brendan j. babb, frank moore, and pat marshall university of alaska, anchorage and afit ciisp 2007
DESCRIPTION
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
![Page 1: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/1.jpg)
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
![Page 2: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/2.jpg)
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.
![Page 3: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/3.jpg)
Overview
Why I might care? Wavelet image compression and
quantization Evolving wavelet like transforms Results Future Research Questions
![Page 4: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/4.jpg)
Applications
JPEG 2000 FBI Fingerprints database – 200
million cards – 2000 Terabytes of data
Web Digital Cameras Video MP3s
![Page 5: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/5.jpg)
Wavelet Compression
Forward Wavelet Transfor
m
Inverse Wavelet Transfor
m
Quantizer
Dequantizer
Encoder
Decoder
Compressor
Decompressor 10011…
Original Image
Lossy Image
![Page 6: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/6.jpg)
Multiresolution Analysis
![Page 7: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/7.jpg)
Quantization
Quantization of 64 Y value is 300 300/64 = 4.6875 = 4 Dequantization multiplies 4 * 64 = 256 17 times smaller file size
![Page 8: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/8.jpg)
Original “Zelda” Image
![Page 9: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/9.jpg)
Quantization 64
![Page 10: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/10.jpg)
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
![Page 11: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/11.jpg)
Information Entropy
n
iii xxnxEntropy
12log)(
n
iii yx
nyxMSE
1
2)(1
),(
![Page 12: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/12.jpg)
Genetic Algorithms
Optimization techniques inspired by Darwinian evolution
![Page 13: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/13.jpg)
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
![Page 14: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/14.jpg)
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
![Page 15: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/15.jpg)
Genetic Operators
Initial Population Fitness Selection Mutation Cross-over
![Page 16: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/16.jpg)
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
![Page 17: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/17.jpg)
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)
![Page 18: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/18.jpg)
Resulting images
23% MSE improvement for the same filesize for Fruits.bmp that generalizes
40% MSE improvement for Zelda image
![Page 19: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/19.jpg)
Original “Zelda” Image
![Page 20: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/20.jpg)
Quantization 64
![Page 21: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/21.jpg)
Evolved 40%
![Page 22: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/22.jpg)
Original “Zelda” Image
![Page 23: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/23.jpg)
Test Images (Partial)
![Page 24: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/24.jpg)
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
![Page 25: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/25.jpg)
Error Difference for D4
![Page 26: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/26.jpg)
Error Difference for Evolved
![Page 27: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/27.jpg)
Multiresolution Analysis
![Page 28: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/28.jpg)
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
![Page 29: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/29.jpg)
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
![Page 30: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/30.jpg)
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%)
![Page 31: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/31.jpg)
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
![Page 32: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/32.jpg)
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
![Page 33: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/33.jpg)
Fingerprint Image
![Page 34: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/34.jpg)
IE 110% - 60%
![Page 35: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/35.jpg)
Original “Zelda” Image
![Page 36: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/36.jpg)
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
![Page 37: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/37.jpg)
Questions
![Page 38: Brendan J. Babb, Frank Moore, and Pat Marshall University of Alaska, Anchorage and AFIT CIISP 2007](https://reader036.vdocument.in/reader036/viewer/2022062422/56813391550346895d9aa041/html5/thumbnails/38.jpg)
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