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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
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Outline
1. Lossless image compression 2. Predictive coding 3. LOCO-I (JPEG-LS) 4. CALIC 5. The proposed scheme 6. Experimental results 7. Conclusions
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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• …
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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
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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
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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
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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
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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
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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
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6. Experimental results6. Experimental results Test images: gray scale, 512 × 512
LOCO-I CALIC AGSP
Amplitude images for prediction errors
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6. Experimental results (cont.)6. Experimental results (cont.) Compression performance
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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