Presentation in Aircraft Satellite Image Identification Using Bayesian

Decision Theory And Moment Invariants Feature Extraction

Dickson Gichaga Wambaa

Supervised By Professor Elijah MwangiUniversity Of Nairobi

Electrical And Information Engineering Dept.

• 9th May 2012 IEK Presentation

OUTLINE

Introduction

Statistical Classification

Satellite images Denoising

Results

Conclusion

References

All aircraft are built with the same basic elements: Wings Engine(s) Fuselage Mechanical Controls Tail assembly. The differences of these elements distinguish one aircraft type from another and therefore its identification.

STAGES OF STATISTICAL PATTERN RECOGNITION

• PROBLEM FORMULATION• DATA COLLECTION

AND EXAMINATION• FEATURE

SELECTION OR EXTRACTION

• CLUSTERING• DISCRIMINATION• ASSESSMENT OF

RESULTS• INTERPRETATION

Classification ONE

• There are two main divisions of classification: • Supervised•unsupervised

SUPERVISED CLASSIFICATION

• BAYES CLASSIFICATION IS SELECTED SINCE IT IS POSSIBLE TO HAVE EXTREMELY HIGH VALUES IN ITS OPTIMISATION.

A decision rule partitions the measurement space into C regions.

Preprocessing

PREPROCESSING

IMAGE ACQUISITION

IMAGE ENHANCEMENT

IMAGE BINARIZATION

AND THRESHOLDING

FEATURES EXTRACTION

NOISEIMAGES ARE CONTAMINATED BY

NOISE THROUGH– IMPERFECT INSTRUMENTS– PROBLEMS WITH DATA ACQUISITION PROCESS– NATURAL PHENOMENA INTERFERENCE– TRANSMISSION ERRORS

SPECKLE NOISE(SPKN)

• THE TYPE OF NOISE FOUND IN SATELLITE IMAGES IS SPECKLE NOISE AND THIS DETERMINES THE ALGORITHM USED IN DENOISING.

Speckle Noise (SPKN) 2

• This is a multiplicative noise. The distribution noise can be expressed by:

J = I + n*I • Where, J is the distribution speckle

noise image, I is the input image and n is the uniform noise image.

CHOICE OF FILTER

FILTERING CONSISTS OF MOVING A WINDOW OVER EACH PIXEL OF AN IMAGE AND TO APPLY A MATHEMATICAL FUNCTION TO ACHIEVE A SMOOTHING EFFECT.

CHOICE OF FILTER II

• THE MATHEMATICAL FUNCTION DETERMINES THE FILTER TYPE.• MEAN FILTER-AVERAGES THE

WINDOW PIXELS• MEDIAN FILTER-CALCULATES THE

MEDIAN PIXEL

CHOICE OF FILTER II

• LEE-SIGMA AND LEE FILTERS-USE STATISTICAL DISTRIBUTION OF PIXELS IN THE WINDOW

• LOCAL REGION FILTER-COMPARES THE VARIANCES OF WINDOW REGIONS.

• THE FROST FILTER REPLACES THE PIXEL OF INTEREST WITH A WEIGHTED SUM OF THE VALUES WITHIN THE NxN MOVING WINDOW AND ASSUMES A MULTIPLICATIVE NOISE AND STATIONARY NOISE STATISTICS.

LEE FILTER

Adaptive Lee filter converts the multiplicative model into an additive one.

It preserves edges and detail.

BINARIZATION AND THRESHOLDING

TRAINING DATA SET

AH64 C5 B2

RESULTS: FEATURE EXTRACTION ORIGINAL IMAGES

AircraftsClasses

Ø1 Ø2 Ø3 Ø4 Ø5 Ø6 Ø7

B2(Class 1)

6.6132 14.0538 15.2462 17.4521 33.9469 24.6798 39.2648

AH64(Class 2)

7.1729 16.6723 19.7413 21.8784 42.8038 30.2146 47.1336

C5(Class3)

7.1487 20.2793 22.4129 24.4962 48.0614 34.6401 50.1980

NOISE ADDITION

•Noise with Probabilities of 0.1, 0.2, 0.3 and 0.4 was used for simulation.

FEATURE EXTRACTION:SAMPLE IMAGES

Ø1 Ø2 Ø3 Ø4 Ø5 Ø6 Ø7

B2 Class 1 6.6132 14.0538 15.2462 17.4521 33.9469 24.6798 39.2648

Test Image NOISE FILTERED

6.6001 13.9810 15.1678 17.4434 33.8456 24.6578 40.9765

Test Image ( 0.1 Noise Prob)

6.5579 13.9115 15.0382 17.2442 33.5329 24.4031 41.0169

Test Image (0.2 Noise Prob)

6.5406 13.8898 14.9673 17.1737 33.3923 24.3223 38.6145

Test Image (0.3 Noise Prob)

6.4703 13.7136 14.6351 16.8403 32.7292 23.9045 38.4642

Test Image (0.4 Noise Prob)

6.4124 13.5763 14.2593 16.4614 31.9765 23.4609 36.7216

WHY BAYES CLASSIFICATION 1

Bayes statistical method is the classification of choice because of its minimum error rate.

WHY BAYES CLASSIFICATION 2

• Probabilistic learning: among the most practical approaches to certain types of learning problems• Incremental: Each training example can

incrementally increase/decrease the probability that a hypothesis is correct

WHY BAYES CLASSIFICATION 3

•Probabilistic prediction: Predict multiple hypotheses•Benchmark: Provide a

benchmark for other algorithms

Bayesian Classification

• For a minimum error rate classifier the choice is on the class with maximum posterior probability.

Probabilities

• Let λ be set of 3 classes C1,C2 ,C3.• x be an unknown feature vector of

dimension 7.• Calculate the conditional posterior

probabilities of every class Ci and choose the class with maximum posteriori probability.

Prior Probabilities

• 3 classes of Data which are all likely to happen therefore

P(Ci)= 0.333

Posterior Probability 1

• Posterior = likelihood x prior evidence

• P(Ci\x) = P(x\Ci)P(Ci)

P(x)

POSTERIOR PROBABILITY 2

• Posterior(AH 64)=P(AH 64)P(x/ AH 64) p(evidence)

• Posterior(C5)=P(C5)P(x/ C5) p(evidence)• Posterior(B2)=P(B2)P(x/ B2) p(evidence)

POSTERIOR PROBABILITY 3

Posteriorprobability

Test Image NOISE FILTERED

Test Image ( 0.1 Noise Prob)

Test Image ( 0.2 Noise Prob)

Test Image ( 0.3 Noise Prob)

Test Image ( 0.4 Noise Prob)

AH 64 1.6954X10-2 1.6789X10-2 1.6034X10-2 1.5674X10-2 1.5045X10-2

C5 1.9653X10-2 1.8965X10-2 1.8463X10-2 1.8062X10-2 1.7453X10-2

B2 2.4239X10-2 2.2346X10-2 2.21567X10-2 2.1866X10-2 1.9889X10-2

CONCLUSION

• COMBINING MOMENTS FEATURES EXTRACTION WITH BAYESIAN CLASSIFICATION WHILE USING LEE FILTERS IN PREPROCESSING

• INCREASES THE CHANCES OF CORRECT IDENTIFICATION AS COMPARED TO NON USE OF THE FILTERS

• USE OF OTHER TYPES OF FILTERS THIS IS SEEN BY THE INCREASE OF THE POSTERIOR PROBABILITY VALUES.

References

• [1] Richard O. Duda,Peter E. Hart and David G. Stork.Pattern Classification 2nd edition John Wiley and Sons,US,2007

• [2] Rafael C. Gonzalez,Richard E. Woods and Steven L. Eddins . Digital image processing using matlab 2nd edition Pearson/Prentice Hall,US,2004

• [3] William K. Pratt. Digital image processing 4th edition John Wiley,US,2007• [4] Anil K. Jain. Fundamentals of Digital Image

Processing Prentice Hall,US,1989

References

• [5] Wei Cao, Shaoliang Meng, “Imaging systems and Techniques”,IEEE International Workshop,

IST.2009.5071625,pp 164-167, Shenzhen, 2009• [6] Bouguila.N, Elguebaly.T , “A Bayesian approach

for texture images classification and retrieval”,International Conference on Multimedia Computing and Systems, ICMS.2011.5945719,pp 1-6,Canada, 2011

References

• [7] Dixit. M, Rasiwasia. N, Vasconcelos. N, “Adapted Gaussian models for image classification” ,2011 IEEE Conference on Computer Vision and Pattern, CVPR.2011.5995674, pp 937-943, USA,2011

• [8] Mukesh C. Motwani,Mukesh C. Gadiya,Rakhi C. Motwani, Frederick C. Harris Jr. , “Survey Of Image Denoising Techniques”,University of Nevada Reno, US, 2001