Image Compression Based on Regression Equation

1

Image Compression Based on Regression Equation

Advisor: H. C. Wu, Y. K. Chan

Speaker: Hsin-Nan Tsai (蔡信男 )

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

YIQ

0.299 0.587 0.1140.596 -0.275 -0.3210.212 -0.523 0.311

RGB

= ×

5

Image compression (cont.)

• Quadtree

(128x128)(128x128) (128x128) (128x128)

(64x64)(64x64)(64x64)(64x64)

NW NE SW SE

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

129 192 188 191

123 192 188 185

122 178 180 183

126 173 175 175

∆X

∆Y

22X YPCD

If PCD > DiffTH Count = Count + 1

If Count > CountTH quadtree()

7

Image compression (cont.)

• Quadratic regression equation2

i2i10i YaYaaI

n

1ii

2i

n

1i

2i2

n

1i

3i1

n

1i

2i0

n

1iii

n

1i

3i2

n

1i

2i1

n

1ii0

n

1ii

n

1i

2i2

n

1ii10

IYYaYaYa

IYYaYaYa

IYaYaan

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

.

,

, and

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 equation2

i2i10i YbYbbQ

The coefficients b0, b1, and b2 of this equation can be figured out by following three equations:

n

1i

n

1ii

2i

n

1i

2i2

3i1

n

1i

2i0

n

1i

n

1iii

n

1i

3i2

2i1

n

1ii0

n

1i

n

1ii

2i2

n

1ii10

QYYbYbYb

QYYbYbYb

QYbYbbn

.

,

, and

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

2,1,0,2,1,0,2,21,20,22,21,20,22,11,10,12,11,10,1 ,,,,,,,,,,,,,,,,,, iiiiii bbbaaabbbaaabbbaaa

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Image compression (cont.)

• Compress Y values

100 251 … 3 25

12 …

256

256

Y values

JPEG compressionYdata…

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Image compression (cont.)

Compressed file: treelist || colorlist || Ydata

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Image decompression

• Extract treelist

r is the numbers of 1-bitss is the numbers of 0-bits

treelist: 1 0 0 1 0 0 0 0 0

3 × r + 1 = s

Compressed file: treelist || colorlist || Ydata

13

Image decompression (cont.)

• Extract colorlist

Compressed file: colorlist || Ydata

6 × s

2,1,0,2,1,0,2,21,20,22,21,20,22,11,10,12,11,10,1 ,,,,,,,,,,,,,,,,,, iiiiii bbbaaabbbaaabbbaaa

14

Image decompression (cont.)

• Decompress Ydata

YdataJPEG Decompression

101 253 … 6 25

12 …

256

256

Y values

…

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Image decompression (cont.)

• Restore quadtree

Y values

256

2561 0 0 1 0 0 0 0 0

root(256x256)

128x128 128x128 128x128 128x128

64x64 64x64 64x64 64x64

1 0 0 1 0 0 0 0 0

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Image decompression (cont.)

• Substitution coefficientsroot(256x256)

128x128 128x128 128x128 128x128

64x64 64x64 64x64 64x64

1

10 0 0

0 0 0 0 YIQ values

256

256

2210 iii YaYaaI

2210 iii YbYbbQ

2,1,0,2,1,0,2,21,20,22,21,20,22,11,10,12,11,10,1 ,,,,,,,,,,,,,,,,, iiiiii bbbaaabbbaaabbbaaa

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Image decompression (cont.)

• YIQ RGB

YIQ values

256

256

Lena

256

256

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Experimental results

The PSNRs of the decompressed images in different sizes of regression equation coefficients

34.00

35.00

36.00

37.00

38.00

39.00

40.00

15 16 17 18 19 20 bits/per coefficient

PSNR (dB)

F16

GIRL5

HOUSE

SAILBOAT

SPLASH

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Experimental results (cont.)

The PSNRs and CRs of the testing image compressed by JPEG method

28.0029.0030.0031.0032.0033.0034.0035.0036.0037.0038.00

3 4 5 6 7 8 9 10 11 12 13 CR

PSNR (dB)

F16

GIRL5

HOUSE

SAILBOAT

SPLASH

20

Experimental results (cont.)

The PSNRs and CRs of the testing image compressed by our method

24.0026.0028.0030.0032.0034.0036.0038.0040.0042.00

3 4 5 6 7 8 9 10 11 12 13 CR

PSNR (dB)

F16

GIRL5

HOUSE

SAILBOAT

SPLASH

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Experimental results (cont.)

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

The PSNRs of the testing images encoded by JPEG method in different CRs in different CRs

CRImage

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Experimental results (cont.) CR Image

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

The PSNRs of the testing images encoded by our method in different CRs

CRImage

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Experimental results (cont.)

• Blocking and Gibbs effects

The decompressed images of GIRL4 decoded by our and JPEG methods

(a) PSNR: 31.503 dB (b) PSNR: 31.542 dB

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Conclusions

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

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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

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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)

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Color & Texture Analyzing ~ Training Image

nn

jji c

nnm

1

1

2/1

1

21

nn

jiji mc

nn

nn

j i

iji

mc

nns

1

31

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Color & Texture Analyzing ~ Training Image (cont.)

Background

Cytoplasm

Nucleus

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Regression Function (cont.)

Background

30

Regression Function (cont.)

Cytoplasm

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Regression Function (cont.)

Nucleus

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Initial Contour Segmentation

bD

cD

nD

i = arg(min(Dx)), for x = b, c, n.

Query Image

Background

arg(min(Dx))

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Initial Contour Segmentation (cont.)

Background

34

Initial Contour Segmentation (cont.)

Cytoplasm

35

Initial Contour Segmentation (cont.)

Nucleus

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Experimental Results ~ Image 1

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Experimental Results~ Image 2

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Experimental Results ~ Image 3

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Experimental Results ~ Image 4

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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.

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Future Work

• SVM (Support Vector Machine)

• Neighboring Block