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The JPEG Standard

Jiun-De Huang

E-mail: [email protected]

Graduate Institute o !ommuni"ation Engineering#ational $aiwan %ni&ersit'( $ai)ei( $aiwan( *+!

Abstract

J,EG Joint ,otogra)i" E/)erts Grou) is an international "om)ression

standard or "ontinuous-tone still image( ot gra's"ale and "olor. $is standard is

designed to su))ort a wide &ariet' o a))li"ations or "ontinuous-tone images.

e"ause o te distin"t re3uirement or ea" o te a))li"ations( te J,EG standard

a&e two asi" "om)ression metods. $e D!$-ased matod is s)e"iied or loss'

"om)ression( and te )redi"ti&e matod is s)e"iied or lossless "om)ression.

sim)le loss' te"ni3ue "alled aseline( wi" is a D!$-ased metods( as een

widel' used toda' and is sui"ient or a large numer o a))li"ations. In tis )a)er(we will sim)l' introdu"e te J,EG standard and o"uses on te aseline metod.

1 Introduction

$e J,EG standard is a "ollaoration among te International

$ele"ommuni"ation %nion I$%( International +rganiation or 6tandardiation

I6+( and International Ele"trote"ni"al !ommission IE!. Its oi"ial name is

7I6+8IE! 1091-1 Digital "om)ression and "oding o "ontinuous-tone still image7(

and 7I$%-$ *e"ommendation $.17. J,EG a&e te ollowing modes o o)erations :

a Lossless mode:$e image is en"oded to guarantee e/a"t re"o&er' o e&er' )i/el

o original image e&en toug te "om)ression ratio is lower tan te loss'

modes.

Sequential mode:It "om)resses te image in a single let-to-rigt( to)-to-ottom

s"an.

" Progressive mode:It "om)resses te image in multi)le s"ans. en transmission

time is long( te image will dis)la' rom indistin"t to "lear a))earan"e.

d Hierarchical mode:!om)ress te image at multi)le resolutions so tat te lower

resolution o te image "an e a""essed irst witout de"om)ressing te wole

resolution o te image.

$e last tree D!$-ased modes ( "( and d are loss' "om)ression e"ause

)re"ision limitation to "om)ute D!$ and te 3uantiation )ro"ess introdu"e distortion

in te re"onstru"ted image. $e lossless mode uses )redi"ti&e metod and does not

a&e 3uantiation )ro"ess. $e ierar"i"al mode "an use D!$-ased "oding or

)ridi"ti&e "oding o)tionall'. $e most widel' used mode in )ra"ti"e is is "alled te

aseline J,EG s'stem( wi" is ased on se3uential mode( D!$-ased "oding and

Human "oding or entro)' en"oding. ;ig. 1 is te lo"< diagram o aseline s'stem.

$e J,EG standard deines onl' te s'nta/ o te "om)ressed itstream. It does

not s)e"i' an' ting aout ile ormat. noter standard "alled J;I; J,EG ;ile

Inter"ange ;ormat( "reated ' IJG Inde)endend J,EG Grou)( ma


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!olor S"ace !onversion and #o$nsam"ling

In order to a"ie&e good "om)ression )erorman"e( "orrelation etween te "olor

"om)onents is irst redu"ed ' "on&erting te RGB"olor s)a"e into a de"orrelated

"olor s)a"e. In aseline J,EG( a RGBimage is irst transormed into a luminan"e-

"rominan"" "olor s)a"e su" as YCbCr. $e ad&antage o "on&erting te image into

luminan"e-"rominan"e "olor s)a"e is tat te luminan"e and "rominan"e

"om)onents are &er' mu" de"orrelated etween ea" oter. =oreo&er( te

"rominan"e "annels "ontain mu" redundant inormation and "an easil' e

susam)led witout sa"rii"ing an' &isual 3ualit' or te re"onstru"ted image. $e

transormation rom RGB to YCbCr( is ased on te ollowing matemati"al

e/)ression:

0.299000 0.5>000 0.114000 0

0.1?>? 0.12?4 0.500002 12

0.500000 0.41? 0.0112 12

b

r

Y R

C G

C B

= +

$e &alue YA 0.299RB 0.5>GB 0.114Bis "alled te luminan"e. It is te &alue

used ' mono"rome monitors to re)resent an RGB "olour. ,'siologi"all'( it

re)resents te intensit' o anRGB"olor )er"ei&ed ' te e'e. $e ormula is li


3/12


4/12

In&erse D!$ :> >

0 0

1 2 1 2 1 ( ( "os "os

4 1? 1?

or 0(...(> and 0(...(>

u v

x u y vf x y C u C v F u v

x y

= =

+ + =

= =

$eFu(v is "alled te D!$ "oei"ient( and te D!$ asis is :

(

2 1 2 1 ( "os "os

4 1? 1?x y

C u C v x u y vu v

+ + =

$en we "an rewrite te in&erse D!$ to :> >

(

0 0

( ( ( or 0(...(> and 0(...(>x y

u v

f x y F u v u v x y= =

= = =

;ig. $e D!$ asis ( ( x y u v

48 39 40 68 60 38 50 12

1

14

9 82 79

10

1

11

3

10

6 27 62

58 63 77 69 12

4

10

7 74

12

5

80 97 74 54 59 71 91 66

18 34 33 46 64 61 32 37

14

9

10

8 80

10

6

11

6 61 73 92

21

1

23

3

15

9 88

10

7

15

8

16

1

10

9

699.2

5

43.1

8

55.2

5

72.1

1

24.0

0

-

25.5

1

11.2

1

-

4.14

-

129.7

8

-

71.5

0

-

70.2

6

-

73.3

5

59.4

3

-

24.0

2

22.6

1

-

2.05

85.7130.3

2

61.7

8

44.8

7

14.8

4

17.3

5

15.5

1

-

13.1

9

-

40.81

10.1

7

-

17.5

3

-

55.8

1

30.5

0

-

2.28

-

21.0

0

-

1.26

- -af x(y : &alues o luminan"e Fu(v : D!$ "oei"ients

;ig. 4 n e/am)le o D!$ "oei"ients or a lo"


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% ,uanti-ation

$e transormed lo"< now "onsists o ?4 D!$ "oei"ients. $e irst"oei"ient F0(0 is te D! "om)onent and te oter ? "oei"ients are !

"om)onent. $e D! "om)onentF0(0 is essentiall' te sum o te ?4 )i/els in te

in)ut )i/el lo"< multi)lied ' te s"aling a"tor 184C0C0A18 as sown ine3uation orFu(v.

$e ne/t ste) in te "om)ression )ro"ess is to 3uantie te transormed

"oei"ients. Ea" o te ?4 D!$ "oei"ients are uniorml' 3uantied. $e ?4

3uantiation ste)-sie )arameters or uniorm 3uantiation o te ?4 D!$ "oei"ients

orm an 3uantiation matri/. Ea" element in te 3uantiation matri/ is an integeretween 1 and 255. Ea" D!$ "oei"ient Fu(v is di&ided ' te "orres)onding

3uantier ste)-sie )arameter Qu(v in te 3uantiation matri/ and rounded to te

nearest integer as :

- ( 0- ( 0- ( 0

qF u vF u v RoundQ u v

=

$e J,EG standard does not deine an' i/ed 3uantiation matri/. It is te

)rerogati&e o te user to sele"t a 3uantiation matri/. $ere are two 3uantiation

matri"es )ro&ided in nne/ o te J,EG standard or reeren"e( ut not

re3uirement. $ese two 3uantiation matri"es are sown elow :

1? 11 10 1? 24 40 51 ?1

12 12 14 19 2? 5 ?0 55

14 1 1? 24 40 5> ?9 5?14 1> 22 29 51 > 0 ?2

1 22 > 5? ? 109 10 >>

24 5 55 ?4 1 104 11 92

49 ?4 > > 10 121 120 101

>2 92 95 9 112 100 10 99

1> 1 24 4> 99 99 99 99

1 21 2? ?? 99 99 99 99

24 2? 5? 99 99 99 99 994> ?? 99 99 99 99 99 99

99 99 99 99 99 99 99 99

99 99 99 99 99 99 99 99

99 99 99 99 99 99 99 99

99 99 99 99 99 99 99 99

a Fuminan"e 3uantiation matri/ !rominan"e 3uantiation matri/

;ig. 5 Cuantiation matri/

699.2

5

43.1

8

55.2

5

72.1

1

24.0

0

-25.5

1

11.2

1

-

4.14

-

129.7

8

-

71.5

0

-

70.2

6

-

73.3

5

59.4

3

-

24.0

2

22.6

1

-

2.05

85.7130.3

2

61.7

8

44.8

7

14.8

4

17.3

5

15.5

1

-

13.1

9

-

40.81

10.1

7

-

17.5

3

-

55.8

1

30.5

0

-

2.28

-

21.0

0

-

1.26

44 4 ? 5 1 -1 0 0-11 -? -5 -4 2 0 0 0

? 2 4 2 0 0 0 0

- 1 -1 -2 1 0 0 0

-9 -2 0 0 0 0 0 0

4 0 1 -1 -1 0 0 0

-1 -1 0 0 1 0 0 0

0 -1 0 0 0 0 0 0

aFu(v : D!$ "oei"ients Fqu(v : ter 3uantiation

;ig. ? n e/am)le o 3uantiation or a D!$ "oei"ients

5


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7/12

E+ End o lo" 0(45 4(2 1(-0 0(-1? 2(1 0(0

e gi&e anoter e/am)le. ;or te 3uantied &e"tor as ollows :

5>( eigteen eroes( ( 0( 0( 0( 0( 2( tirt'-tree eroes( 95( E+

$e J,EG Human "oding ma 15(0 2( 4(2 15(0 15(0 1(95 0(0

15(0 is a s)e"ial "oded &alue wi" indi"ates tat tere are 1? "onse"uti&e eroes.

+ #i&&erence !oding o& #! !oe&&icients

e"ause te D! "oei"ients "ontains a lot o energ'( it usuall' as mu" larger

&alue tan ! "oei"ients( and we "an noti"e tat tere is a &er' "lose "onne"tion

etween te D! "oei"ients o ada"ent lo"


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Hu&&man !oding

Instead o storing te a"tual &alue ( te J,EG standard s)e"iies tat we store te

minimum sie in its in wi" we "an (-?(-5(-4(4(5(?(> 000(001(010(011(100(101(110(111

4 -15(...(-((...(15 0000(...(0111(1000(...(1111

5 -1(...(-1?(1?(...1 00000(...(01111(10000(...(11111

? -?(...(-2(2(...? 000000(...(011111(100000(...(111111

> -12>(...(-?4(?4(...(12> 0000000(...(0111111(1000000(...(1111111

-255(..(-12(12(..(255 ...

9 -511(..(-25?(25?(..(511 ...10 -102(..(-512(512(..(102 ...

11 -204>(..(-1024(1024(..(204> ...

;ig. 9 $ale o te "ategor' and it-"oded &alues

In "onse3uen"e or te )re&ious e/am)le o ! "oei"ients:

0(5> 0(45 4(2 1(-0 0(- 2(1 0(0

e en"ode onl' te rigt &alue o tese )airs as "ategor' and its or te &alue( e/"e)t

te )airs tat are s)e"ial mar


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...

15810 1? 1111111111111110

;ig. 10 Human tale o luminan"e ! "oei"ients

$e inal ste) is en"oding tis 'te using Human "oding. ;or e/am)le( i te

Human "ode o 'te 0(? is 111000( and te Human "ode o 'te 4(5 is

1111111110011001( and so on. $e inal stream o its written in te J,EG ile on

dis< or te )re&ious e/am)le o ? "oei"ients is :

1111000 1111001 ( 111000 101101 ( 1111111110011000 10111 (

11111110110 00001 ( 1011 0111 ( 11100 1 ( 1010

"ategor' "ode lengt "ode word

0 2 00

1 0102 011

100

4 101

5 110

? 4 1110

> 5 11110

? 111110

9 > 1111110

10 11111110

;ig. 11 Human tale o luminan"e D! "oei"ients

#ow we "osider te en"oding o te dieren"e o D! "oei"ients. $e

dieren"e will e re)resented ' "ategor' and its its or te &alue( and it will e

Human en"oded onl' te "ategor' &alue. ;or e/am)le( i dieren"e is e3ual to -511(

ten it will e re)resented as 9(000000000. I te Human "ode o 9 is 1111110( te

stream o its written in te J,EG ile on dis< or te dieren"e is :

1111110 000000000

;inall'( we "omine tis e/am)le o D! and to te )re&ious e/am)le o !s( or tis

&e"tor wit ?4 "oei"ients( te inal stream o its written in te J,EG ile will e :

1111110 000000000 ( 1111000 1111001 ( 111000 101101 (

1111111110011000 10111 ( 11111110110 00001 ( 1011 0111 ( 11100 1 ( 1010

2 !onclusions

e a&e introdu"ed te asi" "om)ression metods o J,EG standard. ltoug

tis standard as e"ome te most )o)ular image ormat( it still as some )ro)erties

to im)ro&ement. ;or e/am)le( te new J,EG 2000 standard use wa&elet-ased

"om)ression metod( and it "an o)erate at iger "om)ression ratio witoutgenerating te "ara"teristi" lo"


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J,EG standard.

10


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0e&erences

K1L 2004

K2L $. "ar'a( . . *a'( 7Image ,ro"essing: ,rin"i)les and ))li"ations7( Jon

ile' M 6ons( 2005( )).51-?.KL *. !. Gonole( *. E. oods( 6. F. Eddins( 7Digital Image ,ro"essing %sing

=atla7( ,renti"e Hall( 2004.

K4L G. . alla"e( $e J,EG 6till ,i"ture !om)ression 6tandard( !ommuni"ations

o te !=( ol. 4( Issue 4( )).0-44.

K5L !. !uturi"u( note aout te J,EG de"oding algoritm(

a&ailale in tt):88www.o)ennet.ru8do"s8ormats8)eg.t/t( 1999.

K?L I$%-$ *e"ommendation $.1( Digital "om)ression and "oding o "ontinuous-

tone still images - *e3uirements and guidelines(

a&ailale in tt):88www.itu.int8re"8$-*E!-$8eK>L $e Inde)endent J,EG Grou)( ! sour"e "ode o J,EG En"oder resear" ?(

199.

Simulation 0esults

I1: +riginal image wit widt Wand eigtH

C: En"oded )eg stream romI1

I2: De"oded image rom C

!om)ression ratio A sieoC 8 sieoI1

*oot mean s3uare error A [ ]2

1 2

1 1

( ( 8 H W

y x

I x y I x y H W= =

Cuantiation : 1 ( Downsam)ling : 444 Cuantiation : 1 ( Downsam)ling : 420

!om)ression ratio : 0.04524

*oot mean s3uare error : ?.

!om)ression ratio : 0.059011

*oot mean s3uare error : .0


!om)ression ratio : 0.0?14

*oot mean s3uare error : 11.5?

!om)ression ratio : 0.02>>

*oot mean s3uare error : 12.4?

;rom te tale ao&e and te igure ne/t )age( we "an see tat te t')e 420 o

downsam)ling "an de"rease te "om)ression ratio wit little &ision error( and te

3uantiation le&el 4 "an also de"rease te "om)ression ratio ut generating te "lear

"ara"teristi" lo"


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+riginal image : lena.m)

!om)ression image :



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