Mu ltim e d ia C o d in g a n d T ra n s m is s io n

Im a g e C o d in g

Ifi, U iO N o rs k R e g n e s e n tra lV å rs e m e s te r 2 0 0 3W o lfg a n g L e is te r

T h is p a rt o f th e c o u rs e ...

• ... is h e ld a t Ifi, U iO ...(W o lfg a n g L e is te r)

• … a n d a t U n iv e rs ity C o lle g e K a rls ru h e(P e te r O e l, C le m e n s K n o e rz e r)

T h e s to ry s o fa r ...

• D a ta c o m p re s s io n– in fo rm a tio n th e o ry– ru n le n g th e n c o d in g– H u ffm a n c o d in g– Z if-L e m p e l(-W e lc h ) a lg o rith m– A rith m e tic c o d in g

O v e rv ie w

• C o d in g w ith lo s s– J P E G /MP E G– W a v e le t-C o d in g – F ra c ta l C o d in g

L o s s y C o d in g

• A p p lic a b le o n ly fo r d a ta ty p e s lik e :– Im a g e s– F ilm s (im a g e s e q u e n c e s )– A u d io

• U s e p h y s io lo g ic a l c a p a b ilitie s a n d lim ita tio n s o f th e s e n s e s to d e s ig n c o m p re s s io n m e th o d s

C a p a b ilitie s o f th e s e n s e s• E y e

– E y e re c o g n is e s fre q u e n c ie s– B rig h tn e s s is b e tte r re c o g n is e d th a n c o lo u rs .– Mo v e m e n t a n d flic k e r is re c o g n is e d v e ry

s tro n g ly !

• E a r– D e n s e ly s itu a te d fre q u e n c ie s c o v e r e a c h o th e r.

J P E G

• J o in t P h o to g ra p h ic E x p e rt G ro u p• 1 9 9 1 - 1 9 9 3• C C IT T , IS O 1 0 9 1 8• L o s s le s s c o d in g (C o m p . 2 :1 )• C o d in g w ith lo s s (1 0 :1 -4 0 :1 )• P a ra m e te r c o n tro ls im a g e q u a lity• N o t lim ite d fo r c e rta in im a g e ty p e s

J P E G

• D is c re te C o s in e T ra n s fo rm a tio n (D C T )• H u ffm a n - o r A rith m e tic C o d in g• Mo d e s :

– L o s s le s s C o d in g– S e q u e n tia l C o d in g– P ro g re s s iv e C o d in g– H ie ra rc h ic a l C o d in g

• N o t a file fo rm a t !!! →→→→ J F IF F

L o s s le s s C o d in g

XABC

0 -1 A2 B3 C4 A + B -C5 A + (B -C )/26 B + (A -C )/27 (A + B )/2

N r. P re d ic tio n

(V h s . D iff.)(V h s . D iff.)(V h s . D iff)...

L o s s y C o d in g

• S u b d iv is io n in 8 x 8 B lo c k s• T ra n s fo rm a tio n in fre q u e n c y s p a c e• Q u a n tis in g• C o d in g (H u ffm a n o r a rith m e tic C o d in g )

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

W h y D C T ?

• W h y u s e fre q u e n c y d o m a in ?– b e tte r s ta tis tic d is trib u tio n– m a n y lo w fre q u e n c y p a rts– fe w h ig h fre q u e n t p a rts– q u a n tis in g b e tte r p o s s ib le– H u m a n s s e e h ig h fre q u e n c ie s o n ly fo r h ig h

c o n tra s t v a lu e s

W h y D C T ?

• W h y n o t F o u rie r T ra n s fo rm ?– 8 x 8 B lo c k s– F T : rin g in g a t b lo c k e d g e s

W h y D C T ?

• W h y n o t F o u rie r T ra n s fo rm ?– 8 x 8 B lo c k s– F T : rin g in g a t b lo c k e d g e s

W h y D C T ?

• W h y n o t F o u rie r T ra n s fo rm ?– 8 x 8 B lo c k s– F T : rin g in g a t b lo c k e d g e s– Mirro rin g p ro d u c e s e v e n fu n c tio n– S in u s c o e ffic ie n ts d is a p p e a r

D C T

c o s in e , s in e fu n c tio n s

s a m p lin g o f fu n c tio n

t)c o s (f(t) ⋅= u

D C T - b a s is fu n c tio n s

D C T - e x a m p le

D C T 1 D - 2 D

(F o rw a rd )D C T

• u n s ig n e d →→→→ s ig n e d• F D C T :

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

e ls e 1 = C (v )C (u ),

0=vu , fo r = C (v )C (u ), w ith

c o sc o sy )f(x ,C (u )C (v )=v )F (u ,

21

7

0x

7

0y1 6

1 )v(2 y1 61 )u(2 x

41

������

∗= =

�+�+

(F o rw a rd )D C T

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

1 3 9 1 4 4 1 4 9 1 5 3 1 5 5 1 5 5 1 5 5 1 5 5

1 4 4 1 5 1 1 5 3 1 5 6 1 5 9 1 5 6 1 5 6 1 5 6

1 5 0 1 5 5 1 6 0 1 6 3 1 5 8 1 5 6 1 5 6 1 5 6

1 5 9 1 6 1 1 6 2 1 6 0 1 6 0 1 5 9 1 5 9 1 5 9

1 5 9 1 6 0 1 6 1 1 6 2 1 6 2 1 5 5 1 5 5 1 5 5

1 6 1 1 6 1 1 6 1 1 6 1 1 6 0 1 5 7 1 5 7 1 5 7

1 6 2 1 6 2 1 6 1 1 6 3 1 6 2 1 5 7 1 5 7 1 5 7

1 6 2 1 6 2 1 6 1 1 6 1 1 6 3 1 5 8 1 5 8 1 5 8

1 1 1 6 2 1 2 5 2 7 2 7 2 7 2 7

1 6 2 3 2 5 2 8 3 1 2 8 2 8 2 8

2 2 2 7 3 2 3 5 3 0 2 8 2 8 2 8

3 1 3 3 3 4 3 2 3 2 3 1 3 1 3 1

3 1 3 2 3 3 3 4 3 4 2 7 2 7 2 7

3 3 3 3 3 3 3 3 3 2 2 9 2 9 2 9

3 4 3 4 3 3 3 5 3 4 2 9 2 9 2 9

3 4 3 4 3 3 3 3 3 5 3 0 3 0 3 0

2 3 5 .6 -1 .0 -1 2 .1 -5 .2 2 .1 -1 .7 -2 .7 1 .3

-2 2 .6 -1 7 .5 -6 .2 -3 .2 -2 .9 -0 .1 0 .4 -1 .2

-1 0 .9 -9 .3 -1 .6 1 .5 0 .2 -0 .9 -0 .6 -0 .1

-7 .1 -1 .9 0 .2 1 .5 0 .9 -0 .1 0 .0 0 .3

-0 .6 -0 .8 1 .5 1 .6 -0 .1 -0 .7 0 .6 1 .3

1 .8 -0 .2 1 .6 -0 .3 -0 .8 1 .5 1 .0 -1 .0

-1 .3 -0 .4 -0 .3 -1 .5 -0 .5 1 .7 1 .1 -0 .8

-2 .6 1 .6 -3 .8 -1 .8 1 .9 1 .2 -0 .6 -0 .4

u n s ig n e d →→→→ s ig n e d→→→→

F D C T

Q u a n tis in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

F (u , v ) = In te g e rF (u , v )Q (u , v )

Q

Q u a n tis in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

1 5 0 -1 0 0 0 0 0

-2 -1 0 0 0 0 0 0

-1 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

1 6 1 1 1 0 1 6 2 4 4 0 5 1 6 1

1 2 1 2 1 4 1 9 2 6 5 8 6 0 5 5

1 4 1 3 1 6 2 4 4 0 5 7 6 9 5 6

1 4 1 7 2 2 2 9 5 1 8 7 8 0 6 2

1 8 2 2 3 7 5 6 6 8 1 0 9 1 0 3 7 7

2 4 3 5 5 5 6 4 8 1 1 0 4 1 1 3 9 2

4 9 6 4 7 8 8 7 1 0 3 1 2 1 1 2 0 1 0 1

7 2 9 2 9 5 9 8 1 1 2 1 0 0 1 0 3 9 9

2 3 5 .6 -1 .0 -1 2 .1 -5 .2 2 .1 -1 .7 -2 .7 1 .3

-2 2 .6 -1 7 .5 -6 .2 -3 .2 -2 .9 -0 .1 0 .4 -1 .2

-1 0 .9 -9 .3 -1 .6 1 .5 0 .2 -0 .9 -0 .6 -0 .1

-7 .1 -1 .9 0 .2 1 .5 0 .9 -0 .1 0 .0 0 .3

-0 .6 -0 .8 1 .5 1 .6 -0 .1 -0 .7 0 .6 1 .3

1 .8 -0 .2 1 .6 -0 .3 -0 .8 1 .5 1 .0 -1 .0

-1 .3 -0 .4 -0 .3 -1 .5 -0 .5 1 .7 1 .1 -0 .8

-2 .6 1 .6 -3 .8 -1 .8 1 .9 1 .2 -0 .6 -0 .4

Q u a n tis e r T a b le

C o d in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

1 5 0 -1 0 0 0 0 0

-2 -1 0 0 0 0 0 0

-1 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

A C

D C

• 1 D C -C o e ffic ie n t• 6 3 A C -C o e ffic ie n te s

D C -C o d in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

D C 0 -1 0 0 0 0 0

-2 -1 0 0 0 0 0 0

-1 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

D C 0 -1 0 0 0 0 0

-2 -1 0 0 0 0 0 0

-1 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

D C 0 -1 0 0 0 0 0

-2 -1 0 0 0 0 0 0

-1 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

D C 0 -1 0 0 0 0 0

-2 -1 0 0 0 0 0 0

-1 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

∆D C i= D C i-D C i-1

D C -C o d in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

∆D C i= D C i-D C i-1

∆D C i= (L e n g th , V a lu e )

L e n g th = H u ffm a n -C o d e d

V a lu e = (S ig n , a b s V a lu e )

D C -C o d in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

0-1 , 1

-3 ,-2 , 2 ,3-7 ..-4 , 4 ..7

-1 5 ..-8 , 8 ..1 5-3 1 ..-1 6 , 1 6 ..3 1-6 3 ..-3 2 , 3 2 ..6 3

-1 2 7 ..-6 4 , 6 4 ..1 2 7-2 5 5 ..-1 2 8 , 1 2 8 ..2 5 5-5 1 1 ..-2 5 6 , 2 5 6 ..5 1 1

-1 0 2 3 ..-5 1 2 , 5 1 2 ..1 0 2 3-2 0 4 7 ..-1 0 2 4 , 1 0 2 4 ..2 0 4 7

0123456789

1 01 1

L e n g th V a lu e E x a m p le s :-3 : (2 ).1 .1-1 : (1 ).1 .0 : (0 )..5 : (3 ).0 .0 16 7 : (7 ).0 .0 0 0 0 1 1

D C -C o d in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

0 00 1 00 1 11 0 01 0 11 1 01 1 1 01 1 1 1 01 1 1 1 1 01 1 1 1 1 1 01 1 1 1 1 1 1 01 1 1 1 1 1 1 1 0

0123456789

1 01 1

L e n g th C o d e E x a m p le s :-3 : (2 ).1 .1 : 0 1 1 .1 .1-1 : (1 ).1 . : 0 1 0 .1 .0 : (0 ).. : 0 0 ..5 : (3 ).0 .0 1 : 1 0 0 .0 .0 16 7 : (7 ).0 .0 0 0 0 1 1 : 1 1 1 1 0 .0 .0 0 0 0 1 1

A C -C o d in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

• Z ig -Z a g S e ria lis in g• Z e ro ru n le n g th• H u ffm a n -C o d in g

Z ig -Z a g S e ria lis in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

D C 0 -1 0 0 0 0 0

-2 -1 0 0 0 0 0 0

-1 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

A C -C o d in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

1 5 0 -1 0 0 0 0 0

-2 -1 0 0 0 0 0 0

-1 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

• 0 ,-2 ,-1 ,-1 ,-1 ,0 ,0 ,-1 ,0 ,0 ,0 ,0 ,...• (1 x 0 ),-2 ,(0 x 0 ),-1 ,(0 x 0 ),-1 ,(0 x 0 ),-1 ,

(2 x 0 ),-1 ,< E O B >• (1 ),-2 ,(0 ),-1 ,(0 ),-1 ,(0 ),-1 ,(2 ),-1 ,< E O B >

A C -C o d in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

1 5 0 -1 0 0 0 0 0

-2 -1 0 0 0 0 0 0

-1 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

• 0 ,-2 ,-1 ,-1 ,-1 ,0 ,0 ,-1 ,0 ,0 ,0 ,0 ,...• (1 x 0 ),-2 ,(0 x 0 ),-1 ,(0 x 0 ),-1 ,(0 x 0 ),-1 ,

(2 x 0 ),-1 ,< E O B >• (1 ),-2 ,(0 ),-1 ,(0 ),-1 ,(0 ),-1 ,(2 ),-1 ,< E O B >• (1 ),((2 ).1 .0 ),(0 ),((1 ).1 ),(0 ),((1 ).1 ),(0 ),

((1 ).1 ),(2 ),((1 ).1 ),< E O B >

A C -C o d in g

F D C T Q u a n tis e r E n c o d e r 0 1 0 1 1 0 1 0 ..

T a b le T a b le

1 5 0 -1 0 0 0 0 0

-2 -1 0 0 0 0 0 0

-1 -1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

• 0 ,-2 ,-1 ,-1 ,-1 ,0 ,0 ,-1 ,0 ,0 ,0 ,0 ,...• (1 x 0 ),-2 ,(0 x 0 ),-1 ,(0 x 0 ),-1 ,(0 x 0 ),-1 ,

(2 x 0 ),-1 ,< E O B >• (1 ),-2 ,(0 ),-1 ,(0 ),-1 ,(0 ),-1 ,(2 ),-1 ,< E O B >• (1 ),((2 ).1 .0 ),(0 ),((1 ).1 ),(0 ),((1 ).1 ),(0 ),

((1 ).1 ),(2 ),((1 ).1 ),< E O B >• (1 /2 ).1 .0 ,(0 /1 ).1 ,(0 /1 ).1 ,(0 /1 ).1 ,(2 /1 ).1 ,< E O B >

A C -C o d in g• 0 ,-2 ,-1 ,-1 ,-1 ,0 ,0 ,-1 ,0 ,0 ,0 ,0 ,...• (1 x 0 ),-2 ,(0 x 0 ),-1 ,(0 x 0 ),-1 ,(0 x 0 ),-1 ,

(2 x 0 ),-1 ,< E O B >• (1 ),-2 ,(0 ),-1 ,(0 ),-1 ,(0 ),-1 ,(2 ),-1 ,< E O B >• (1 ),((2 ).1 .0 ),(0 ),((1 ).1 ),(0 ),((1 ).1 ),(0 ),

((1 ).1 ),(2 ),((1 ).1 ),< E O B >• (1 /2 ).1 .0 ,(0 /1 ).1 ,(0 /1 ).1 ,(0 /1 ).1 ,(2 /1 ).1 ,< E O B >

< E O B > 1 0 1 0 1 /1 1 1 0 00 /1 0 0 1 /2 1 1 0 1 10 /2 0 1 ....0 /3 1 0 0 2 /1 1 1 1 0 00 /4 1 0 1 1 2 /2 1 1 1 1 1 0 0 10 /5 1 1 0 1 0 ....0 /6 1 1 1 1 0 0 0 1 5 /1 ...0 /7 1 1 1 1 1 0 0 0 ...... 1 5 /1 0 ...0 /1 0 ..... < Z R 1 6 > 1 1 1 1 1 1 1 1 0 0 1

• 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0

• 6 3 A C -C o e ffic ie n ts → 2 6 B it

C o m p re s s io n R e s u lts

n:1 Q u a lity

3 0 - 2 0 u s a b le - g o o d2 0 - 1 0 g o o d - v e ry g o o d1 0 - 5 e x c e lle n t5 - 4 n o t d is tin g u is h a b le fro m o rig in a l

D e c o m p re s s io n

• D e C o d in g• R e s c a le b y D e Q u a n tis in g• In v e rs e D C T

ID C TD e Q u a n tis e rD e c o d e r0 1 0 1 1 0 1 0 ..

T a b le T a b le

In v e rs e D C T

• ID C T :

e ls e 1 = C (v )C (u ),

0=vu , w h e n = C (v )C (u ), fo r

c o sc o sv )u ,C (u )C (v )F (=y )f(x ,

21

7

0u

7

0v1 61 )v(2 y

1 61 )u(2 x

41 ��

���� ∗= =

�+�+

P ro g re s s iv e Mo d e

• T ra n s fe r c o e ffic ie n ts p a rtia lly in s e v e ra lru n s .

• T w o P o s s ib ilitie s :– S p e c tra l T ra n s fe r– A p p ro x im a te d T ra n s fe r

P ro g re s s iv e Mo d e

01

.

.

.

6 26 3

D C TK o e ff.

B lo c k s .

B its .

7 6 ..... 1 0

0

345

12

6 16 26 3

D C

A C

S p e c tra l T ra n s fe r

P ro g re s s iv e r Mo d u s

01

.

.

.

6 26 3

D C TK o e ff.

B lo c k s .

B its .

7 6 ..... 1 0

0D C

A C

A p p ro x im a te d T ra n s fe r7 6 5 4

12

.

.

.

6 26 3

3 0...

H ie ra rc h ic a l Mo d e

• C o d e im a g e w ith lo w re s o lu tio n firs t• C o d e h ig h e r re s o lu tio n a s d iffe re n c e to

p re v io u s lo w e r re s o lu tio n• Im a g e is re p re s e n te d in s e v e ra l

re s o lu tio n s• U n n e c e s s ry d a ta a re n o t tra n s fe rre d

Im a g e s w ith s e v e ra l c h a n n e ls

• J P E G c a n u s e s e v e ra l (C o lo u r)-C h a n n e ls (e .g ., Y C b C r)

• C h a n n e ls c a n h a v e d iffe re n t re s o lu tio n• R e s o lu tio n fa c to r a s w h o le n u m b e r• J P E G m e th o d d o e s n o t b o th e r a b o u t

c h a n n e ls

J F IF F

• J P E G d e fin e s a lg o rith m o n ly .• J P E G is n o t a file fo rm a t• J P E G is c o lo u r-b lin d• P a ra m e te rs a n d ta b le s a re p re -d e fin e d• B a s e d o n J P E G m o d e o f T IF F 6 .0• C o n s is ts o f s e g m e n ts w h ic h a re d e fin e d

b y m a rk e rs (lik e T IF F )

W a v e le t-C o d in g

• W h y d o w e n e e d a n a lte rn a tiv e c o d in g to J P E G ?– V is ib le b lo c k s fo r h ig h c o m p re s s io n ra te s– fro m c o m p re s s io n ra te o f 4 0 :1 a n d

o n w a rd s J P E G d o e s n o t w o rk .– lo w fre q u e n c ie s a re n o t ta k e n in to a c c o u n t.

W a v e le t-C o d in g

• G o o d q u a lity u p to 6 0 :1• L in e a r d e g ra d a tio n fo r h ig h e r

c o m p re s s io n ra te s• N o v is ib le b lo c k s• N o h a rd w a re s o lu tio n a v a ila b le• J P E G 2 0 0 0

W a v e le t C o d in g

S u b je c t to a la te r s e s s io n !S u b je c t to a la te r s e s s io n !

F ra c ta l C o d in g

• “T h e w h o le w o rld is fra c ta l …• ... b u t y o u ’ll h a v e to fin d th e rig h t ite ra tin g

fu n c tio n s y s te m !”• Im a g e s o fte n c o m p ris e o f s im ila rly lo o k in g

a re a s w ith s e v e ra l s c a lin g fa c to rs .• Ite ra tin g fu n c tio n s y s te m s a llo w th e

g e n e ra tio n o f c o m p le x im a g e s w ith o n ly fe wn u m b e rs o f p a ra m e te rs .

Ite ra tin g F u n c tio n s

f0 (x )= xf1 (x )= f(x )f2 (x )= f(f(x ))...fi+ 1 (x )= f(fi(x )) fo r i> = 0

F ix p o in t: fn + 1 (x )≡fn (x ) ∀x , n > N

Ite r. F u n c tio n s y s te m (IF S )

M V e c to r: (m 0 ,m 1 ,...,m n )

kIF S : F (M) = U fk (M)M0 = M

kMi+ 1 = U fk (Mi) = F (Mi) = F i+ 1 (M0 )

Ite ra tio n

S ta rt s e tM0

D a ta s e tMi {fk }

{fk }

IF S

• S e a rc h fo r {fk }, s o th a t fo r a n y s ta rt s e t M0th e re e x is ts a n N , s o th a t:a ) fo r a ll n > = N is Mn = Mn + 1

b ) Mn d e n o te s th e in fo rm a tio n to b e c o d e d .

• If a ) a p p lie s , {fk } is c a lle d c o n tra c tiv e• Mn = Mn + 1 = Mn + 2 ... is c a lle d F ix P o in t

IF S fo r Im a g e C o d in g

Mi+ 1 Mi

IF S fo r Im a g e C o d in g

• E a c h im a g e a re a is a tta c h e d to s o m e o th e r, b ig g e r, e q u a lly fo rm e d a re a .

• R o ta tio n , S c a lin g , D is to rtio n• A d ju s t to b rig h tn e s s• A d ju s t to c o n tra s t

T a s k s fo r C o d in g

• F in d a s u ita b le s e g m e n ta tio n• E a c h s e g m e n t m u s t b e a tta c h e d to

s o m e o th e r, b ig g e r s e g m e n t• A d ju s tm e n ts :

– B rig h tn e s s a n d c o n tra s t

• C o d e p a ra m e te rs a n d s to re

S e g m e n ta tio n

S e g m e n ta tio n

M0

M1

M2

M1 0

C o m p a ris o n

L ite ra tu re

• J P E G :– P e n n e b a k e r,Mitc h e ll: J P E G , S till Im a g e

D a ta C o m p r e s s io n S ta nd a r d , V a nN o s tra n d R e in h o ld (1 9 9 3 )

• W a v e le t-C o d in g :– D a u b e c h ie s : T e n L e c tu r e s o n W a v e le ts ,

S o c ie ty fo r In d u s tria l a n d A p p lie d Ma th e m a tic s

L ite ra tu re

– F o u rn ie r: W a v e le ts a n th e ir A p p lic a tio nsin C o m p u te r G r a p h ic s , S IG G R A P H `9 4C o u rs e N o te s

• F ra c ta l C o d in g :– B a rn s le y ,H u rd : F r a c ta l Im a g e

C o m p r e s s io n, A K P e te rs L td (1 9 9 3 )– F is h e r: F r a c ta l Im a g e C o m p r e s s io n,

S IG G R A P H `9 2 C o u rs e N o te s

T h e E n d o f th is L e c tu re