brendan j. babb, frank moore, and pat marshall university of alaska, anchorage and afit ciisp 2007
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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. - PowerPoint PPT PresentationTRANSCRIPT
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
Forward Wavelet Transfor
m
Inverse Wavelet Transfor
m
Quantizer
Dequantizer
Encoder
Decoder
Compressor
Decompressor 10011…
Original Image
Lossy Image
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
iii xxnxEntropy
12log)(
n
iii yx
nyxMSE
1
2)(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
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
GA Parameters
• 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
image IE % Size SE % SE imprv image 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
avg 97.69 77.16 22.84 avg 99.91 76.12 23.88 avg 104.86 61.38 38.62
Run #1 Run #2 Run #3
Error Difference for D4
Error Difference for Evolved
Multiresolution Analysis
MRA3 Same at each level
Trained on Zelda SAME coeffs at each level MRA 3
image 512 IE % MSE % MSEI %
airplane 100.06 92.32 7.68
baboon 101 88.01 11.99
barb 100.8 91.86 8.14
boat 100.41 91.94 8.06
couple 100.45 90.67 9.33
fruits 100.29 95.92 4.08
goldhill 100.49 90.06 9.94
lenna 99.94 92.86 7.14
park 100.18 92.24 7.76
peppers 100.08 94.41 5.59
susie 100.06 91.37 8.63
zelda 99.99 89.82 10.18
100.31 91.79 8.21
Trained on Fruits SAME coeffs at each level MRA 3
image 512 IE % MSE % MSEI %
airplane 100 92.14 7.86
baboon 99.95 90.28 9.72
barb 99.95 92.77 7.23
boat 100.08 92.18 7.82
couple 99.99 91.81 8.19
fruits 99.95 93.9 6.1
goldhill 100.06 91.99 8.01
lenna 99.94 92.86 7.14
park 100.03 92.6 7.4
peppers 100.08 93.44 6.56
susie 99.84 92.78 7.22
zelda 100.12 91.98 8.02
100.00 92.39 7.61
MRA 3 different at each level
Trained on Zelda DIFFERENT coeffs at each level MRA 3
image 512 IE % MSE % MSEI %
airplane 100.17 89.51 10.49
baboon 100.89 93.59 6.41
barb 100.61 106.97 -6.97
boat 100.31 88.45 11.55
couple 100.43 88.34 11.66
fruits 100.43 88.34 11.66
goldhill 100.34 88.24 11.76
lenna 100.23 88.49 11.51
park 100.47 90.13 9.87
peppers 100.16 97.58 2.42
susie 100.25 93.66 6.34
zelda 100 87.79 12.21
100.36 91.76 8.24
Trained on Fruits DIFFERENT coeffs at each level MRA 3
Image 512 IE % MSE % MSEI %
airplane 99.98 87.38 12.62
baboon 100.07 88.14 11.86
barb 100.04 97.56 2.44
boat 100.09 86.99 13.01
couple 99.97 86.87 13.13
fruits 100.43 88.34 11.66
goldhill 100.02 89.1 10.9
lenna 99.9 88.89 11.11
park 100 88.09 11.91
peppers 100.02 93 7
susie 99.84 91.01 8.99
zelda 100.16 89.96 10.04
100.04 89.61 10.39
Evolved Coeffs
Set MRA Level Values (% Change Relative to D4 Wavelet)h1 (Lo_D) 1 -0.1278, 0.2274, 0.8456, 0.4664 (-1.24%, +1.47%, +1.09%, -3.44%)
2 -0.1274, 0.2289, 0.8446, 0.4661 (-1.55%, +2.14%, +0.97%, -3.50%)3 -0.1278, 0.2281, 0.8455, 0.4670 (-1.24%, +1.78%, +1.08%, -3.31%)
g1 (Hi_D) 1 0.4791, 0.8474, -0.2347, -0.1278 (-0.81%, +1.30%, +4.73%, -1.24%) 2 -0.4894, 0.8447, -0.2317, -0.1279 (+1.33%, +0.98%, +3.39%, -1.16%) 3 -0.4901, 0.8462, -0.2291, -0.1288 (+1.47%, +1.16%, +2.23%, -0.46%)
h2 (Lo_R) 1 0.4811, 0.8152, 0.2274, -0.1069 (-0.39%, -2.55%, +1.47%, -17.39%) 2 0.4805, 0.8159, 0.2279, -0.1093 (-0.52%, -2.46%, +1.70%, -15.53%) 3 0.4820, 0.8172, 0.2278, -0.1097 (-0.21%, -2.31%, +1.65%, -15.22%)
g2 (Hi_R) 1 -0.2008, 0.0274, 0.5960, -0.1472 (+55.18%, -87.78%, -28.75%, -69.52%) 2 -0.1618, -0.1105, 0.6870, -0.3201 (+25.04%, -50.69%, -17.87%, -33.73%)
3 -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
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