Image Compression Based on Regression Equation

1
Image Compression Based on Regression Equation

• Advisor H. C. Wu, Y. K. Chan
• Speaker Hsin-Nan Tsai (???)
• Date May 4, 2005

2
Outline

• Introduction
• The proposed method
• Experimental results
• Conclusions

3
Introduction

• YIQ model
• Quadtree structure
• Edge detection
• Quadratic regression equation

4
Image compression

• RGB YIQ

5
Image compression (cont.)

• Quadtree

1
0
0
1
0
0
0
0
0
Breadth First Traversal Order
treelist 1 0 0 1 0 0 0 0 0
6
Image compression (cont.)

• Edge detection

?X
129 192 188 191
123 192 188 185
122 178 180 183
126 173 175 175
?Y
If PCD gt DiffTH Count Count 1
If Count gt CountTH quadtree()
7
Image compression (cont.)

• Quadratic regression equation

The coefficients a0, a1, and a2 of this equation
can be figured out by following three equations
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.)

• Quadratic regression equation

The coefficients b0, b1, and b2 of this equation
can be figured out by following three equations
i is the i-th pixel in an image block, and n is
the number of pixels in the image block.
9
Image compression (cont.)

• Compute coefficients

colorlist
10
Image compression (cont.)

• Compress Y values

256
100 251 3 25
12



JPEG compression
256

Y values
11
Image compression (cont.)
Compressed file treelist colorlist Ydata
12
Image decompression

• Extract treelist

Compressed file treelist colorlist Ydata
r is the numbers of 1-bits s is the numbers of
0-bits
3 r 1 s
13
Image decompression (cont.)

• Extract colorlist

Compressed file colorlist Ydata
6 s
14
Image decompression (cont.)

• Decompress Ydata

256
101 253 6 25
12



JPEG Decompression
256

Y values
15
Image decompression (cont.)

• Restore quadtree

256
1
0
0
1
0
0
0
0
0
1 0 0 1 0 0 0 0 0
256
Y values
16
Image decompression (cont.)

• Substitution coefficients

root(256x256)
1
256
1
0
0
0
128x128
128x128
128x128
128x128
256
0
0
0
0
YIQ values
64x64
64x64
64x64
64x64
17
Image decompression (cont.)

• YIQ RGB

256
256
256
256
YIQ values
Lena
18
Experimental results
19
Experimental results (cont.)
20
Experimental results (cont.)
21
Experimental results (cont.)
The PSNRs of the testing images encoded by JPEG
method in different CRs in different CRs
3 4 5 6 7 8 9 10 11 12 13
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
CR
Image
22
Experimental results (cont.)
The PSNRs of the testing images encoded by our
method in different CRs
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
CR
Image
23
Experimental results (cont.)

• Blocking and Gibbs effects

24
Conclusions

• Comparing to JPEG, the proposed method has good
  performance with low compression rate

25
????????????????

• Speaker Jun-Dong Chang
• Advisor Yung-Kuan Chan, Hsien-Chu Wu
• Date 2005/05/04

26
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, Nucleus)

27
Color Texture Analyzing Training Image
28
Color Texture Analyzing Training Image
(cont.)
Background
Cytoplasm
Nucleus
29
Regression Function (cont.)
Background
30
Regression Function (cont.)
Cytoplasm
31
Regression Function (cont.)
Nucleus
32
Initial Contour Segmentation
arg(min(Dx))
Background
Query Image
i arg(min(Dx)), for x b, c, n.
33
Initial Contour Segmentation (cont.)
Background
34
Initial Contour Segmentation (cont.)
Cytoplasm
35
Initial Contour Segmentation (cont.)
Nucleus
36
Experimental Results Image 1
37
Experimental Results Image 2
38
Experimental Results Image 3
39
Experimental Results Image 4
40
Conclusions

• Most of blocks are segmented at the correct
  layers.
• Blocks of Background Layer are segmented to
  Cytoplasm Layer.
• Regression Function just analyses 2D relation.
• We have to correct segmentation errors to improve
  the accuracy of initial contour segmentation.

41
Future Work

• SVM (Support Vector Machine)

• Neighboring Block