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JPEG 2000 Image AnalysisJPEG 2000 Image Analysis
Darius FennellDarius Fennell
University of RochesterUniversity of Rochester
Experiment ObjectiveExperiment Objective
Using JPEG 2000 calculate and analyze Using JPEG 2000 calculate and analyze the following:the following:– Distortion vs. RateDistortion vs. Rate– Distortion vs. QuantizationDistortion vs. Quantization– Time vs. QuantizationTime vs. Quantization– Time vs. ResolutionTime vs. Resolution
Experiment MaterialsExperiment Materials
Dell ComputerDell Computer– 2.79 GHz Processing2.79 GHz Processing– 2.00 GB of RAM2.00 GB of RAM
Matlab 7.0.1 R14Matlab 7.0.1 R14
Kakadu JPEG 2000 softwareKakadu JPEG 2000 software
5 Standard images5 Standard images
Standard ImageryStandard Imagery
Originally 3 bands @ 512x512Originally 3 bands @ 512x512
Reduced to single band 128x128Reduced to single band 128x128
Basic JPEG 2000 Compression ChainBasic JPEG 2000 Compression Chain
ExpectationExpectation
Distortion vs. RateDistortion vs. Rate– As rate increases distortion decreasesAs rate increases distortion decreases
Distortion vs. QuantizationDistortion vs. Quantization– As step size decreases distortion decreasesAs step size decreases distortion decreases
Time vs. QuantizationTime vs. Quantization– As quantization increases time decreasesAs quantization increases time decreases
Time vs. Spatial ResolutionTime vs. Spatial Resolution– As Spatial Resolution increases time As Spatial Resolution increases time
increasesincreases
Distortion vs. RateDistortion vs. Rate
Imagery compressed at multiple rates:Imagery compressed at multiple rates:– 7.0,4.0,2.0,1.0,0.5, and 0.257.0,4.0,2.0,1.0,0.5, and 0.25– Average Bit Rate per pixelAverage Bit Rate per pixel
Imagery decompressed to each rate and Imagery decompressed to each rate and compared to the original.compared to the original.– MSE=var(original-decompressed)MSE=var(original-decompressed)
Distortion vs. Rate ResultsDistortion vs. Rate Results
0 1 2 3 4 5 6 70
100
200
300
400
500
600
700
800
Rate
MS
E
Error Vs. Rate
baboon
house
splashjet
peppers
1 2 3 4 5 60
100
200
300
400
500
600
700
800
Bit bin
MS
E
MSE vs. BitRate Across all Images
1--0.252--0.503--1.004--2.005--5.006--7.00
min
max
mean
std
QuantizationQuantization
Imagery compressed using varying step Imagery compressed using varying step sizes:2^-7 to 2^7sizes:2^-7 to 2^7
MSE calculatedMSE calculated
Processing time determined by Matlab’s Processing time determined by Matlab’s tic/toc commandtic/toc command
Distortion vs. Quantization ResultsDistortion vs. Quantization Results
10-3
10-2
10-1
100
101
102
103
0
1000
2000
3000
4000
5000
6000
Step Size
MS
E
Error Vs. Quantization
baboon
house
splashjet
peppers
1 2 3 4 5 6 7 8 9 10 11 12 13 14 150
1000
2000
3000
4000
5000
6000
Quantization BinM
SE
MSE vs. Quantization across all Images
min
maxmean
std
Time vs. Quantization ResultsTime vs. Quantization Results
1 2 3 4 5 6 7 8 9 10 11 12 13 14 150
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Quantization Bin
Tim
e
Time vs. Quantization across all Images
min
maxmean
std
10-5
100
105
0
0.05
0.1
0.15
0.2Baboon--Step Size vs. Time
Step Size
Tim
e
10-5
100
105
0
0.02
0.04
0.06
0.08House--Step Size vs. Time
Step Size
Tim
e
10-5
100
105
0
0.02
0.04
0.06
0.08Splash--Step Size vs. Time
Step Size
Tim
e
10-5
100
105
0
0.02
0.04
0.06
0.08Jet--Step Size vs. Time
Step Size
Tim
e
10-5
100
105
0
0.02
0.04
0.06
0.08Peppers--Step Size vs. Time
Step Size
Tim
e
Time vs. Spatial ResolutionTime vs. Spatial Resolution
Images Sizes: Images Sizes: – 512x512512x512– 256x256256x256– 128x128128x128– 64x6464x64
Processing time determined by Matlab’s Processing time determined by Matlab’s tic/toc commandtic/toc command
Time vs. Spatial ResolutionTime vs. Spatial Resolution
1 2 3 40
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Square Image Size
Tim
e
Time vs. Image Size across all Images
1--512x5122--256x2563--128x1284--64x64
min
maxmean
std
0 200 400 6000
0.05
0.1
0.15
0.2Baboon--Time vs. Image Size
Square Image Size
Tim
e (s
ec)
0 200 400 6000
0.05
0.1House--Time vs. Image Size
Square Image Size
Tim
e (s
ec)
0 200 400 6000
0.05
0.1
0.15
0.2Splash--Time vs. Image Size
Square Image Size
Tim
e (s
ec)
0 200 400 6000
0.05
0.1Jet--Time vs. Image Size
Square Image Size
Tim
e (s
ec)
0 200 400 6000
0.05
0.1
0.15
0.2Peppers--Time vs. Image Size
Square Image Size
Tim
e (s
ec)
ConclusionConclusion
Rate & quantization have a drastic effect Rate & quantization have a drastic effect on the error.on the error.
Step size does not significantly effect Step size does not significantly effect compression time for quantization.compression time for quantization.
Increased spatial resolution increases Increased spatial resolution increases compression time yet other factors are compression time yet other factors are involved that affect the over processing involved that affect the over processing chain.chain.
ReferencesReferences
http://www.kakadusoftware.comhttp://www.kakadusoftware.com
http://www.gvsu.edu/math/wavelets/http://www.gvsu.edu/math/wavelets/student_work/EF/index.htmlstudent_work/EF/index.html
