1

A Gradient Based Predictive Coding for Lossless Image Compression

A Gradient Based Predictive Coding for Lossless Image Compression

Source: IEICE Transactions on Information and Systems, Vol. E89-D, No. 7, July 2006.Authors: Haijiang Tang and Sei-ichiro KamataSpeaker: Chia-Chun Wu Date: 2006/10/19

2

Outline

1. Lossless image compression 2. Predictive coding 3. LOCO-I (JPEG-LS) 4. CALIC 5. The proposed scheme 6. Experimental results 7. Conclusions

3

1. Lossless image compression1. Lossless image compression

Lossless: reconstruct the coded image identically to the original image

Applications:• Medical imaging• Remote sensing• Fax• Image archiving• Art work preserving• …

4

2. Predictive coding2. Predictive coding

Practice:The value of a pixel can be accurately predicted using a simple predictor of previously observed neighbor pixels.

c ba x

ˆError e x x x: current pixel

x̂: predictive value

5

3. LOCO-I (JPEG-LS)3. LOCO-I (JPEG-LS) median edge detector

min(a,b), max(a,b)

x̂ max(a,b), min(a,b)

a b c,

if c

if c

otherwise

Example:

60105

100

105

50100

102

60

60105

100

105

50e = {+5, +2, -45}

Original image Predictive values

LOCO-I: Low complexity lossless compression for images

6

4. CALIC4. CALIC gradient adjusted predictor

|hi||gb||ca|

|ib||cb||da|

v

h

d

d

g h

c b i

d a x

Causal template

42x

ciba

CALIC: Context-based, adaptive, lossless image coder

, ( > 80) //sharp horizontal edge

( + ), ( > 32) // horizontal edge

2(3 + )

, ( > 8) // weak horizontal edge4x̂

, ( < -80) //sharp vertic

v h

v h

v h

v h

a if d d

x aif d d

x aif d d

b if d d

al edge

( + ) , ( < -32) // vertical edge

2(3 + )

, ( < -8) // weak vertical edge 4

v h

v h

x bif d d

x bif d d

7

4. CALIC (cont.)4. CALIC (cont.) gradient adjusted predictor

|hi||gb||ca|

|ib||cb||da|

v

h

d

dg h

c b i

d a x

Causal template

40 30 15

45 20 20 25

102

105

100

dv-dh=105-8=97>80 dv-dh=69-29=40 >32 dv-dh=70-60=10 >8

40 55 50

45 50 65 54

102

105

100

55 60 60

60100

50 45

50 55100

Example:

105x̂

86x 39x

42x

ciba

=(86+105)/2=96

x̂ x̂

Sharp horizontal

Weak horizontal

Horizontal

e = -5 e = +4

e = +57

=(3*39+55)/4 = 43

8

min1 min 2 min1 min 2

min1 min 2

x̂D C D C

D D

5. The proposed scheme5. The proposed scheme Accurate gradient selection predictor (AGSP)

15/)|gi||fb|2|ea|2(

16/|)gc||dc||hb|2|ab|2(

17/|)fc||ed||hi||gb|2|ca|2(

19/|)ec||hg||fg||ib|2|cb|2|da|2(

D

D

D

D

v

h

f g h

e c b i

d a x

Causal template

a

b

i

c

h

v

C

C

C

C

9

5. The proposed scheme (cont.)5. The proposed scheme (cont.)

Example2:

Ch=55, Cv=50, C+=45, C-=100

=(8*55 + 19*100)/(8+19)=87

x̂

55 60 60

60100

50 45

50 55 100

40 55 50

45 50 65 54

102

105

100

Example1:

Ch=105, Cv=65, C+=54, C-=50

=(10*54 + 29*105)/(10+29)=92

x̂

e = +8

e = +13

Dh=10, Dv=30, D+=29, D-=35

Dh=19, Dv=27, D+=21, D-=8

10

6. Experimental results6. Experimental results Test images: gray scale, 512 × 512

LOCO-I CALIC AGSP

Amplitude images for prediction errors

11

6. Experimental results (cont.)6. Experimental results (cont.) Compression performance

12

7. Conclusions7. Conclusions A new adaptive prediction algorithm based

on accurate gradient estimation and selection

All the possible contexts are considered in context modeling

Handles complex structures more robustly Maintain the simplicity of implementation

and computation