EC

E/O

PT

I533 Digital Im

age Processing class notes 288 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

sto

rag

e v

ers

us tra

nsm

issio

n a

pp

lica

tion

s

sto

rag

e v

ers

us tra

nsm

issio

n a

pp

lica

tion

s

sou

rce

ima

ge

sou

rce c

od

er

sou

rce d

ecod

er sto

rag

e

retrie

ved

ima

ge

sou

rce

ima

ge

sou

rce c

od

er

sou

rce d

ecod

er

retrie

ved

ima

ge

ch

an

nel c

od

er

ch

an

nel d

ecod

er

ch

an

nel

Motiv

atio

n

•La

rge a

mou

nt o

f da

ta in

ima

ges

Colo

r vid

eo: 2

00

Mb

/sec

La

nd

sa

t TM m

ultis

pectra

l sa

tellite

ima

ge: 2

00

MB

•H

igh

pote

ntia

l for c

om

pre

ssio

n

Red

un

da

ncy (a

ka

corre

latio

n) in

ima

ges – s

pa

tial, te

mp

ora

l, sp

ectra

l

EC

E/O

PT

I533 Digital Im

age Processing class notes 289 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

Join

t pro

ba

bility

plo

ts (s

ca

tterg

ram

s) b

etw

een

p

ixels

with

giv

en

horiz

on

tal s

pa

cin

g

∆ =

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

•H

igh

corre

latio

n fo

r clo

se

neig

hb

ors

•A

s p

ixel s

ep

ara

tion

in

cre

ases, c

orre

latio

n

decre

ases

EC

E/O

PT

I533 Digital Im

age Processing class notes 290 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

Lossy c

od

ing

•Som

e a

ccep

tab

le lo

ss o

f da

ta, w

ithou

t loss o

f “in

form

atio

n”

•Erro

r mea

su

res

Mea

n S

qu

are

Erro

r

Root M

ea

n S

qu

are

Erro

r

Norm

aliz

ed

Mea

n S

qu

are

Erro

r

Sig

na

l-to-N

ois

e R

atio

Pea

k-to

-pea

k S

NR

•Pro

ble

ms

Erro

r mea

su

res d

on

’t em

ph

asiz

e v

isu

ally

imp

orta

nt fe

atu

res s

uch

as c

on

trast e

dg

es

• C

an

imp

rove c

orre

latio

n o

f an

y o

f these e

rror m

ea

su

res w

ith v

isu

al q

ua

lity b

y re

stric

ting

to

“ed

ge p

ixels

” o

nly

How

to d

efin

e a

nd

qu

an

tify “

ima

ge q

ua

lity?”

MSE

DN

()

Variance

f̂f

–(

)=

RM

SED

N(

)M

SE

=

NM

SE%(

)100

MSE

()

Variance

⁄f()

=

SNR

dB(

)10

100N

MSE

⁄(

)log

=

PSN

RdB

()

10fm

axfm

in–

() 2

MSE

⁄[

]log

=

EC

E/O

PT

I533 Digital Im

age Processing class notes 291 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

exa

mp

le w

ith JP

EG c

od

ing

1/8

1/1

6

1/3

2

NM

SE =

0.1

6%

NM

SE =

0.4

2%

NM

SE =

1.0

5%

RM

SE =

7.3

7 D

N

RM

SE =

4.6

3 D

N

RM

SE =

2.9

1 D

N

SN

R =

27

.9d

B

SN

R =

23

.8d

B

SN

R =

19

.8d

dB

EC

E/O

PT

I533 Digital Im

age Processing class notes 292 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

Ru

n-L

en

gth

Cod

ing

•Sim

ple

, ima

ge d

om

ain

, lossy

com

pre

ssio

n a

lgorith

m

•Exp

loits

neig

hb

orin

g p

ixel

corre

latio

n, lin

e-b

y-lin

e

Work

s b

est fo

r sim

ple

, low

-freq

uen

cy

con

ten

t, nea

r-bin

ary

ima

ges, e

.g. fa

xes

•D

N th

resh

old

con

trols

qu

ality

loss

an

d c

om

pre

ssio

n ra

te

•Look fo

r “ru

ns”

con

tigu

ou

s p

ixels

with

sim

ilar v

alu

es (w

ithin

th

resh

old

of s

tartin

g p

ixel v

alu

e)

•Cod

e s

tartin

g p

ixel v

alu

e (Q

bits

) a

nd

len

gth

of lin

e (≤

log

N/lo

g2

b

its)

typ

ica

l beh

avio

r (ima

ge d

ep

en

den

t)

T

compression ratio

T

number of runs

T

average runlength 0 00

“intrinsic” runlength

EC

E/O

PT

I533 Digital Im

age Processing class notes 293 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

Lossle

ss C

od

ing

•N

o d

ata

loss

•M

inim

al c

om

pre

ssio

n (ty

pic

ally

2:1

)

•Exa

mp

le a

lgorith

ms

Ru

n-L

en

gth

(with

zero

thre

sh

old

)

Lem

pel-Z

iv-W

els

h (L

ZW

)

Hu

ffma

n C

od

ing

EC

E/O

PT

I533 Digital Im

age Processing class notes 294 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

Com

pon

en

ts o

f sou

rce c

od

er

•D

ata

tran

sfo

rma

tion

wa

vefo

rm c

od

er

tran

sfo

rm c

od

er

ima

ge m

od

el c

od

er

•Q

ua

ntiz

atio

n

bits

, tran

sfo

rm c

oeffic

ien

ts, o

r mod

el p

ara

mete

rs

•Cod

ew

ord

Assig

nm

en

t

un

iqu

e b

it strin

g fo

r ea

ch

qu

an

tized

pa

ram

ete

r

EC

E/O

PT

I533 Digital Im

age Processing class notes 295 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

Wa

vefo

rm C

od

ing

•Pu

lse C

od

e M

od

ula

tion

(PCM

)

Ima

ge in

ten

sity

qu

an

tized

by u

nifo

rm

qu

an

tizer

At lo

w b

it rate

s (ty

pic

ally

less th

an

4 b

its/

pix

el), q

ua

ntiz

atio

n n

ois

e a

pp

ea

rs a

s

fals

e c

on

tou

rs in

are

as o

f low

inte

nsity

slo

pe

16 levels

8 levels

4 levels

EC

E/O

PT

I533 Digital Im

age Processing class notes 296 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

Exa

mp

le 2

-bit u

nifo

rm q

ua

ntiz

er

3∆/2

−3

∆/2

∆/2

−∆/2

+∆−∆

bits

00

01

10

11

in

ou

t

∆

=1

MSE =

0.0

62

8

in codew

ordout

error

1.211

1.5-0.3

1.511

1.50

-200

-1.5-0.5

-0.501

-0.50

0.510

0.50

0.610

0.50.1

-0.7501

-0.5-0.25

1.211

1.5-0.3

Alte

rna

te re

pre

sen

tatio

n:

−3

∆/2

−∆/2

∆/2

3∆/2

+∆−∆

bits

00

01

10

11

mid

-rise u

nifo

rm q

ua

ntiz

er

mid

-trea

d u

nifo

rm q

ua

ntiz

er

−∆/2

∆/2

3∆/2

+∆−∆

bits

00

00

10

10

01

01

−3

∆/2

0

00

1

EC

E/O

PT

I533 Digital Im

age Processing class notes 297 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

•PCM

with

Non

un

iform

Qu

an

tiza

tion

Assig

n q

ua

ntiz

atio

n le

vels

accord

ing

to im

ag

e in

ten

sity

dis

tribu

tion

Sm

all im

pro

vem

en

t for ty

pic

al im

ag

es

• D

ep

en

ds o

n n

on

un

iform

ity o

f ima

ge h

isto

gra

m

For e

xa

mp

le, u

se C

DF a

s n

on

linea

r tran

sfo

rm, i.e

. his

tog

ram

eq

ua

liza

tion

• A

ssig

ns m

ore

levels

wh

ere

there

are

more

pix

els

sou

rce

ima

ge

non

linea

rcod

ed

ima

ge

un

iform

PCM

tran

sfo

rmn

on

linea

rtra

nsfo

rm-1

EC

E/O

PT

I533 Digital Im

age Processing class notes 298 D

r. Robert A

. Schowengerdt 2003

IM

AGE C

OD

ING

PCM

with

Pseu

do-n

ois

e

•A

dd

ran

dom

nois

e to

ima

ge b

efo

re P

CM

•Su

btra

ct s

am

e ra

nd

om

nois

e a

fter P

CM

•R

em

oves s

pa

tial c

orre

latio

n o

f qu

an

tiza

tion

nois

e

sou

rce

ima

ge

decod

ed

ima

ge

un

iform

PCM

η(m

,n)

EC

E/O

PT

I533 Digital Im

age Processing class notes 299 D

r. Robert A

. Schowengerdt 2003

IMA

GE C

OD

ING

exa

mp

le w

ith 3

bits

/pix

el a

nd

un

iform

ran

dom

nois

e

un

iform

min

us n

ois

e

ad

d n

ois

ePCM

(3b

its/p

ixel)

PCM

(3b

its/p

ixel)

EC

E/O

PT

I533 Digital Im

age Processing class notes 300 D

r. Robert A

. Schowengerdt 2003

IMA

GE C

OD

ING

Delta

Mod

ula

tion

•Cod

e d

iffere

nce o

f neig

hb

orin

g

pix

els

with

1 b

it

Assu

me s

om

e “

sca

n” p

atte

rn in

ima

ge

•R

ed

uces s

pa

tial c

orre

latio

n b

efo

re

cod

ing

exa

mp

le ro

w-b

y-ro

w im

ag

e s

ca

n

pa

ttern

EC

E/O

PT

I533 Digital Im

age Processing class notes 301 D

r. Robert A

. Schowengerdt 2003

IMA

GE C

OD

ING

Exa

mp

le

ima

ge:

67

88

59

10

8

68

97

79

11

9

diffe

ren

ces:

61

10

-4-1

20

12

1-2

-2-2

22

diffe

ren

ce ≥

0: c

od

ew

ord

= 1

diffe

ren

ce < 0

: cod

ew

ord

= 0

indifference

codeword

outerror

66

11

-0.3

71

17

0

81

18

-0.5

80

19

0

102

10

9-1

00.1

5-4

0-0.25

61

1-0.3

82

1

91

1

7-2

0

92

1

112

1

9-2

0

7-2

0