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Image Compression Based on Regression Equation
Advisor: H. C. Wu, Y. K. Chan
Speaker: Hsin-Nan Tsai (蔡信男 )
Date: May 4, 2005
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Outline
• Introduction
• The proposed method
• Experimental results
• Conclusions
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Introduction
• YIQ model
• Quadtree structure
• Edge detection
• Quadratic regression equation
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Image compression
• RGB YIQ
YIQ
0.299 0.587 0.1140.596 -0.275 -0.3210.212 -0.523 0.311
RGB
= ×
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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
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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()
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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.
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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.
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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
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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
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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
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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
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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
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Initial Contour Segmentation (cont.)
Cytoplasm
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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