Image Compression Based on
Regression Equation
Advisor: H. C. Wu, Y. K. Chan
Speaker: Hsin-Nan Tsai (蔡信男)
Date: May 4, 2005
1
Outline
•
•
•
•
Introduction
The proposed method
Experimental results
Conclusions
2
Introduction
•
•
•
•
YIQ model
Quadtree structure
Edge detection
Quadratic regression
equation
3
Image compression
• RGB
Y
I
Q
YIQ
=
0.299 0.587 0.114
0.596 -0.275 -0.321
0.212 -0.523 0.311
×
R
G
B
4
Image compression (cont.)
• Quadtree
1
0
NW
(128x128)
0
1
NE
(128x128)
0
SW
(128x128)
0
(64x64)
0
0
(64x64)
SE
(128x128)
0
(64x64)
(64x64)
Breadth First Traversal Order
treelist: 1 0 0 1 0 0 0 0 0
5
Image compression (cont.)
• Edge detection
∆X
129
PCD  X 2  Y 2
192
188
191
∆Y
123
192
188
185
122
178
180
183
126
173
175
175
If PCD > DiffTH
Count = Count + 1
If Count > CountTH
quadtree()
6
Image compression (cont.)
• Quadratic regression equation
I i  a0  a1  Yi  a 2  Yi 2
The coefficients a0, a1, and a2 of this equation can be figured out by
following three equations:
n
n
n

2
n  a 0  a 1   Yi  a 2   Yi   I i ,
i 1
i 1
i 1

n
n
n
n

2
3
a 0   Yi  a 1   Yi a 2   Yi   Yi  I i  , and
i 1
i 1
i 1
i 1

n
n
n
n

2
3
2
2
a

Y

a

Y

a

Y

Y
 Ii .




0
i
1
i
2
i
i

i 1
i 1
i 1
i 1



i is the i-th pixel in an image block, and n is the number of pixels in the image block.
7
Image compression (cont.)
• Quadratic regression equation
Qi  b0  b1  Yi  b2  Yi 2
The coefficients b0, b1, and b2 of this equation can be figured out by
following three equations:
n
n
n

2
 n  b0  b1   Yi  b2   Yi   Q i ,
i 1
i 1
i 1

n
n
n
n

2
3
b0   Yi  b1   Yi  b2   Yi   Yi  Q i  , and
i 1
i 1
i 1
i 1

n
n
n
n

2
3
2
2
b

Y

b

Y

b

Y

Y
 Qi .




0
i
1
i
2
i
i

i 1
i 1
i 1
i 1



i is the i-th pixel in an image block, and n is the number of pixels in the image block.
8
Image compression (cont.)
• Compute coefficients
a1,0 , a1,1 , a1, 2 , b1,0 , b1,1 , b1, 2 , a2,0 , a2,1 , a2, 2 , b2,0 , b2,1 , b2, 2 , , ai ,0 , ai ,1 , ai , 2 , bi ,0 , bi ,1 , bi , 2
colorlist
9
Image compression (cont.)
• Compress Y values
256
100 251
…
12
…
3
25
JPEG compression
Ydata
256
Y values
10
Image compression (cont.)
Compressed file: treelist || colorlist || Ydata
11
Image decompression
• Extract treelist
Compressed file: treelist || colorlist || Ydata
3×r+1=s
r is the numbers of 1-bits
s is the numbers of 0-bits
treelist: 1 0 0 1 0 0 0 0 0
12
Image decompression (cont.)
• Extract colorlist
Compressed file: colorlist || Ydata
6×s
a1,0 , a1,1 , a1, 2 , b1,0 , b1,1 , b1, 2 , a2,0 , a2,1 , a2, 2 , b2,0 , b2,1 , b2, 2 , , ai ,0 , ai ,1 , ai , 2 , bi ,0 , bi ,1 , bi , 2
13
Image decompression (cont.)
• Decompress Ydata
256
JPEG Decompression
Ydata
101 253
…
12
…
6
25
256
Y values
14
Image decompression (cont.)
• Restore quadtree
root(256x256)
256
100100000
256
128x128
128x128
128x128
128x128
Y values
64x64
64x64
64x64
64x64
15
Image decompression (cont.)
• Substitution coefficients
root(256x256)
a1,0 , a1,1 , a1,2 , b1,0 , b1,1 , b1,2 , a2,0 , a2,1 , a2,2 , b2,0 , b2,1 , b2,2 , ai,0 , ai,1 , ai,2 , bi,0 , bi,1 , bi,2
1
I i  a0  a1  Yi  a2  Yi 2
Qi  b0  b1  Yi  b2  Yi 2
256
0
0
128x128
1
128x128
0
128x128
128x128
256
0
0
64x64
0
64x64
0
64x64
64x64
YIQ values
16
Image decompression (cont.)
• YIQ
RGB
256
256
256
256
YIQ values
Lena
17
Experimental results
PSNR (dB)
40.00
F16
39.00
GIRL5
38.00
HOUSE
37.00
SAILBOAT
36.00
SPLASH
35.00
34.00
15
16
17
18
19
20
bits/per coefficient
The PSNRs of the decompressed images in different sizes of regression
equation coefficients
18
Experimental results (cont.)
PSNR (dB)
38.00
37.00
36.00
35.00
34.00
33.00
32.00
31.00
30.00
29.00
28.00
3 4 5
F16
GIRL5
HOUSE
SAILBOAT
SPLASH
6 7
8 9 10 11 12 13
CR
The PSNRs and CRs of the testing image compressed by JPEG method
19
Experimental results (cont.)
PSNR (dB)
42.00
40.00
38.00
36.00
34.00
32.00
30.00
28.00
26.00
24.00
F16
GIRL5
HOUSE
SAILBOAT
SPLASH
3
4
5
6
7
8
9 10 11 12 13
CR
The PSNRs and CRs of the testing image compressed by our method
20
Experimental results (cont.)
The PSNRs of the testing images encoded by JPEG method in different CRs in different CRs
CR
3
4
5
6
7
8
9
10
11
F16
37.07
36.59
36.12
35.67
35.23
34.81
34.40
34.00
33.62
33.25
32.89
GIRL5
36.12
35.83
35.55
35.27
35.00
34.74
34.49
34.24
34.00
33.76
33.53
HOUSE
34.38
34.17
33.96
33.76
33.56
33.37
33.18
33.00
32.82
32.64
32.47
SAILBOAT
33.44
32.91
32.40
31.91
31.44
30.99
30.56
30.15
29.75
29.37
29.01
SPLASH
36.94
36.63
36.33
36.04
35.76
35.48
35.22
34.95
34.70
34.45
34.21
Image
12
13
21
Experimental results (cont.)
CR
Image
The PSNRs of the testing images encoded by our method in different CRs
CR
3
4
5
6
7
8
9
10
11
12
13
F16
39.13
38.32
37.52
36.72
35.91
34.65
33.43
32.17
30.89
30.11
28.31
GIRL5
39.04
38.23
37.41
36.60
35.82
35.08
34.22
33.30
32.17
30.38
27.98
HOUSE
37.50
37.12
36.73
36.35
35.97
35.59
35.12
34.64
34.07
33.41
32.80
SAILBOAT
34.71
34.00
33.29
32.48
31.52
30.53
29.73
29.04
28.15
27.13
25.95
SPLASH
40.18
39.58
38.99
38.39
37.80
37.19
36.55
35.74
34.84
33.60
31.84
Image
22
Experimental results (cont.)
• Blocking and Gibbs effects
(a) PSNR: 31.503 dB
(b) PSNR: 31.542 dB
The decompressed images of GIRL4 decoded by our and JPEG methods
23
Conclusions
• Comparing to JPEG, the proposed method
has good performance with low
compression rate
24
子宮頸癌細胞抹片影像初始輪廓切割
• Speaker: Jun-Dong Chang
• Advisor: Yung-Kuan Chan, Hsien-Chu Wu
• Date: 2005/05/04
25
Introduction
• Automatic recognition reduces
the carelessness and mistakes
caused in artificial recognition.
• Initial Contour Segmentation is
a pre-process of ACM (Active
Contour Model) System.
• Initial Contour Segmentation
(Background, Cytoplasm, Nucl
eus)
26
Color & Texture Analyzing ~
Training Image
1 nn
mi 
cj

n  n j 1
 1
2
c j  mi  
 i  

 n  n j 1

1/ 2
 c j  mi
1

si 

n  n j 1   i
3
nn
nn
27



Color & Texture Analyzing ~
Training Image (cont.)
Background
Cytoplasm
Nucleus
28
Regression Function (cont.)
Background
29
Regression Function (cont.)
Cytoplasm
30
Regression Function (cont.)
Nucleus
31
Initial Contour Segmentation
Db
arg(min(Dx))
Dc
Background
Dn
Query Image
i = arg(min(Dx)), for x = b, c, n.
32
Initial Contour Segmentation (cont.)
Background
33
Initial Contour Segmentation (cont.)
Cytoplasm
34
Initial Contour Segmentation (cont.)
Nucleus
35
Experimental Results
~ Image 1
36
Experimental Results
~ Image 2
37
Experimental Results
~ Image 3
38
Experimental Results
~ Image 4
39
Conclusions
• Most of blocks are segmented at the correct lay
ers.
• Blocks of Background Layer are segmented to
Cytoplasm Layer.
• Regression Function just analyses 2D relation.
• We have to correct segmentation errors to impr
ove the accuracy of initial contour segmentation.
40
Future Work
• SVM (Support Vector Machine)
• Neighboring Block
41