13imagecompression-120321055027-phpapp02.pptx

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DIGITAL IMAGE PROCESSING

IMAGE COMPRESSION

byParesh Kamble



Introducton

Ima!e Com"resson# It s the Art $ Scence o%reducn! the amount o% data re&ured tore"resent an ma!e'

It s the most use%ul and commercally success%ultechnolo!es n the (eld o% D!tal Ima!eProcessn!'

The number o% ma!es com"ressed anddecom"ressed daly s nnumerable'



Introducton To understand the need %or com"act ma!e

re"resentaton) consder the amount o% datare&ured to re"resent a * hour Standard De(nton+SD, usn! -*. / 01. / *0 bt "/el arrays'

A 2deo s a se&uence o% 2deo %rames 3here each%rame s a %ull color stll ma!e'

4ecause 2deo "layer must ds"lay the %ramesse&uentally at rates near 5.%"s) SD 2deo data

must be accessed at

5.%"s / +-*./01.,""% / 5b"" 6 57)7.0)... b"s

%"s 8 %rames "er second)% 8 /els er %rame)



Introducton

Thus a * hour mo2e conssts o%

57)7.0)... b"s / +9.*, s"h / * hrs : *'*0 / 7.77 bytes'

OR

**0G4 o% data

s"h 6 second "er hour

T3enty se2en 1';G4 dual layer D<Ds are neededto store t'

To "ut a *hr mo2e on a sn!le D<D) each %ramemust be com"ressed by a %actor o% around *9'5'

The com"resson must be e2en h!her %or =D)3here ma e resoluton reach 7>*. / 7.1. / *0



Introducton@eb "a!e ma!es $ =!hresoluton d!tal

camera "hotos also are also com"ressed to sa2estora!e s"ace $ reduce transmsson tme'

Resdental Internet connecton del2ers data ats"eeds ran!n! %rom ;9Bb"s +con2entonal "hone

lne, to more than 7*mb"s +broadband,'

Tme re&ured to transmt a small 7*1 / 7*1 / *0bt %ull color ma!e o2er ths ran!e o% s"eed s%rom -'. to .'.5 sec'

Com"resson can reduce the transmsson tme bya %actor o% around * to 7. or more'

Smlarly) number o% uncom"ressed %ull color

ma!es that an 1 Me!a"/el d!tal camera canstore on a 7G4 Memory card can be ncreased'



Introducton Alon! 3th these a""lcatons ) ma!e

com"resson "lays an m"ortant role n manyother areas ncludn!#



undamentalsData Com"resson# It re%ers to the "rocess o%

reducn! the amount o% data re&ured tore"resent a !2en &uantty o% n%ormaton'

Data <s

In%ormatonData and In%ormaton are not the same thn!

data are the means by 3hch n%ormaton scon2eyed'

4ecause 2arous amount o% data can be used to



undamentals



undamentals Let b $ b denote the number o% bts n t3o

re"resentatons o% the same n%ormaton) therelat2e data redundancy R o% the re"resentaton3th b bts s

•

R 6 7 8 +7?C, 3here) C commonly called the com"ressonrato) s de(ned as

• C 6 b ? b

I% C 6 7. +or 7.#7,) %or lar!er re"resentaton has7. bts o% data %or e2ery 7 bt o% data n smallerre"resentaton'

So) R 6 .'>) ndcatn! that >.F o% ts data sredundant'



undamentals *D ntensty arrays suers %rom 5 "rnc"al ty"es

o% data redundances#

7, Codn! redundancy# A code s a system o%symbols used to re"resent a body o% n%ormaton

or sets o% e2ents'

Each "ece o% e2ent s ass!ned a code 3ord+code symbol,' The number o% symbols n eachcode 3ord s ts len!th'

The 1bt codes that are used to re"resent thentenstes n most *D ntensty arrays contanmore bts than are needed to re"resent the

ntenstes'



undamentals

*, S"atal $ Tem"oral redundancy#

4ecause the "/els o% most *D ntensty arrays arecorrelated s"atally) n%ormaton s re"lcatedunnecessarly'

In 2deo se&uence) tem"orally correlated "/elsalso du"lcate n%ormaton'

5, Irrele2ant In%ormaton#

Most *D ntensty arrays contan n%ormaton thats !nored by the human 2sual system' It sredundant n the sense that t s not used'



undamentals

7, Codn! Redundancy#

) Assume a dscrete random 2arable rB n nter2alH. 8 L7 s used to re"resent the ntenstes o% anM / N ma!e'

) Also the each rB occurs 3th "robablty "r +rB,'

) "r+rB, 6 nB ? MN B 6 .) 7) *) JJJJ'L7 +a,

) @here) L s no' o% ntensty 2alues $nB s no' o% tmes Bth ntensty a""ears n the

ma!e'

I% no' o% bts used to re"resent each 2alue o% rB s

l+rB,) then a2! no o% bts re&ured to re"resent

each "/el s L 7



undamentals I% the ntenstes are re"resented usn! a natural

mbts (/ed len!th code) the R=S reduces to mbts'

'e' La2! 6 m 3here m s substtuted %or l+rB,'

Constant m can be taBen out the summaton

lea2n! only sum o% "r+rB, %or . B L7) 3hch6 7'

rB "r+rB, code 7 l7+rB, code *

l*+rB,r1- 6 1- .'*; .7.7.777 1 .7*

r7*1 6 7*1 .'0- 7....... 1 77

r719 6 719 .'*; 77...7.. 1 ...



undamentals

@th res"ect to the abo2e table) I% a natural 1bt

bnary code s used to re"resent ts 0 "ossblentenstes) La2! 6 1) co l7+rB, 6 1 bts %or all rB'

On the other hand) I% code * scheme s used) the a2!len!th o% encoded "/els s)

La2! 6 .'*;+*, .'0-+7, .'*;+5, .'.5+5, 6 7'17bts'

Total no' o% bts r&d to re"resent entre ma!e 6 MNLa2!

6 *;9 / *;9 / 7'17 6 771)9*7

Resultn! com"ressonC 6 *;9 / *;9 / 1 ? 771)9*7 6 1 ? 7'17 : 0'0*Relat2e redundancyR 6 7 8 7?0'0* 6 .'--0 Thus) --'0F o% data n or!nal 1bt *D ntensty array

s redundant'



delty Crteradelty Crtera#•

Remo2al o% rrele2ant 2sual n%ormaton n2ol2es aloss o% real or &uanttat2e ma!e n%ormaton'

• Snce n%ormaton s lost) a means o% &uant%yn! thenature o% loss s needed'

Obect2e (delty crtera Subect2e (deltycrtera

Obect2e (delty crtera# @hen n%ormaton loss canbe e/"ressed as a mathematcal %uncton o% n"ut $out"ut o% a com"resson "rocess' E! RMS error

bet3een * ma!es'Error bet3een t3o ma!ese+/) y, 6 %+/) y, 8 %+/) y,So) total error bet3een t3o ma!es M7 N7

H%+/) y, 8 %+/) y, /6. y 6 .



delty Crtera

RMS error s !2en by

M7 N7

erms 6 H+7?MN, H%+/) y, 8 %+/) y,*7?*

/6. y 6 .

I% %+/) y, s consdered to be the sum o% or!nalma!e %+/) y, $ an error or nose s!nal e+/) y,)the Mean S&uare SNR o% out"ut ma!e denotedby SNRrms can be de(ned as

MA7 NA7

%+/) y,*

SNRrms 6 /6. y 6 .

MA7 NA7

H%+/) y, 8 %+/) y,*

/6. y 6 .



delty Crtera Subect2e (delty crtera#•

A Decom"ressed ma!e s "resented to a crosssecton o% 2e3ers and a2era!n! ther e2aluatons'

• It can be done by usn! an absolute ratn! scaleOr

• 4y means o% sde by sde com"arsons o% %+/) y, $%+/) y,'

• Sde by Sde com"arson can be done 3th a scale

such as Q5) *) 7) .) 7) *) 5to re"resent the subect2e 2aluatons

Qmuch 3orse) 3orse) sl!htly 3orse) the same)sl!htly better) better) much better res"ect2ely'



Ima!e Com"resson Models• In"ut ma!e %+/)J'', s %ed nto the encoder) 3hch

creates a com"ressed re"resentaton o% n"ut'

• It s stored %or %uture %or later use or transmtted%or stora!e and use at a remote locaton'

• @hen the com"ressed ma!e s !2en to decoder) areconstructed out"ut ma!e %+/)J'', s !enerated'

• In stll ma!e a""lcatons) the encoded n"ut anddecoder out"ut are %+/) y, $ %+/) y, res"'

• In 2deo a""lcatons) they are %+/) y) t, $ %+/) y) t,3here t s tme'

• I% both %unctons are e&ual then the system scalled lossless) error %ree' I% not then t s re%erred to

as lossy '



Ima!e Com"resson Models

Ma""eruante

rSymbolcoder

SymbolDecode

r

In2erseMa""er




Encodn! or Com"resson "rocess#

Encoder s used to remo2e the redundancesthrou!h a seres o% 5 nde"endent o"eratons'

Mapper# It trans%orms %+/)J, nto a %ormatdes!ned to reduce s"atal and tem"oralredundances'

• It s re2ersble• It may ? may not reduce the amount o% data to

re"resent ma!e'

E/' Run Len!th codn!

• In 2deo a""lcatons) ma""er uses "re2ous

%rames to remo2e tem"oral redundances'




Quantizer: It Bee"s rrele2ant n%ormaton out o%

com"ressed re"resentatons'

• Ths o"eraton s rre2ersble'

• It must be omtted 3hen error %ree com"ressons desred'

• In 2deo a""lcatons) bt rate o% encoded out"uts o%ten measured and used to adust the

o"eraton o% the &uanter so that a"redetermned a2era!e out"ut s mantaned'

• The 2sual &ualty o% the out"ut can 2ary %rom

%rame to %rame as a %uncton o% ma!e content'




Symbol Encoder# Generates a (/ed or 2arable

len!th code to re"resent the &uanter out"utand ma"s the out"ut n accordance 3th thecode'

• Shortest code 3ords are ass!ned to the most%re&uently occurrn! &uanter out"ut 2alues'

Thus mnmn! codn! redundancy'

• It s re2ersble'

• "on ts com"leton) the n"ut ma!e has been"rocessed %or the remo2al o% all 5 redundances'




Decoding or Decompression process#

• uantaton results n rre2ersble loss) ann2erse &uanter blocB s not ncluded n thedecoder blocB'



Some 4asc Com"resson MethodsHufman Coding#•

Most "o"ular techn&ue %or remo2n! codn!redundances'

• It yelds smallest "ossble code symbol "er sourcesymbol'

Or!nal Source Source reductonSymbol Probablty 7 * 5 0

a* .'0 .'0 .'0 .'0 .'9 a9 .'5 .'5 .'5 .'5 .'0 a7 .'7 .'7 .'* .'5

a0 .'7 .'7 .'7 a5 .'.9 .'7

a; .'.0



Some 4asc Com"resson MethodsHufman Coding#

Or!nal Source Source reductonSymbol Probablty Code 7 * 5

0

a* .'0 7 .'0 7 .'0 7 .'0 7.'9 .

a9 .'5 .. .'5 .. .'5 .. .'5 ..

.'0 7 a7 .'7 .77 .'7 .77 .'* .7. .'5 .7

a0 .'7 .7.. .'7 .7.. .'7 .77

a5 .'.9 .7.7. .'7 .7.7 a; .'.0 .7.77

La2! 6 +.'0,+7, +.'5,+*, +.'7,+5, +.'.9,+;, +.'.0,+;,

6 *'* bts ? "/el'



Some 4asc Com"resson Methods

Hufman Coding#•

It s nstantaneous'• Co each code 3ord n a strn! o% code symbols

ca be decoded 3thout re%erencn! succeedn!symbols'

• It s un&uely decodable'• Co any strn! o% code symbols can be decoded

by e/amnn! nd2dual symbols o% strn! %romle%t to r!ht'

E/' .7.7..7777..



Some 4asc Com"resson MethodsHufman Coding#•

It s nstantaneous'• Co each code 3ord n a strn! o% code symbols ca

be decoded 3thout re%erencn! succeedn! symbols'

• It s un&uely decodable'

• Co any strn! o% code symbols can be decoded bye/amnn! nd2dual symbols o% strn! %rom le%t tor!ht'

E/' .7.7. .77 7 7 ..

rst 2ald code#.7.7. 8 a5).77 8 a7)

Thus) com"letely decodn! the messa!e) 3e !et)

a5a7a*a*a9




Arthmetc codn!#

It !enerates non blocB codes'One to One corres"ondence bet3een source

symbols and code 3ords does not e/st'Instead) an entre se&uence o% source symbols s

ass!ned a sn!le arthmetc code'Code 3ord de(nes an nte!er o% real numbers

bet3een . $ 7'

As No' o% symbols n ms!'

nter2al to re"resent tno' o% bts to

re"resent n%oEach symbol o% ms! se o% nter2al n

accordance 3th ts "robablty o% occurrence'




4asc Arthmetc codn! "rocess#

; symbol messa!e) a7a*a5a5a0 %rom 0 symbolsource s coded'

SourceSymbol

Probability InitialSubinterval

a7 .'* H.'.) .'*,

a* .'* H.'*) .'0,

a5 .'0 H.'0) .'1,

a0 .'* H.'1) 7'.,



Some 4asc Com"resson MethodsArthmetc codn!# a7 a* a5 a5 a0

7 .'* .'.1 .'.-* .'.911 a0 a0 a0 a0

a0

a5 a5 a5 a5a5

a* a* a* a*a*

a7 a7 a7 a7a7

. . .'.0 .'.;9 .'.9*0




7 .'* .'.1 .'.-* .'.911 a0 a0 a0 a0

a0

a5 a5 a5 a5a5

a* a* a* a*a*

a7 a7 a7 a7a7

. . .'.0 .'.;9 .'.9*0



Some 4asc Com"resson MethodsArthmetc codn!# Encodn! Se&uence a7 a* a5 a5 a0

7 .'* .'.1 .'.-* .'.911 a0 a0 a0 a0

a0

a5 a5 a5 a5a5

a* a* a* a*a*

a7 a7 a7 a7a7

. . .'.0 .'.;9 .'.9*0




The (nal messa!e symbol narro3s to H.'.9-;*)

.'.911,'

Any number bet3een ths nter2al can be used tore"resent the messa!e'

E!' .'.91

5 decmal d!ts are used to re"resent the ; symbolmessa!e'




!" Coding:

LU@ 8 Lem"elU2@elch codn!

Error %ree com"resson a""roach that alsoaddresses s"atal redundances n an ma!e'

It ass!ns (/edlen!th code 3ords to 2arablelen!th se&uences o% source symbols'

It re&ures no "ror Bno3led!e o% "robablty o%occurrence o% the symbols to be encoded'




LU@ Codn!#

It s conce"tually 2ery sm"le'

Intally) a codebooB or dctonary contann! thesource symbols to be coded s constructed'

or an 1bt 4@ ma!es) the (rst *;9 3ords o%dctonary are ass!ned to ntenstes .) 7) *) J')*;;'



Some 4asc Com"resson MethodsLU@ Codn!#

Consder the 0 / 0 1bt ma!e ha2n! a 2ertcal ed!e' 5> 5> 7*9 7*9 5> 5> 7*9 7*9 5> 5> 7*9 7*9 5> 5> 7*9 7*9

A ;7*3ord dctonary 3th %ollo3n! content sassumed#

Dctonary Locaton Entry . . 7 7 # # # #

*;; *;; *;9 ' ' ;77



Some 4asc Com"resson MethodsCurrently P/el 4en! Encoded Dctonary DctonaryReco!ned Processed Out"ut Locaton Entry

Se&uence 5>

5> 5> 5> *;9 5>5> 5> 7*9 5> *;- 5>7*9 7*9 7*9 7*9 *;1 7*97*9 7*9 5> 7*9 *;> 7*95>

5> 5> 5>5> 7*9 *;9 *9. 5>5>7*9 7*9 7*97*97*9 5> *;1 *97 7*97*95> 5> 5>5>5> 7*9

5>5>7*9 7*9 *9. *9* 5>5>7*97*9 7*9 5>7*95> 5> *;> *95 7*95>5> 5> 7*95>7*9 7*9 *;- *90 5>7*97*9 7*9 7*9




n&ue %eature o% LU@ codn!#

Codn! dctonary or code booB s created 3hledata are ben! encoded'



Some 4asc Com"resson Methods$it%plane coding:

Another eect2e method to reduce nter"/elredundances'

Ima!es bt "lanes are "rocessed nd2dually'

4ased on decom"osn! a multle2el +monochrome ?color, ma!e nto a seres o% bnary ma!es $com"ressn! each bnary usn! any bnarycom"resson method'

4t "lane decom"oston# Gray le2els o% an mbt !ray le2el ma!e can be

re"resented n %orm o% base * "olynomal'

am7*m7am**m*JJ''a7*7a.*. JJJ+7,



Some 4asc Com"resson Methods A sm"le method o% decom"osn! the ma!e nto

a collecton o% bnary ma!e s to se"arate the mcoeVcents o% the "olynomal nto m7 bt "lanes'

Dsad2anta!e#

Small chan!es n !ray le2el can ha2e s!n(cantm"act on com"le/ty o% bt "lanes'

E/' I% t3o adacent "/els ha2e ntensty o% 7*- +.7777777, and 7*1 +7.......,) e2ery bt "lane3ll contan a corres"ondn! . to 7 +or 7 to .,transton'



Some 4asc Com"resson MethodsAlternate decom"oston a""roach#

Reduces the eect o% small !ray le2el 2aratons'

Re&ures the re"resentaton o% ma!e nto mbt !raycode'

mbt !ray code !m7J''!*!7!. can be com"uted %rom! 6 a /or a7 . m*

!m7 6 am7

Ths code has un&ue "ro"erty that success2e code

3ords der by only 7 bt "oston'

Small chan!es n !ray le2el are less lBely to aectall m bt "lanes'

E/' 7*- +77......, $ 7*1 +.7......,'



Some 4asc Com"resson Methods• Althou!h Run len!th codn! s n tsel% an eect2e

method o% com"ressn! an ma!e) addtonalcom"resson can be realed by 2arablelen!th codn!'

• 4lacB $ 3hte run len!ths may be coded se"aratelyusn! 2arablelen!th codes'

E/' I% a re"resent a blacB run o% len!th ) 3e can estmatets "robablty'

• The a""ro/mate runlen!th entro"y o% the ma!e s# =RL 6 +=. =7, ? +L. L7,

•

3here) L. $ L7 denote a2era!e 2alues o% blacB $ 3hterun len!ths res"'

• Abo2e e&uaton also "ro2des an estmate o% thea2era!e no' o% bts "er "/el re&ured to code the runlen!ths n a bnary ma!e'




ossless predictive coding#

• 4ased on elmnatn! the nter"/el redundanceso% closely s"aced "/els by e/tractn! $ codn!only the ne3 n%ormaton n each "/el'

•

Ne3 n%ormaton# derence bet3een the actual $"redcted 2alue o% that "/el'



Some 4asc Com"resson Methods• !ure sho3s basc com"onent o% a lossless"redct2e codn! system'

• It conssts o% an encoder $ a decoder eachcontann! an dentcal "redctor'

• As each success2e "/el o% n"ut ma!e %+n, s

ntroduced to the encoder) "redctor !enerates tsantc"ated 2alue'

Out"ut o% the "redctor s then rounded to thenearest nte!er %+n,bar $ used to %orm the

derence or "redcton error'



Some 4asc Com"resson Methods• It s coded usn! a 2arable len!th to !enerate the ne/t

element o% the com"ressed data stream'

• The decoder reconstruct the %n %rom the rece2ed2arablelen!th code 3ords $ "er%orm the n2erseo"eraton

• %+n, 6 e+n, %+n,bar

• %+n,bar s !enerated by "redcton %ormed by a lnearcombnaton o% m "re2ous "/els'

m

%+n,bar 6 roundH X %+n, 3here) m 8 order o% lnear

"redctor 6 7

round 8 %uncton used to denote roundn!

X 8 %or 6 7) *) 5) J'' m are "redcton coeVcents'




Lossy Predct2e codn!#




Lossy Predct2e codn!#•

In ths method 3e add a &uanter to the lossless"redct2e codn! model'

• It re"laces the nearest nte!er %uncton $ s "lacedbet3een symbol encoder $ "ont 3here "redcton

error %orms'

• It ma"s the "redcton error nto a lmted ran!e o%out"uts denoted by Y+n,) 3hch establsh the amounto% com"resson $ dstorton'

• In order to accommodate the nserton o% the&uantaton ste") the error %ree encoder must bealtered so that the "redctons by the encoder $

decoder are e&u2alent'

h d




Lossy Predct2e codn!#

• Ths s accom"lshed by "lacn! the "redctor3thn a %eedbacB loo") 3here ts n"ut Z+n,dot s!enerated as a %uncton o% "ast "redctons $&uanted errors'

Z+n,dot 6 e+n,dot %+n,bar

• Ths closed loo" con(!uraton "re2ents error

buldu" at the decoders out"ut'

S C h d




uestons asBed n RTMN e/ams

7, Enlst derent ma!e com"resson techn&ues'E/"lan any one n bre%'*, =uman codn! al!orthm %or ma!e com"resson5, aeou[0, E/"lan !eneraled ma!e com"resson model

3th neat blocB da!ram';, Dscuss about ma!e com"resson' E/"lan the

need o% ma!e com"resson n ma!e "rocessn!'9, Short note on ma!e com"resson standard'

-, Short note on Lossy Predct2e codn!'1, Short note on LU@ codn!'>, E/"lan 2arous ty"es o% data redundances used

n d!tal ma!e com"resson'

13imagecompression-120321055027-phpapp02.pptx

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