JPEG 2000 Image Analysis Darius Fennell University of Rochester

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