Transcript
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The JPEG Standard
Jiun-De Huang
E-mail: r95942104@ntu.edu.tw
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. $e ormula is li
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In&erse D!$ :> >
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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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.
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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
Cuantiation : 4 ( Downsam)ling : 444 Cuantiation : 4 ( Downsam)ling : 420
!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 :
Cuantiation : 1 ( Downsam)ling : 444 Cuantiation : 1 ( Downsam)ling : 420
Cuantiation : 4 ( Downsam)ling : 444 Cuantiation : 4 ( Downsam)ling : 420
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