of the statistic is computed 

as

stat s SE n = (14)

where stat s is the standard deviation of the distribution of values of the replicated statistic, e.g., median of 

measurements, and n is the number of bootstrap replications. For any statistic, the 95 % confidence 

interval for the estimate is ±1.96(SE). Note that 95 % of the area of the standard normal distribution falls 

within ±1.96(σ), where σ denotes the standard deviation. Here we model the distribution of the 10,000 

medians using the standard normal distribution.
14

4. Results – Part One: Decomposition Levels

4.1. Examiner Ratings

As may be recalled from section 3.3.4 each image pair was compared by exactly three fingerprint 

examiners each of whom assigned a score indicating the relative degradation on a four point scale. For 

analysis, the three scores for each image pair were sorted in ascending order and concatenated to form a 

composite rating as a three digit integer. A Friedman’s test [31] was applied to the 3-digit composite 

ratings to determine if any of the six decomposition levels showed a statistically significant difference 

from at least one other decomposition specification. The test yielded a probability estimate of p = 0.1569, 

well above the threshold of p < 0.05 required for rejection of the null hypothesis. Accordingly, we conclude

that in this test, trained latent fingerprint examiners observed no systematic greater or lesser degradation 

among the six decomposition level specifications used in the JPEG 2000 compression. It should be noted 

that the examiner ratings were predominantly rating “2” indicating that the effect of compression to 10:1 

was noticeable, but deemed to have no effect on features used in identification (see Table 4).

4.2. Computational image fidelity measures

4.2.1. Counts of Changed Pixels

For the FIXT dataset, Friedman’s test yielded a probability estimate of p = 0.5668 failing to support 

rejection of the null hypothesis that any of the decomposition levels differed significantly from any other 

with respect to the number of pixels changed by compression.

The larger SD27 dataset, however, did find statistically significant differences in counts of changed pixels 

among the six decomposition level specifications, allowing rejection of the null hypothesis at the p < 

0.0001 level and acceptance of the alternative hypothesis that at least one of the decomposition level 

specifications generates images that differ from at least one other decomposition level encoding 

selection. An ordering of the mean ranks observed for each of the decomposition levels is shown in Table 

6. The ordering of the mean ranks shows counts of changed pixels to increase with decrease in the 

number of decomposition levels used in the JPEG 2000 encoding. The post hoc analysis of pairwise 

comparisons of the treatments indicates groupings of treatments within which no statistically significant 

difference was observed. (Note that such lettered groupings of treatments in Table 6 through Table 20

indicate that differences between mean ranks are greater than or equal to the critical values computed for 

each post hoc multiple comparison procedure as described in section 3.4.2.)

As shown in Table 6, comparison of counts of pixels changed in intensity value due to compression of the 

SD27 images finds no significant difference using DWT decomposition levels 8, 7, and 6 at the Type I error

rate (alpha) of 0.05. Decomposition levels 7, 6, and 5 differ from 8 levels, but are statistically 

indistinguishable from 7 and 6 decomposition levels. Decomposition using 4 and 3 levels differ from each 

other as well as differ with members of groupings A and B.
15

Table 6 - Friedman’s Test With Post Hoc Analysis For Counts of Changed Pixels , SD27 (alpha = 0.05, n=2484, critical 

difference = 0.1513)

Sample Sum of ranks Mean of ranks Groups

8 Levels 8156.000 3.283 A

7 Levels 8219.000 3.309 A B

6 Levels 8339.000 3.357 A B

5 Levels 8536.500 3.437 B

4 Levels 8973.500 3.613 C

3 Levels 9940.000 4.002 D

Figure 3 shows the decrease in the median number of image pixels changed via JPEG 2000 compression 

from three DWT decompositions to eight levels applied to the SD27 1000 ppi source images. The 95 % 

confidence intervals indicated by the brackets on each of the median values reflect the degree of stability 

of the median estimate rather than relationship among the decomposition levels. That the confidence 

intervals of the median estimates do not overlap would suggest significant differences in distributions of 

measurements for the six decomposition level specifications. However, Friedman’s test and the pairwise 

post hoc test provides a better description of the compression behavior on a block-by-block basis. Hence, 

the post hoc multiple comparison tests summarized in Table 6 indicate that while counts of changed pixels 

diminishes with increase in decomposition levels, the differences among levels five through seven are not 

2 3 4 5 6 7 8 9

5.42

5.43

5.44

5.45

5.46

5.47

5.48

5.49

5.5

5.51

5.52

x 104 Median Counts of Changed Pixels (SD27) with 95 % CI

Number of DWT Decomposition Levels

Median Counts

Figure 3 - Median number of changed pixel values with 95 % confidence intervals 

for each of six decomposition level specifications used in JPEG 2000 compression 

of SD27 1000 ppi source images. (Note Median Counts values on the axis are 

times 104.)
16

statistically significant, i.e. mean rank differences among these treatments are less than the critical value 

for significance at the 0.05 type I error rate.

4.2.2. Image Mean Squared Error

Comparison of image MSE values show the lowest fidelity loss using five decomposition levels, with this 

specification having the lowest mean rank score for both the 100-sample FIXT image set as well as for the 

much larger SD27 image collection (see Table 7 and Table 8). No significant difference is found between 

five and six decomposition levels for the FIXT images, but a significant difference is evident between five 

and six levels with the SD27 images, with a probability, p < 0.0001.

Table 7 - Friedman’s Test With Post Hoc Analysis For Image MSE, FIXT Sample (alpha = 0.05, n=100, critical difference 

= 0.7540)

Sample Sum of ranks Mean of ranks Groups

5 Levels 225.000 2.250 A

6 Levels 264.000 2.640 A B

7 Levels 314.000 3.140 B C

4 Levels 329.000 3.290 B C

8 Levels 386.000 3.860 C

3 Levels 582.000 5.820 D

Table 8 - Friedman’s Test With Post Hoc Analysis For Image MSE, SD27 (alpha = 0.05, n=2484, critical difference = 

0.1513)

Sample Sum of ranks Mean of ranks Groups

5 Levels 5205.000 2.095 A

6 Levels 6340.500 2.553 B

7 Levels 8010.500 3.225 C

4 Levels 8166.500 3.288 C

8 Levels 10138.000 4.081 D

3 Levels 14303.500 5.758 E
17

In contrast to the situation described above with counts of changed pixels, we see a somewhat different 

situation with the image MSE measurements. Figure 4 indicates lowest mean squared error with five 

decomposition levels. This is consistent with the post hoc pairwise comparison tests summarized in Table 8

that finds five levels significantly different from all other decomposition level specifications. Overlap 

among the 95 % confidence intervals on the estimates of the medians indicates that when taken in 

aggregate, decomposition levels four through seven are closer than indicated by the pairwise comparison 

tests.

4.2.3. Structural Analysis Based Measures

SIVV RMSE

Comparison of the frequency structures of non-compressed to decoded compressed images show no 

significant differences using any decomposition level specification higher than three levels, with six levels 

appearing at the top of the list, i.e. showing lowest fidelity loss, for both the 100-sample FIXT images as 

well as for the SD27 fingerprints, though Table 9 and Table 10 show different ordering of mean ranks for 

the two datasets. 

2 3 4 5 6 7 8 9

15.11

15.12

15.13

15.14

15.15

15.16

15.17

15.18

15.19

Median Image MSE (SD27) with 95 % CI

Number of DWT Decomposition Levels

Median Image MSE

Figure 4 - Median of image MSE with 95 % confidence intervals for each of six 

decomposition level specifications used in JPEG 2000 compression of SD27 1000 

ppi source images. (CI = confidence interval)
18

Table 9 - Friedman’s Test with Post Hoc Multiple Comparisons – SIVV RMSE – FIXT (alpha = 0.05, n=100, critical 

difference = 0.7540)

Sample Sum of ranks Mean of ranks Groups

6 Levels 295.000 2.950 A

7 Levels 320.000 3.200 A B

4 Levels 329.000 3.290 A B

5 Levels 353.000 3.530 A B

8 Levels 371.000 3.710 A B C

3 Levels 432.000 4.320 C

Table 10 - Friedman’s Test with Post Hoc Multiple Comparisons – SIVV RMSE – SD27, (alpha = 0.05, n=2484, critical 

difference = 0.1513)

Sample Sum of ranks Mean of ranks Groups

6 Levels 8509.000 3.426 A

5 Levels 8532.000 3.435 A

8 Levels 8541.000 3.438 A

7 Levels 8551.000 3.442 A

4 Levels 8818.000 3.550 A

3 Levels 9213.000 3.709 B

Medians of SIVV RMSE measurements shown in Figure 5 point to five DWT levels as exhibiting the least 

error in frequency spectrum in comparison to that of source images. Pairwise comparison tests, however, 

as shown in Table 10 indicate that four through eight levels of decomposition are statistically 

indistinguishable.
19

MSSIM ́

Our second image structural fidelity metric, MSSIM ́, shows five decomposition levels at the top of the list 

for both the 100-sample FIXT images as well as with the SD27 data4. Table 11 shows a grouping of 5, 6, 7, 

and 4 levels for the smaller dataset whereas Table 12 again finds five decomposition levels at the top 

position with a significant difference (p < 0.0001) with the next in order, six decomposition levels. This 

relationship between five and six levels is similar to that observed for the MSE measurements shown in 

Table 7 and Table 8, possibly due to the inclusion of luminance measures in the MSSIM ́ which might be 

expected to correlate with the MSE measure to an extent greater than that of the SIVV RMSE.

 

4 Note that the maximum MSSIM is 1.0, indicating no loss in fidelity. Hence, in contrast to the other fidelity 

measures used here, mean ranks are ordered highest to lowest for this metric. 

2 3 4 5 6 7 8 9

8.075

8.08

8.085

8.09

8.095

8.1

8.105

x 10-3 Median SIVV RMSE (SD27) with 95 % CI

Number of DWT Decomposition Levels

Median SIVV RMSE

Figure 5 - Median SIVV RMSE with 95 % confidence intervals for each of six 

decomposition level specifications used in JPEG 2000 compression of SD27 1000 

ppi source images. (Note that median values on ordinate are multiplied by 10-3.)
20

Table 11 - Friedman’s Test with Post Hoc Multiple Comparisons – MSSIM ́ – FIXT Sample, (alpha = 0.05, n=100, critical 

difference = 0.7540)

Sample Sum of ranks Mean of ranks Groups

5 Levels 447.000 2.530 A

6 Levels 421.000 2.790 A

7 Levels 401.000 2.990 A

4 Levels 375.000 3.250 A B

8 Levels 321.000 3.790 B

3 Levels 135.000 5.650 C

Table 12 - Friedman’s Test with Post Hoc Multiple Comparisons – MSSIM ́ – SD27, , (alpha = 0.05, n=2484, critical 

difference = 0.1513)

Sample Sum of ranks Mean of ranks Groups

5 Levels 11695.000 2.292 A

6 Levels 10821.000 2.644 B

7 Levels 9556.000 3.153 C

4 Levels 9173.000 3.307 D

8 Levels 7796.000 3.862 E

3 Levels 3123.000 5.743 F

Inasmuch as the MSSIM ́ has a maximum value of 1.0, we subtract the values from this maximum to put 

the medians of this error measure on a scale similar to that for other error metrics. Median and 95 % 

confidence intervals are plotted in Figure 6. We see that the pattern of medians for this structural error 

metric is similar to that of the other structural metric, the SIVV RMSE. As with the SIVV RMSE, the median 

MSSIM ́ suggests five decomposition levels as the having the least fidelity loss relative to the source 

images. In this case, the difference between five levels and the next closest, six decomposition levels, is 

statistically significant.
21

4.2.4. Conclusions: DWT Decomposition Levels

Five and six decompositions levels rank at the top of the list of decomposition level specifications or are 

found in the top performing group among all the fidelity measurements. As measurements on the SD27 

image dataset are more likely to yield stable statistics, five decomposition levels might appear best for 

JPEG 2000 compression of 1000 ppi images. However, to support additional flexibility in the decoding of 

compressed codestreams at lower than maximum resolution, six levels could be justified as acceptable as 

well as five DWT decomposition levels. Lepley [3] suggests that inasmuch as 500 ppi fingerprint images 

have been compressed via the Wavelet Scalar Quantization (WSQ) CODEC [35] [36] [37] [38] [39] using 

five decomposition levels, it is reasonable to provide an additional DWT level for images having twice the 

initial resolution.

2 3 4 5 6 7 8 9

0.0353

0.0353

0.0354

0.0354

0.0354

0.0354

0.0354

0.0355

0.0355

0.0355

0.0355

Median [1-MSSIM] (SD27) with 95 % CI

Number of DWT Decomposition Levels

Median (1-MSSIM)

Figure 6 - Median MSSIM ́ with 95 % confidence intervals for each of six 

decomposition level specifications used in JPEG 2000 compression of SD27 1000 

ppi source images.
22

5. Results - Part Two: Quality Layers

5.1. Computational Image Fidelity Measures

5.1.1. Counts of Changed Pixels

The Friedman’s test comparison of counts of changed pixels showed significant differences among the 

quality layer specifications for both the 100-sample FIXT images as well as for the SD27 images. Post hoc

analyses summarized in Table 13 and Table 14 show increasing differences from the single quality layer to 

nine quality layers. For the FIXT sample, the groupings overlap whereas with the larger SD27 dataset, all 

quality level specifications differ from all others.

Table 13 - Friedman’s Test with Post Hoc Multiple Comparisons – Counts of changed Pixels, FIXT Sample (alpha = 0.05, 

n=100, critical difference = 1.2013)

Sample Sum of ranks Mean of ranks Groups

1 Layers 191.500 1.915 A

2 Layers 306.500 3.065 A B

3 Layers 418.000 4.180 B C

4 Layers 497.000 4.970 C D

5 Layers 551.500 5.515 D E

6 Layers 587.500 5.875 D E F

7 Layers 609.500 6.095 D E F

8 Layers 656.500 6.565 E F

9 Layers 682.000 6.820 F

Table 14 - Friedman’s Test with Post Hoc Multiple Comparisons – Counts of changed Pixels, SD27 (alpha = 0.05, 

n=2484, critical difference = 0.2410)

Sample Sum of ranks Mean of ranks Groups

1 Layers 3606.000 1.452 A

2 Layers 6349.000 2.556 B

3 Layers 9015.000 3.629 C

4 Layers 11671.500 4.699 D

5 Layers 13736.500 5.530 E

6 Layers 15320.500 6.168 F

7 Layers 16521.500 6.651 G

8 Layers 17440.500 7.021 H

9 Layers 18119.500 7.294 I
23

The Friedman’s test considers within block rankings of treatment options, hence such tests may be 

performed without normalization to adjust for differences in image sizes. Computation of confidence 

intervals on the median of counts is complicated by the interaction of data resampling with the large 

variation in image sizes. Hence, for estimation of sample medians, we convert the counts to proportion or 

percent of pixels by dividing counts by the image size in pixels. Medians of percent pixels changed are thus 

displayed in Figure 7 with 95 % confidence intervals on the estimates of this statistic. We see the single 

quality layer as showing the lowest percentage of changed pixels and an almost linear increase with each 

additional quality layer up to seven layers. beyond seven layers, the rate of increase decreases to almost 

level off. The overlap of confidence intervals in seven to nine quality layers reflects potential similarity 

among medians and aggregate similarity of treatments. Such uncertainty among sample statistics does 

not over-rule comparisons of treatments on a block by block (image by image basis.) Hence, the 

separation of, and ordering of, the medians remains consistent with the pairwise comparisons summarized 

in Table 14. We note, however, that while statistically significant, the incremental increase in percent 

changed pixels is quite small (on the order of only hundredths of a percent ) relative to the initial impact of 

around 44.5 % compressing only to the single 10:1 rate.

0 1 2 3 4 5 6 7 8 9 10

44.505

44.51

44.515

44.52

44.525

44.53

Median Percent of Changed Pixels (SD27) with 95 % CI

Number of Quality Layers

Median Percent

Figure 7 - Median of counts of changed pixels with 95 % confidence intervals for 

each of nine quality layer specifications used in JPEG 2000 compression of SD27 

1000 ppi source images.
24

5.1.2. Image Mean Squared Error

Image MSE measures show fidelity results similar to that of counts of changed pixels with ordering of 

fidelity loss successively greater with larger numbers of quality layers from one to nine, with some 

grouping for the smaller FIXT sample (Table 15) and complete separation for the SD27 images (Table 16).

Table 15 - Friedman’s Test with Post Hoc Multiple Comparisons – Image MSE, FIXT Sample (alpha = 0.05, n=100, critical 

difference = 1.2013)

Sample Sum of ranks Mean of ranks Groups

1 Layers 123.000 1.230 A

2 Layers 239.000 2.390 A

3 Layers 381.000 3.810 B

4 Layers 471.500 4.715 B C

5 Layers 560.000 5.600 C D

6 Layers 614.000 6.140 D E

7 Layers 664.000 6.640 D E

8 Layers 714.000 7.140 E

9 Layers 733.500 7.335 E

Table 16 - Friedman’s Test with Post Hoc Multiple Comparisons – Image MSE, SD27 (alpha = 0.05, n=2484, n=2484, 

critical difference = 0.2410)

Sample Sum of ranks Mean of ranks Groups

1 Layers 3221.500 1.297 A

2 Layers 5967.000 2.402 B

3 Layers 8714.000 3.508 C

4 Layers 11428.000 4.601 D

5 Layers 13649.500 5.495 E

6 Layers 15403.000 6.201 F

7 Layers 16823.000 6.773 G

8 Layers 17908.000 7.209 H

9 Layers 18666.000 7.514 I
25

Median MSE of Figure 8 shows the steepest increase in error in going from the single quality layer to two 

layers and a leveling off of the increase by seven quality layers. Pairwise comparisons summarized in Table 

16 show all differences among quality layers to be statistically significant, though it appears that when 

taken as aggregate samples described by median estimates, some of the quality layer specifications 

appear similar in MSE.

5.1.3. Structural Analysis Based Measures

SIVV RMSE

Differences in the SIVV spectral signals indicate less variability than that seen with the pixel-based 

measures described above. We find that addition of one quality layer to the single target compression rate 

to have no significant impact on the power spectrum, but observe additional layers to fall into a cluster of 

similar degree of degradation.

Table 17 shows the beginning of this pattern with the FIXT sample images, but Table 18 covering the larger 

image dataset shows a fully developed pattern of three overlapping clusters in which fidelity decreases 

with increasing number of quality layers. 

0 1 2 3 4 5 6 7 8 9 10

15

15.05

15.1

15.15

Median Image MSE (SD27) with 95 % CI

Number of Quality Layers

Median Image MSE

Figure 8 - Median of image MSE with 95 % confidence intervals for each of nine 

quality layer specifications used in JPEG 2000 compression of SD27 1000 ppi 

source images.
26

Table 17 - Friedman’s Test with Post Hoc Multiple Comparisons – SIVV RMSE, FIXT Sample (alpha = 0.05, n=100, 

critical difference = 1.2013)

Sample Sum of ranks Mean of ranks Groups

1 Layers 307.000 3.070 A

2 Layers 374.000 3.740 A B

3 Layers 475.000 4.750 B C

4 Layers 519.500 5.195 C

5 Layers 552.000 5.520 C

6 Layers 562.000 5.620 C

7 Layers 564.000 5.640 C

8 Layers 573.000 5.730 C

9 Layers 573.500 5.735 C

Table 18 - Friedman’s Test with Post Hoc Multiple Comparisons – SIVV RMSE, SD27 (alpha = 0.05, n=2484, n=2484, 

critical difference = 0.2410)

Sample Sum of ranks Mean of ranks Groups

1 Layers 11589.500 4.666 A

2 Layers 12094.000 4.869 A B

3 Layers 12320.000 4.960 B C

4 Layers 12511.000 5.037 B C

5 Layers 12538.500 5.048 B C

6 Layers 12601.000 5.073 B C

7 Layers 12647.000 5.091 B C

9 Layers 12739.000 5.128 C

8 Layers 12740.000 5.129 C
27

The plot of median values (Figure 9) of the first of our structural metrics reinforces the contrast between 

the single quality layer and two or more layers as well as the pairwise similarity among the multiple layer 

JPEG 2000 specifications.

MSSIM ́

With the 100 sample FIXT image set, we find no significant difference in the MSSIM ́ between a single 

quality layer and two layers (see Table 19). These two quality layer configurations then differ significantly 

with several other clusters. No significant differences in MSSIM ́ are found from six to nine quality layers.

Table 19 Friedman’s Test with Post Hoc Multiple Comparisons – MSSIM ́, FIXT Sample (alpha = 0.05, n=100, critical 

difference = 1.2013)

Sample Sum of ranks Mean of ranks Groups

1 Layers 877.000 1.230 A

2 Layers 760.000 2.400 A

3 Layers 618.000 3.820 B

4 Layers 530.500 4.695 B C

5 Layers 440.000 5.600 C D

6 Layers 386.000 6.140 D E

7 Layers 336.000 6.640 D E

8 Layers 286.000 7.140 E

9 Layers 266.500 7.335 E

0 1 2 3 4 5 6 7 8 9 10

8.055

8.06

8.065

8.07

8.075

8.08

8.085

8.09

8.095

x 10-3 Median SIVV RMSE (SD27) with 95 % CI

Number of Quality Layers

Median SIVV RMSE

Figure 9 - Median of image SIVV RMSE with 95 % confidence intervals for each 

of nine quality layer specifications used in JPEG 2000 compression of SD27 

1000 ppi source images.
28

With the much larger SD27 image dataset we find all quality layer specifications significantly different from 

all others (see Table 20).

Table 20 - Friedman’s Test with Post Hoc Multiple Comparisons – MSSIM ́, SD27 (alpha = 0.05, n=2484, n=2484, critical 

difference = 0.2410)

Sample Sum of ranks Mean of ranks Groups

1 Layers 21604.500 1.303 A

2 Layers 18865.000 2.405 B

3 Layers 16115.000 3.512 C

4 Layers 13407.000 4.603 D

5 Layers 11191.500 5.495 E

6 Layers 9432.000 6.203 F

7 Layers 8032.000 6.767 G

8 Layers 6953.000 7.201 H

9 Layers 6180.000 7.512 I

As we mentioned earlier, for purposes of median plots, we subtract the MSSIM ́ values from 1.0 such that 

increasing error is shown as increasing values of the metric. As with the other metrics, we see via Figure 10

0 1 2 3 4 5 6 7 8 9 10

0.0351

0.0352

0.0352

0.0353

0.0353

0.0353

0.0354

0.0355

Median [1-MSSIM] (SD27) with 95 % CI

Number of Quality Layers

Median (1-MSSIM)

Figure 10 - Median of MSSIM ́ with 95% confidence intervals for each of nine 

quality layer specifications used in JPEG 2000 compression of SD27 1000 ppi 

source images.
29

an increase in error with increasing numbers of quality layers. Pairwise comparisons summarized in Table 

20 show all quality layer configurations to differ significantly from all others. That the median estimates 

are very stable over the bootstrap replications reinforces the statistical significance observed and that 

JPEG 2000 compression using quality layers does degrade structural features of the image beyond that 

observed using only a single target compression rate. In the next section we address whether the 

magnitude of the observed fidelity degradation should be considered problematic to fingerprint 

identification via visual examination by trained fingerprint examiners.

5.2. Comparison of relative error: Decomposition Levels vs. Quality Layers

As indicated previously, trained examiners’ ratings showed no significant difference among the six DWT 

decomposition specifications used for encoding fingerprint images. An examiner study was not included in 

Part Two of the present investigation. Hence, we are unable to directly test the effects of using more than 

a single quality layer for JPEG 2000 encoding of fingerprints. However, we are able to perform an indirect 

assessment of the likelihood that image fidelity loss due to use of multiple quality layers might be visible to 

trained examiners.

We may compare our measures of fidelity loss among the six decomposition levels on an image by image 

basis to measures similarly computed for the quality layer specifications in order to infer potential fidelity 

loss as being below, or possibly above, the visual threshold of trained fingerprint examiners.

For this, we consider the 100 sample images from the FIXT dataset used in the examiner portion of the 

study. For each image, we find the maximum of the values of MSE, SIVV RMSE, and MSSIM ́ for the six 

decomposition levels5. We find the corresponding maximum values of these computational metrics for 

the quality layers, excluding that for the single quality layer.

Table 21 - Wilcoxon Tests of Extreme Error of Decomposition Levels vs. that for Quality Layers (alpha = 0.05, n=2484)

Differences

Metric Positive Negative Zero Wilcoxon Probability

MSE 99 0 1 p<0.0001

SIVV RMSE 87 6 7 p<0.0001

MSSIM 84 0 16 p<0.0001

Table 21 summarizes the Wilcoxon Signed Rank Tests of the difference between maximum values of 

fidelity error metrics for images encoded using each of the six DWT decomposition level specifications and 

those for corresponding images compressed using quality layer specifications shown in Table 3. For each 

of the metrics we find a significant difference between fidelity of the two JPEG 2000 encoding treatments 

with p < 0.0001 in each case, significantly less than the accepted Type I error rate, α = 0.05.

 

5 We exclude counts of changed pixels from this analysis as the criteria for counting are different in Part 

One and Part Two of the study.
30

As the Wilcoxon Signed Rank Test evaluates the differences between paired observations of the two 

treatments, the predominantly positive differences of each tests indicate that maximum fidelity loss of 

decomposition level treatments exceeds that of quality layer treatments with most of the 100 images 

processed. We are accordingly able to infer that given that trained latent fingerprint examiners could not 

differentiate among the decomposition levels at measured fidelity error, it is unlikely that images 

exhibiting lesser error due to encoding with multiple quality layers would be differentiable by the visual 

examination. 

6. Conclusions 

6.1. WAVELET DECOMPOSITION LEVELS

6.1.1. To what extent does the number of decomposition levels affect computational measures of 

image fidelity with respect to source, non-compressed images? 

For 1000 ppi fingerprint images, DWT decomposition at five and six levels appears to be a “sweet spot” 

exhibiting less fidelity loss than fewer, or even greater, decompositions.

6.1.2. Are potential fidelity differences detected by trained latent fingerprint examiners?

While computational fidelity metrics find statistically significant differences among images compressed at 

different numbers of decomposition levels, the differences appear to be largely insignificant with respect 

to visual comparison by trained fingerprint examiners.

6.2. EFFECT OF MULTIPLE QUALITY LAYERS

6.2.1. What is the effect on image fidelity of using more than a single quality layer?

Computational measurements show that JPEG 2000 compression using more than a single quality level will 

result in small, but statistically significant loss in fidelity in comparison of non-compressed source images 

with those decoded from compressed codestreams. While the fidelity losses are statistically significant, 

they have no observed effect with respect to use of the once-compressed images for fingerprint 

identification by certified latent fingerprint examiners.

6.2.2. What is the effect on image fidelity of increasing numbers of quality layers?

Fidelity loss increases with the each additional quality layer. Again, while such losses are statistically 

significant, they appear to have no observed effect with respect to judgements of certified fingerprint 

examiners. Moreover, incremental loss in fidelity is small relative to that incurred by compression at a 

single target rate of, e.g., 10:1. Interestingly, it appears as though the increase in fidelity loss levels out 

around seven quality layers, with little incremental loss with additional low bit rate layers. Still, however, 

we do not yet know the effects of even small incremental fidelity loss on automated matching. Hence, it is 

recommended that selection of quality layers be limited to those having known applications or for which 

potential applications are anticipated. 
31

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