Presentation in Aircraft Satellite Image Identification Using Bayesian Decision Theory And Moment Invariants Feature Extraction Dickson Gichaga Wambaa Supervised By Professor Elijah Mwangi University 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 NOISE IMAGES 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 RESULTS: FEATURE EXTRACTION ORIGINAL IMAGES Aircraf ts Classe s Ø1 Ø2 Ø3 Ø4 Ø5 Ø6 Ø7 B2 (Class 1) 6.6132 14.053 8 15.246 2 17.452 1 33.946 9 24.679 8 39.264 8 AH64 (Class 2) 7.1729 16.672 3 19.741 3 21.878 4 42.803 8 30.214 6 47.133 6 C5 (Class 3) 7.1487 20.279 3 22.412 9 24.496 2 48.061 4 34.640 1 50.198 0 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 B2 Class 1 6.6132 Test Image Ø3 Ø4 Ø5 Ø6 Ø7 14.0538 15.2462 17.4521 33.9469 24.6798 39.2648 6.6001 13.9810 15.1678 17.4434 33.8456 24.6578 40.9765 6.5579 13.9115 15.0382 17.2442 33.5329 24.4031 41.0169 6.5406 13.8898 14.9673 17.1737 33.3923 24.3223 38.6145 6.4703 13.7136 14.6351 16.8403 32.7292 23.9045 38.4642 6.4124 13.5763 14.2593 16.4614 31.9765 23.4609 36.7216 NOISE FILTERED Test Image ( 0.1 Noise Prob) Test Image (0.2 Noise Prob) Test Image (0.3 Noise Prob) Test Image 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 Posterior Test Image probability NOISE FILTERED Test Image ( 0.1 Noise Prob) Test Image ( Test Image 0.2 Noise ( 0.3 Noise Prob) 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. 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