Transcript Document 7190491

Evolving Multiresolution
Analysis Transforms for
Improved Image Compression
and Reconstruction under
Quantization
Brendan J. Babb, Frank Moore, and Pat Marshall
University of Alaska, Anchorage and AFIT
CIISP 2007
Results
We were able to improve image
quality on average by 23% over a
known wavelet transform with
quantization using a Genetic
Algorithm to evolve forward and
reverse transforms.
 For 3 level MRA the improvement is
11% over the standard wavelet.

Overview
Why I might care?
 Wavelet image compression and
quantization
 Evolving wavelet like transforms
 Results
 Future Research
 Questions

Applications
JPEG 2000
 FBI Fingerprints database – 200
million cards – 2000 Terabytes of data

Web
 Digital Cameras
 Video
 MP3s

Wavelet Compression
Compressor
Original Image
Forward
Wavelet
Transform
Quantizer
Decompressor
Encoder
10011…
Lossy Image
Inverse
Wavelet
Transform
Dequantizer
Decoder
Multiresolution Analysis
Quantization
Quantization of 64
 Y value is 300
 300/64 = 4.6875 = 4
 Dequantization multiplies 4 * 64 = 256
 17 times smaller file size

Original “Zelda” Image
Quantization 64
Mean Squared Error (MSE)
The common method for comparing the
quality of a reproduced image is Mean
Squared Error
 The average of the square of the
difference between the desired response
and the actual system output (the error)
 Must consider file size

Information Entropy
n

Entropy( x )  n  xi log 2 xi
i 1
  1 n
MSE ( x , y )   ( xi  yi ) 2
n i 1
Genetic Algorithms

Optimization techniques inspired by
Darwinian evolution
Previous Research
Dr. Moore published papers on 1-D
signals and images, evolving the
Inverse transform
 90% improvement on 1-D and 5 – 9 %
improvement on images over
Wavelets

Specifics
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Matlab code modified from Michael
Peterson’s code based on Dr. Moore’s
code.
Forward and Reverse at the same time
Start with a population of real coefficients
from a known Wavelet
Daubechies 4 ( 8 forward and 8 reverse)
MR Levels 1 through 3
Parallel operation on Supercomputer
Genetic Operators
Initial Population
 Fitness
 Selection
 Mutation
 Cross-over

Fitness Function
Restrain File Size
 A * MSE ratio + B * File Size ratio
 Good MSE but bigger files or vice
versa
 Penalize for bigger file size or bigger
MSE with if statement combinations
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GA Parameters
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Population size: 500 to 10000
Generations: 500 to 2000
Elite Survival Count: 2
Parental Selection: stochastic uniform
Crossover: Heuristic
Mutation: varies by experiment
Population initialization: Random factor times the
original Wavelet
• Crossover to Mutation ratio: 0.7 (unless noted)
Resulting images
23% MSE improvement for the same
filesize for Fruits.bmp that generalizes
 40% MSE improvement for Zelda
image

Original “Zelda” Image
Quantization 64
Evolved 40%
Original “Zelda” Image
Test Images (Partial)
1 Level Runs
Run #1
image
Run #2
IE % Size
SE %
SE imprv
image
Run #3
IE % Size
SE %
SE imprv
image
IE % Size
SE %
SE imprv
airplane
95.34
72
28
airplane
96.26
72.7
27.3
Airplane
99.98
57.86
42.14
baboon
94.38
93.2
6.8
baboon
98.8
85.07
14.93
baboon
105.88
68.6
31.4
barb
97.85
77.12
22.88
barb
100.47
77.72
22.28
barb
105.56
66.09
33.91
boat
98.03
79.28
20.72
boat
99.06
77.34
22.66
boat
105.39
61.73
38.27
couple
96.45
81.61
18.39
couple
100
77.67
22.33
couple
105.35
62.55
37.45
fruits
98.06
96.38
3.62
Fruits
100
74.82
25.18
fruits
105.24
64.61
35.39
goldhill
98.82
72.91
27.09
goldhill
100.97
73.27
26.73
goldhill
105.58
61.93
38.07
lenna
99.11
70.26
29.74
lenna
100.05
76.75
23.25
lenna
104.47
56.6
43.4
park
97.04
81.64
18.36
park
100.76
86.72
13.28
park
104.87
65.17
34.83
peppers
99.61
68.79
31.21
peppers
101.05
69.02
30.98
peppers
105.72
56.49
43.51
susie
97.57
72.55
27.45
susie
100.02
74.45
25.55
susie
104.12
57.4
42.6
Zelda
100
60.22
39.78
zelda
101.51
67.95
32.05
zelda
106.19
57.48
42.52
97.69
77.16
22.84
avg
99.91
76.12
23.88
avg
104.86
61.38
38.62
avg
Error Difference for D4
Error Difference for Evolved
Multiresolution Analysis
MRA3 Same at each level
Trained on Fruits SAME coeffs
at each level MRA 3
image 512
IE %
MSE %
MSEI %
Trained on Zelda SAME coeffs at
each level MRA 3
image 512
IE %
MSE %
MSEI %
airplane
100
92.14
7.86
airplane
100.06
92.32
7.68
baboon
99.95
90.28
9.72
baboon
101
88.01
11.99
barb
99.95
92.77
7.23
barb
100.8
91.86
8.14
boat
100.08
92.18
7.82
boat
100.41
91.94
8.06
couple
99.99
91.81
8.19
couple
100.45
90.67
9.33
fruits
99.95
93.9
6.1
fruits
100.29
95.92
4.08
100.06
91.99
8.01
goldhill
100.49
90.06
9.94
lenna
99.94
92.86
7.14
lenna
99.94
92.86
7.14
park
100.03
92.6
7.4
park
100.18
92.24
7.76
peppers
100.08
93.44
6.56
peppers
100.08
94.41
5.59
susie
99.84
92.78
7.22
susie
100.06
91.37
8.63
zelda
100.12
91.98
8.02
zelda
99.99
89.82
10.18
100.00
92.39
7.61
100.31
91.79
8.21
goldhill
MRA 3 different at each level
Trained on Fruits DIFFERENT
coeffs at each level MRA 3
Image 512
IE %
MSE %
Trained on Zelda DIFFERENT
coeffs at each level MRA 3
MSEI %
image 512
IE %
MSE %
MSEI %
airplane
99.98
87.38
12.62
airplane
100.17
89.51
10.49
baboon
100.07
88.14
11.86
baboon
100.89
93.59
6.41
barb
100.04
97.56
2.44
barb
100.61
106.97
-6.97
boat
100.09
86.99
13.01
boat
100.31
88.45
11.55
99.97
86.87
13.13
couple
100.43
88.34
11.66
fruits
100.43
88.34
11.66
fruits
100.43
88.34
11.66
goldhill
100.02
89.1
10.9
goldhill
100.34
88.24
11.76
lenna
99.9
88.89
11.11
lenna
100.23
88.49
11.51
park
100
88.09
11.91
park
100.47
90.13
9.87
100.02
93
7
peppers
100.16
97.58
2.42
susie
99.84
91.01
8.99
susie
100.25
93.66
6.34
zelda
100.16
89.96
10.04
zelda
100
87.79
12.21
100.04
89.61
10.39
100.36
91.76
8.24
couple
peppers
Evolved Coeffs
Set
h1 (Lo_D)
g1 (Hi_D)
h2 (Lo_R)
g2 (Hi_R)
1
2
3
1
2
3
1
2
3
1
2
3
MRA Level
Values (% Change Relative to D4 Wavelet)
-0.1278, 0.2274, 0.8456, 0.4664 (-1.24%, +1.47%, +1.09%, -3.44%)
-0.1274, 0.2289, 0.8446, 0.4661 (-1.55%, +2.14%, +0.97%, -3.50%)
-0.1278, 0.2281, 0.8455, 0.4670 (-1.24%, +1.78%, +1.08%, -3.31%)
0.4791, 0.8474, -0.2347, -0.1278 (-0.81%, +1.30%, +4.73%, -1.24%)
-0.4894, 0.8447, -0.2317, -0.1279 (+1.33%, +0.98%, +3.39%, -1.16%)
-0.4901, 0.8462, -0.2291, -0.1288 (+1.47%, +1.16%, +2.23%, -0.46%)
0.4811, 0.8152, 0.2274, -0.1069 (-0.39%, -2.55%, +1.47%, -17.39%)
0.4805, 0.8159, 0.2279, -0.1093 (-0.52%, -2.46%, +1.70%, -15.53%)
0.4820, 0.8172, 0.2278, -0.1097 (-0.21%, -2.31%, +1.65%, -15.22%)
-0.2008, 0.0274, 0.5960, -0.1472 (+55.18%, -87.78%, -28.75%, -69.52%)
-0.1618, -0.1105, 0.6870, -0.3201 (+25.04%, -50.69%, -17.87%, -33.73%)
-0.1572, -0.1495, 0.7861, -0.4033 (+21.48%, -33.29%, -6.03%, -16.50%)
Summary
Forward and Inverse Transforms
evolved from Wavelets have better
image quality than the Wavelet under
quantization and multiple levels
 Improves image quality with the same
amount of file size
 Training images exist which
generalize well across other images

Recent Research
Increased Information Entropy results
in 60% improvement for Zelda
 Evolving for fingerprint images results
in 16% improvement over FBI
standard for 80 images (Humie)
 Training over 4 images and using
Differential Evolution
 Evolved Fingerprint wavelet does
poorly on standard test images

Fingerprint Image
IE 110% - 60%
Original “Zelda” Image
Future Research
Evolving different shape wavelets
 Mathematically analyze
 Use of different operators and
techniques
 What makes a good representative
training image
 Improve on JPEG 2000 wavelets
 Custom wavelets for other
applications

Questions
Fitness Logic
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If (SE ratio > 1) and (IE ratio > 1)
then fitness = (SE ratio)^4 +(IE ratio)^4
else if (SE ratio > 1)
then fitness = (SE ratio)^4 + IE ratio
else if (IE ratio > 1)
then fitness = SE ratio + (IE ratio)^4
else
fitness = (SE ratio)^2 + IE
fitness = fitness *1000