Spatial

Sampling

Effects

in

Optical

Character

Recognition

Daniel

Lopresti

George

Nagyy

Prateek

Sarkar

y

Jiangying

Zhou

April

Abstract

We

examine

the

effects

of

random-phase

spatial

sampling

on

the

optical

character

recognition

process

We

start

with

a

detailed

analysis

for

patterns

Empirical

data

demonstrate

that

our

model

is

accurate

We

then

give

experimental

results

for

more

complex

patterns

-LRB-

i.e.

printed

scanned

characters

-RRB-

Spatial

sampling

seems

to

account

for

a

significant

amount

of

the

variability

seen

in

practice

Introduction

The

study

of

noise

in

scanned

characters

along

with

the

development

of

synthetic

character

generators

has

attracted

a

great

deal

of

interest

over

the

past

three

decades

-LSB-

-RSB-

The

issue

of

evaluating

noise

models

from

the

standpoint

of

the

OCR

error

behavior

they

induce

has

also

recently

received

attention

-LSB-

-RSB-

However

little

previous

work

along

these

lines

has

involved

the

direct

comparison

of

real

and

synthetic

characters

As

a

result

it

appears

that

a

very

significant

-LCB-

and

completely

unavoidable

-LCB-

source

of

character

variation

random-phase

spatial

sampling

has

been

largely

overlooked

-LRB-

or

at

least

underemphasized

-RRB-

by

the

OCR

community

The

objective

of

this

communication

is

to

demonstrate

that

random

spatial

sampling

noise

gives

rise

to

several

readily

observable

phenomena

that

bear

directly

on

optical

character

recognition

Greater

appreciation

of

this

type

of

noise

may

also

lead

to

more

realistic

synthetic

character

generators

Spatial

sampling

noise

is

the

consequence

of

the

random

uniformly

distributed

displacement

of

the

scanner

sampling

grid

with

respect

to

the

characters

Its

importance

lies

in

the

fact

that

it

produces

correlated

character-dependent

variations

that

affect

OCR

systems

very

differently

from

independent

identically

distributed

-LRB-

i.i.d.

-RRB-

perturbations

with

the

same

signal-to-noise

ratio

Furthermore

such

sampling-phase

noise

can

not

be

eliminated

by

technical

scanner

refinements

although

its

effect

can

be

mitigated

by

increasing

the

sampling

resolution

Matsushita

Information

Technology

Laboratory

Two

Research

Way

Princeton

NJ

yElectrical

Computer

and

Systems

Engineering

Rensselaer

Polytechnic

Institute

Troy

NY

In

this

paper

we

examine

the

effects

of

spatial

sampling

from

several

standpoints

We

begin

by

presenting

a

brief

theoretical

analysis

for

the

case

of

patterns

in

Section

Our

model

has

been

confirmed

experimentally

-LCB-

Section

gives

data

to

support

this

In

Sections

and

we

consider

the

more

complex

case

of

patterns

-LRB-

i.e.

characters

-RRB-

Finally

we

summarize

the

paper

and

offer

some

conclusions

in

Section

Analysis

of

the

Case

In

this

section

we

explore

the

effects

of

sampling

variation

in

one

dimension

We

shall

assume

that

the

grid

shift

is

a

random

variable

uniformly

distributed

over

a

distance

equal

to

one

sampling

interval

We

assume

that

an

analog

pattern

is

a

binary

waveform

defined

as

a

sequence

of

real

numbers

bk

wk

bk

Here

each

bi

corresponds

to

a

black

stroke

-LRB-

-RRB-

of

width

bi

each

wi

a

white

stroke

-LRB-

-RRB-

of

width

wi

For

example

an

analog

pattern

represents

a

black

stroke

units

long

followed

by

a

white

interval

units

long

followed

by

another

black

stroke

units

long

The

digitized

pattern

is

generated

by

sampling

an

analog

pattern

at

integral

coordinate

points

Similarly

we

use

a

sequence

of

integers

-LRB-

nk

mk

nk

-RRB-

to

represent

the

alternative

black

-LRB-

ni

-RRB-

and

white

-LRB-

mi

-RRB-

runs

of

a

digital

binary

pattern

Figure

depicts

a

binary

waveform

and

the

corresponding

strings

produced

at

eight

successive

displacements

of

the

sampling

grid

Under

the

assumption

of

a

uniformly

distributed

grid

displacement

and

knowing

the

positions

of

the

transitions

the

frequencies

with

which

the

various

patterns

will

appear

can

be

readily

calculated

Figure

plots

frequencies-of-appearance

for

the

four

different

patterns

of

Figure

at

two

sampling

resolutions

From

these

frequencies

other

measures

of

interest

can

be

computed

in

a

straightforward

way

For

example

the

length

histogram

for

a

single

black

stroke

has

a

sidelobe

on

the

right

if

its

length

is

just

under

an

integral

number

of

sampling

intervals

and

on

the

left

if

its

length

is

just

over

as

shown

in

Figure

Such

an

effect

can

also

be

observed

in

real

scanned

patterns

In

general

it

can

be

shown

that

the

number

of

possible

digital

patterns

-LRB-

binary

strings

-RRB-

equals

the

number

of

black-white

transitions

in

the

analog

pattern

-LSB-

-RSB-

We

characterize

the

latter

by

the

coordinate

locations

of

its

black/white

boundaries

Consider

for

example

the

analog

pattern

If

we

assume

that

the

pattern

starts

at

then

black/white

transitions

of

the

above

pattern

happen

at

locations

respectively

For

the

simplest

case

a

single

black

stroke

of

length

L

l

digitization

produces

a

run-length

of

N

black

pixels

with

the

following

probability

distribution

on

N

Pr

-LRB-

N

njL

l

-RRB-

dle

l

if

n

dle

dle

l

if

n

dle

otherwise

-LRB-

-RRB-

assume

here

that

all

lengths

have

been

normalized

to

make

pixel

widths

integral

Sampling

points

Bitmaps

pattern

Reflectance

signal

Figure

Variations

arising

from

spatial

sampling

in

resolution

Figure

Estimated

probabilities

for

digitized

patterns

.00.20.40.60.81.01920210.00.20.40.60.81.0192021

resolution

dpir

esolution

dpi

Figure

Length

histograms

for

a

single

black

stroke

For

the

case

of

multiple

strokes

we

place

the

analog

pattern

along

a

coordinate

axis

-LRB-

recall

Figure

-RRB-

As

we

slide

the

pattern

by

small

amounts

the

resulting

digitized

pattern

changes

We

see

a

new

pattern

as

soon

as

one

of

the

boundaries

crosses

a

sampling

point

and

we

continue

to

see

the

same

pattern

until

another

boundary

crosses

a

sampling

point

Since

we

are

assuming

a

uniform

distribution

for

the

grid

shift

over

a

unit

length

the

distance

by

which

the

analog

pattern

can

be

moved

between

two

successive

crossings

is

equal

to

the

probability

of

appearance

for

the

digital

pattern

in

question

Table

for

example

shows

the

digital

patterns

and

their

predicted

probabilities

that

arise

from

the

analog

pattern

Evaluation

of

the

Case

To

test

the

validity

of

our

model

we

conducted

an

experiment

comparing

the

predicted

and

observed

probabilities

for

a

simple

pattern

For

input

we

used

a

linear

bar-code

from

-LSB-

-RSB-

The

pattern

was

placed

with

the

bars

slightly

tilted

-LRB-

ss

-RRB-

to

simulate

a

uniform

shift-rate

in

the

longitudinal

direction

The

scanning

spot-size

was

set

at

of

an

inch

The

rows

of

the

resulting

scanned

pattern

were

used

as

samples

The

total

number

of

patterns

so

obtained

was

Individual

stroke

widths

were

estimated

from

a

portion

of

the

sample

set

-LRB-

of

the

Grid

Black/White

Digital

ProbaShift

Transitions

Pattern

bility

Table

Digital

variations

resulting

from

sampling

analog

pattern

patterns

-RRB-

These

were

used

to

predict

the

possible

digitized

patterns

and

their

respective

probabilities

of

appearance

The

results

were

then

compared

to

the

observed

frequencies

for

the

remainder

of

the

sample

set

-LRB-

patterns

-RRB-

Table

presents

this

data

Similar

experiments

were

carried

out

with

other

patterns

-LSB-

-RSB-

The

observations

were

quite

similar

In

all

cases

we

found

that

our

spatial

sampling

model

could

predict

the

most

common

digital

patterns

and

also

provide

a

relatively

accurate

estimate

of

their

frequencies-of-appearance

Fewer

than

of

the

patterns

in

each

case

did

not

belong

to

the

predicted

set

of

variations

Evidently

there

are

other

factors

that

affect

the

digitization

process

many

related

to

the

scanning

hardware

and

difficult

to

analyze

but

clearly

random-phase

noise

in

sampling

is

itself

a

major

factor

worth

studying

Models

for

the

Case

While

patterns

are

amenable

to

rigorous

analysis

more

complex

shapes

-LRB-

e.g.

printed

characters

-RRB-

are

not

In

this

section

we

describe

an

empirical

model

for

characterizing

digitization

noise

in

patterns

In

the

following

we

assume

a

rigid

sampling

grid

of

square

cells

arranged

in

vertical

columns

and

horizontal

rows

Each

cell

covers

an

area

equal

to

one

unit

which

is

also

the

size

of

a

pixel

Variations

in

the

scanning

process

arise

from

the

positioning

of

the

grid

with

respect

to

the

analog

pattern

as

well

as

from

threshold

As

before

we

assume

the

grid

displacement

is

a

random

variable

uniformly

distributed

over

the

area

of

one

sampling

cell

Figure

illustrates

the

variability

caused

by

differential

placement

of

the

sampling

grid

For

the

two

grid

positions

in

the

figure

the

sampling

cells

overlap

different

portions

of

the

input

image

yielding

different

output

bitmaps

-LRB-

darker

dots

in

the

figure

represent

's

of

the

bitmaps

-RRB-

We

assume

that

the

point-spread

function

of

the

scanner

can

be

approximated

by

a

Gaussian

function

If

the

binarization

threshold

is

fixed

-LCB-

say

at

-LCB-

then

sampling

lo

Gaussian

assumption

is

quite

peripheral

to

our

argument

-LCB-

a

raised

cosine

half-cosine

or

rectangular

cross-section

would

do

as

well

Probability

Digitized

Pre

Observed

Pattern

dicted

Training

Test

Overall

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

Partial

Sum

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

Table

Experimental

evaluation

of

a

pattern

consisting

of

four

black

strokes

cations

within

the

white

portions

of

the

waveform

will

still

be

converted

to

's

and

locations

within

the

black

portions

to

's

If

however

the

threshold

is

variable

-LRB-

obeying

a

zero-mean

i.i.d.

Gaussian

process

for

example

-RRB-

a

positive

perturbation

will

cause

points

in

the

white

region

near

the

boundary

to

be

quantized

to

be

black

while

a

negative

perturbation

will

cause

points

in

the

black

region

near

the

boundary

to

be

white

This

effect

is

illustrated

in

Figure

If

the

convolution

of

the

point

spread

function

with

an

edge

is

approximately

linear

near

the

threshold

then

the

effect

of

threshold

variation

can

be

approximated

by

a

random

displacement

in

the

sampling

delta

function

-LRB-

sampling

spot

-RRB-

with

respect

to

the

edge

in

the

input

image

-LSB-

-RSB-

However

such

an

approximation

is

valid

only

at

those

edge

points

in

the

vicinity

of

which

the

edge

is

approximately

straight

It

does

not

reflect

accurately

for

example

the

round-up

phenomena

at

corners

induced

by

the

sensor

's

point

spread

function

We

therefore

apply

an

additional

blurring

process

at

the

corners

of

a

contour

prior

to

threshold

variation

Figure

-LRB-

a

-RRB-

simulates

random-phase

spatial

sampling

on

three

instances

of

a

Helvetica

M

Figure

-LRB-

b

-RRB-

is

the

same

reference

character

digitized

with

a

small

amount

of

independent

identically

distributed

threshold

noise

The

effects

of

combining

random-phase

sampling

with

threshold

noise

are

illustrated

in

Figure

-LRB-

c

-RRB-

For

comparison

Figure

-LRB-

d

-RRB-

shows

three

scan-digitized

samples

printed

using

a

dpi

laserprinter

Evaluation

of

the

Case

In

this

section

we

present

a

study

of

the

effects

of

spatial-sampling

on

the

shape

of

dimensional

patterns

Figure

Variation

due

to

sampling

grid

placement

To

date

some

work

has

been

done

concerning

the

effects

of

digitization

on

relatively

simple

shapes

For

example

Haralick

and

Shapiro

have

investigated

the

effects

of

positional

inaccuracy

in

certain

low-level

vision

problems

-LSB-

-RSB-

They

developed

models

to

determine

the

variance

in

the

endpoints

length

and

centroid

of

a

line

and

in

the

centroid

of

a

shape

Others

have

studied

how

sampling

affects

accuracy

when

estimating

properties

of

digital

lines

and

curves

and

digital

planar

shapes

-LSB-

E

-RSB-

We

begin

by

considering

some

simple

statistical

measures

Figure

shows

the

distinct

effects

of

the

sampling

phenomenon

on

the

measured

area

for

instances

of

a

Computer

Modern

Sans

Serif

e

Histogram

-LRB-

a

-RRB-

is

for

spatial

sampling

-LRB-

b

-RRB-

for

i.i.d.

threshold

noise

-LRB-

c

-RRB-

for

the

combined

effects

of

sampling

and

threshold

variation

and

-LRB-

d

-RRB-

for

real

scanned

characters

Similarly

Figure

shows

stroke-width

histograms

for

the

same

sets

of

characters

where

stroke-width

is

defined

as

SW

-LRB-

Q

-RRB-

A

-LRB-

-RRB-

where

Q

is

the

number

of

times

a

black

square

fits

the

pattern

bitmap

and

A

is

the

area

under

the

pattern

-LSB-

-RSB-

It

is

quite

clear

for

example

that

average

stroke

width

is

more

affected

by

sampling

than

by

threshold

noise

Next

we

consider

the

effects

of

digitization

on

a

chain-code

representation

of

the

character

's

boundary

A

chain-code

consists

of

a

string

of

symbols

representing

the

vectors

joining

two

neighboring

pixels

along

the

boundary

of

a

shape

-LSB-

-RSB-

One

commonly

used

chaincode

employs

the

eight

directions

of

the

compass

-LRB-

see

Figure

-RRB-

Using

this

representation

a

character

's

boundary

is

encoded

as

a

string

of

the

digits

from

through

We

measure

the

difference

between

two

shapes

by

comparing

their

chain-codes

using

well-known

string

matching

techniques

-LSB-

-RSB-

Figure

shows

for

example

two

instances

of

the

letter

the

chain-code

for

each

and

the

difference

between

the

two

the

case

of

letters

such

as

O

that

have

two

contours

another

string

can

be

used

to

represent

the

inner

contour

original

edge

blurred

edge

ideal

threshold

positive

threshhold

shift

bitmap

bitmap

white

white

black

black

Figure

The

effect

of

threshold

variation

on

the

location

of

an

edge

images

in

terms

of

string

edit

distance

From

the

results

of

the

string

matching

we

compute

an

error

distribution

profile

along

the

chain-code

of

a

canonical

reference

character

We

would

expect

that

a

chain-code

representation

responds

to

sampling

variations

differently

than

to

other

sources

of

noise

such

as

noise

in

the

scanning

process

due

to

random

perturbations

in

the

threshold

Consider

for

example

a

horizontal

stroke

of

constant

width

-LRB-

e.g.

the

letter

-RRB-

A

shift

in

the

sampling

grid

may

cause

a

complete

row

of

black

pixels

to

turn

white

However

the

chain-code

for

the

result

will

differ

only

slightly

-LRB-

i.e.

only

at

the

corners

-RRB-

from

the

original

stroke

Hence

if

we

compute

a

histogram

of

string

edits

at

each

position

in

the

chain-code

we

would

expect

to

see

sharp

peaks

at

indices

corresponding

to

the

four

corners

while

the

variability

due

to

random

threshold

fluctuations

should

be

more

-LRB-

d

-RRB-

scanned

-LRB-

b

-RRB-

threshold

-LRB-

a

-RRB-

spatial

-LRB-

c

-RRB-

combined

Figure

Synthesized

and

real

character

bitmaps

-LRB-

a

-RRB-

-LRB-

d

-RRB-

-LRB-

b

-RRB-

-LRB-

c

-RRB-

Figure

Area

histograms

for

Computer

Modern

e

or

less

uniform

To

verify

this

hypothesis

we

generated

two

sets

of

experimental

data

both

based

on

characters

typeset

in

Helvetica

Synthesized

characters

produced

by

sampling

the

reference

character

bitmap

Real

characters

that

had

been

printed

and

scanned

For

our

studies

we

used

a

Ricoh

flat-bed

scanner

Under

our

assumptions

of

a

Gaussian

point

spread

function

and

a

Gaussian

perturbance

for

the

threshold

centered

at

we

estimated

the

standard

deviation

of

the

point

spread

function

by

scanning

a

perfect

step

edge

and

studying

the

shape

of

the

output

surface

curve

The

threshold

variance

was

obtained

by

scanning

a

flat

surface

with

gray-level

centered

around

a

given

value

The

standard

deviation

of

the

equivalent

displacement

of

the

sampling

spot

center

is

a

combination

of

both

the

point

spread

function

and

the

variation

in

threshold

-LRB-

see

-LSB-

-RSB-

-RRB-

The

experiments

were

run

with

three

different

character

patterns

e

and

M

identical

characters

were

printed

on

a

page

at

dpi

and

scanned

at

dpi

Two

sets

of

synthetic

data

were

generated

each

containing

samples

In

the

first

set

we

applied

-LRB-

c

-RRB-

-LRB-

b

-RRB-

-LRB-

a

-RRB-

-LRB-

d

-RRB-

Figure

Stroke-width

histograms

for

Computer

Modern

e

only

random

threshold

variation

In

the

second

set

the

samples

were

the

result

of

the

combined

effects

of

random

grid

shifts

and

threshold

variation

Figures

-LRB-

a

-RRB-

-LCB-

-LRB-

a

-RRB-

show

histograms

of

the

number

of

edits

performed

at

each

chaincode

position

for

the

copies

of

e

and

M

respectively

The

upper

half

of

each

figure

represents

the

synthetic

data

and

the

lower

half

the

real

data

As

can

be

seen

the

profiles

for

the

real

data

are

quite

different

from

those

for

the

synthetic

It

is

evident

that

threshold

variation

alone

accounts

for

little

of

the

distortion

we

observed

in

the

digitized

patterns

When

combined

with

spatial

sampling

noise

however

the

results

are

much

closer

to

the

real

data

Figures

-LRB-

b

-RRB-

-LCB-

-LRB-

b

-RRB-

show

histograms

of

the

number

of

edits

performed

at

each

chain-code

position

for

the

copies

of

e

and

M

respectively

As

before

the

upper

half

of

each

figure

represents

the

synthetic

data

and

the

lower

half

the

real

data

The

characters

generated

using

the

combined

spatial/threshold

model

seem

to

match

the

scanned

characters

quite

well

The

effects

of

sampling

noise

on

chain-code

representations

are

not

uniform

rather

they

exhibit

certain

structural

patterns

Each

chart

has

numerous

characteristic

peaks

In

Figure

-LRB-

b

-RRB-

for

example

we

see

that

most

of

the

variation

occurs

at

the

four

locations

corresponding

to

the

corners

of

the

letter

This

result

suggests

that

a

character

shape

-LRB-

b

-RRB-

chain

code

for

a

curve

-LRB-

a

-RRB-

encoding

scheme

Figure

Chain-code

for

boundary

representation

might

assume

a

small

number

of

primary

configurations

-LRB-

in

other

words

the

distribution

is

multi-modal

-RRB-

The

scanned

characters

still

seem

a

bit

richer

This

suggests

there

are

other

sources

of

noise

which

contribute

to

differences

in

the

chain-codes

Even

so

the

locations

of

most

of

the

peaks

are

duplicated

precisely

in

the

synthesized

characters

Conclusions

In

this

paper

we

have

explored

the

effects

of

random-phase

spatial

sampling

on

scanned

patterns

We

verified

that

the

size

of

a

pattern

-LRB-

i.e.

the

number

of

black

pixels

-RRB-

has

a

distinctly

multimodal

distribution

According

to

our

model

the

relative

heights

of

the

peaks

depend

on

minute

variations

in

sampling

resolution

character-dimension

and

stroke

width

Variations

in

the

latter

are

greater

than

can

be

accounted

for

by

i.i.d.

pixel

noise

We

demonstrated

that

there

exists

a

significant

amount

of

structure

in

the

variations

in

chaincode

representations

of

character

boundaries

Furthermore

we

showed

that

it

is

possible

to

statistically

predict

pattern

variation

as

a

function

of

ideal

shape

sampling

frequency

and

threshold

noise

Sampling

variation

played

a

role

in

an

earlier

study

of

ours

We

noted

that

when

a

page

of

characters

was

scanned

three

times

and

the

resulting

images

processed

through

an

OCR

system

each

exhibited

a

slightly

different

set

of

errors

-LSB-

-RSB-

By

applying

consensus

sequence

voting

to

the

three

sets

of

outputs

the

overall

error

rate

was

reduced

by

about

over

the

best

rate

observed

for

any

single

dataset

This

indicates

that

sampling

noise

can

be

mitigated

without

increasing

sampling

resolution

The

models

we

have

discussed

in

the

current

paper

may

help

better

explain

how

variations

in

the

shape

of

a

character

affect

the

performance

of

recognition

systems

At

this

early

stage

we

have

only

investigated

the

effects

of

sampling

noise

on

lowerlevel

features

-LRB-

i.e.

pixels

-RRB-

A

more

difficult

but

very

important

task

is

to

characterize

the

Reference

bitmapS

canned

bitmap

Chain-codes

Locations

of

string

edits

Edit

location

histogram

Figure

Using

string

matching

to

describe

the

differences

between

character

shapes

effects

of

sampling

on

higher-level

features

and

the

performance

of

vision

algorithms

and

systems

as

a

whole

One

such

preliminary

study

is

presented

in

-LSB-

-RSB-

A

goal

of

our

future

work

is

to

study

the

relationships

between

the

scanning

process

pattern

shapes

and

the

mathematical

algorithms

we

use

to

process

them

Acknowledgments

We

would

like

to

thank

Dr.

Tin

Kam

Ho

for

providing

the

character

outlines

we

used

in

some

of

our

studies

George

Nagy

gratefully

acknowledges

the

financial

support

of

the

Northern-Telecom/BNR

Educational

and

Research

Networking

Program

A

portion

of

this

work

was

conducted

at

the

New

York

State

Center

for

Advanced

Technology

-LRB-

CAT

-RRB-

in

Automation

and

Robotics

at

Rensselaer

Polytechnic

Institute

The

CAT

is

partially

funded

by

a

block

grant

from

the

New

York

State

Science

and

Technology

Foundation

Synthesized

Scanned

-LRB-

a

-RRB-

Synthesized

Scanned

-LRB-

b

-RRB-

Figure

String

edit

histogram

for

-LRB-

a

-RRB-

threshold

noise

only

-LRB-

b

-RRB-

combined

spatial/threshold

noise

Synthesized

Scanned

-LRB-

a

-RRB-

Synthesized

Scanned

-LRB-

b

-RRB-

Figure

String

edit

histogram

for

e

-LRB-

a

-RRB-

threshold

noise

only

-LRB-

b

-RRB-

combined

spatial/threshold

noise

50 100 150 200

Synthesized

Scanned

-LRB-

a

-RRB-

50 100 150 200

Synthesized

Scanned

-LRB-

b

-RRB-

Figure

String

edit

histogram

for

M

-LRB-

a

-RRB-

threshold

noise

only

-LRB-

b

-RRB-

combined

spatial/threshold

noise

References

-LSB-

-RSB-

H.

S.

Baird

Document

image

defect

models

In

H.

S.

Baird

H.

Bunke

and

K.

Yamamoto

editors

Structured

Document

Analysis

pages

-LCB-

SpringerVerlag

New

York

NY

-LSB-

-RSB-

H.

S.

Baird

Calibration

of

document

image

defect

models

In

Proceedings

of

the

Symposium

on

Document

Analysis

and

Information

Retrieval

pages

-LCB-

Las

Vegas

NV

April

-LSB-

-RSB-

H.

S.

Baird

Document

image

defect

models

and

their

uses

In

Proceedings

of

the

International

Conference

on

Document

Analysis

and

Recognition

pages

-LCB-

Tsukuba

Science

City

Japan

-LSB-

-RSB-

M.

Bokser

and

K.

Choy

Synthetic

training

for

OCR

In

Proceedings

of

the

DIMUND

Workshop

on

Page

Decomposition

Character

Recognition

and

Data

Standards

Harper

's

Ferry

WV

-LSB-

-RSB-

M.

Buchman

Distortion

modeling

for

document

images

In

Proceedings

of

the

DIMUND

Workshop

on

Page

Decomposition

Character

Recognition

and

Data

Standards

Harper

's

Ferry

WV

August

-LSB-

-RSB-

L.

Dorst

and

A.

W.

M.

Smeulders

Best

linear

unbiased

estimators

for

properties

of

digitized

straight

lines

IEEE

Transactions

on

Pattern

Analysis

and

Machine

Intelligence

-LCB-

-LSB-

E

-RSB-

T.

J.

Ellis

et

al.

Measurement

of

the

lengths

of

digitized

curved

lines

Computer

Vision

Graphics

and

Image

Processing

-LCB-

-LSB-

-RSB-

Jeffrey

Esakov

Daniel

P.

Lopresti

Jonathan

S.

Sandberg

and

Jiangying

Zhou

Issues

in

automatic

OCR

error

classification

In

Proceedings

of

the

Third

Annual

Symposium

on

Document

Analysis

and

Information

Retrieval

pages

-LCB-

Las

Vegas

NV

April

-LSB-

-RSB-

H.

Freeman

Computer

processing

of

line

drawing

images

Computer

Surveys

-LCB-

-LSB-

-RSB-

R.

M.

Haralick

and

L.

G.

Shapiro

Computer

and

Robot

Vision

volume

II

chapter

Addison-Wesley

-LSB-

-RSB-

K.

Ishii

Design

of

a

recognition

dictionary

using

artificially

distorted

characters

Systems

and

Computers

in

Japan

-LRB-

-RRB-

-LCB-

-LSB-

-RSB-

J.

Koplowitz

and

A.

M.

Brukstein

Design

of

perimeter

estimators

for

digitized

shapes

IEEE

Transactions

on

Pattern

Analysis

and

Machine

Intelligence

-LCB-

-LSB-

-RSB-

T.

Kanungo

R.

Haralick

and

I.

Phillips

Global

and

local

document

degradation

models

In

Proceedings

of

the

International

Conference

on

Document

Analysis

and

Recognition

pages

-LCB-

Tsukuba

Science

City

Japan

-LSB-

-RSB-

C.

N.

Liu

and

G.

L.

Shelton

Jr.

An

experimental

investigation

of

a

mixed-font

print

recognition

system

IEEE

Transactions

on

Electronic

Computers

-LCB-

-LSB-

-RSB-

Y.

Li

D.

Lopresti

and

A.

Tomkins

Validation

of

document

image

defect

models

for

optical

character

recognition

In

Proceedings

of

the

Third

Annual

Symposium

on

Document

Analysis

and

Information

Retrieval

pages

-LCB-

Las

Vegas

NV

April

-LSB-

-RSB-

Daniel

Lopresti

and

Jiangying

Zhou

Using

consensus

sequence

voting

to

correct

OCR

errors

In

Proceedings

of

the

IAPR

Workshop

on

Document

Analysis

Systems

pages

-LCB-

Kaiserslautern

Germany

-LSB-

-RSB-

G.

Nagy

On

the

auto-correlation

function

of

noise

in

sampled

typewritten

characters

In

IEEE

Region

III

Convention

Record

New

Orleans

LA

-LSB-

-RSB-

G.

Nagy

Validation

of

simulated

OCR

data

sets

In

Proceedings

of

the

Third

Annual

Symposium

on

Document

Analysis

and

Information

Retrieval

pages

-LCB-

Las

Vegas

NV

April

-LSB-

-RSB-

T.

Pavlidis

Effects

of

distortions

on

the

recognition

rate

of

a

structural

OCR

system

In

Proceedings

of

the

Conference

on

Computer

Vision

and

Pattern

Recognition

pages

-LCB-

Washington

DC

-LSB-

-RSB-

T.

Pavlidis

J.

Swartz

and

Y.

P.

Wang

Fundamentals

of

bar

code

information

theory

In

IEEE

Computer

pages

-LCB-

-LSB-

-RSB-

Prateek

Sarkar

Random

phase

spatial

sampling

effects

in

digitized

patterns

Master

's

thesis

Rensselaer

Polytechnic

Institute

Troy

NY

-LSB-

-RSB-

R.

A.

Wagner

and

M.

J.

Fischer

The

string-to-string

correction

problem

Journal

of

the

ACM

-LRB-

-RRB-

-LCB-

-LSB-

-RSB-

Jiangying

Zhou

and

Daniel

Lopresti

Repeated

sampling

to

improve

classifier

accuracy

In

Proceedings

of

the

IAPR

Workshop

on

Machine

Vision

Applications

pages

-LCB-

Kawasaki

Japan

December

B I O O B I I O O O O O O O O O O O O O O O O O O O O O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

optical character recognition
spatial sampling

document noise models
image digitization