OUTLINE Introduction Supervised ,Unsupervised And Semi-Supervised - PowerPoint PPT Presentation

Presentation in A Bayesian Approach To Satellite Aircraft Image Identification Using Invariant Moments . Dickson Gichaga Wambaa F56/76676/2009 Supervised By Professor Elijah Mwangi University Of Nairobi Electrical And Information Engineering Dept. • 19 th September 2013 SEMINAR PRESENTATION

OUTLINE • Introduction • Supervised ,Unsupervised And Semi-Supervised Learning. • Classifiers • Feature Selection • Clustering • Results • Optimization • Conclusion • References

COMPUTER VISION • A Computer vision system captures images via a camera and analyzes them to produce descriptions of what is imaged.

PATTERN RECOGNITION • Pattern recognition is the discipline whose goal is the classification of objects into a number of categories or classes. These objects can be images or signal waveforms.

Aircraft Images • All aircraft are built with the same basic elements: – Wings – Engine(s) – Fuselage – Mechanical Controls – Tail assembly. • The differences of these elements distinguish their structures or images.

SUPERVISED AND UNSUPERVISED CLASSIFICATION • Supervised learning involves training data of known classes in an image database. • If the training data is not available then it is known as unsupervised learning or clustering. • And if some of the training data is of known classes then it is known as Semi-Supervised learning.

TASK • Design a classifier in a pattern recognition system.

Stages in the design of a classification system. FEATURE FEATURE CLASSIFIER SENSOR EVALUATION GENERATION SELECTION DESIGN

TYPES OF CLASSIFIERS • Classifiers Based on Bayes Decision Theory.

BAYESIAN DECISION THEORY CLASSIFIERS • Based on probabilistic statistical nature of generated features.

LINEAR CLASSIFIERS • Result from a set of linear discriminant functions.

NON-LINEAR CLASSIFIERS • Problems that are not linearly separable

FEATURE SELECTION • The number of features should be reduced to a sufficient minimum to minimize on Computational complexity.

CLASSIFIER PARAMETERS • For a finite number N of training patterns, the number of features l should be as small as possible so as to design a classifier with good generalization capabilities. The ratio N/l is also used in the performance evaluation stage .

FEATURE GENERATION • If I (x, y) Is a continuous image function, Its geometric moment of order p + q is defined as Geometric moments provide rich information about an image.

The Seven Moments of Hu • A set of seven moments that are invariant under the actions of translation, scaling, and rotation.

HU Moments • f1 = h 20 + h 02 • f2 = (h 20 - h 02 ) 2 + 4h 11 2 • f3 = (h 30 - 3h 12 ) 2 + (h 03 - 3h 21 )2 • f 4 = (h 30 + h 12 ) 2 + (h 03 + h 21 ) 2 • f 5 = (3h 30 - 3h 12 )(h 30 + h 12 )[(h 30 + h 12 ) 2 -3(h 21 + h 03 ) 2 ] + (3h 21 - h 03 )(h 21 + h 03 ) [3(h 30 + h 12 ) 2 - (h 21 + h 03 ) 2 ] • f 6 = (h 20 - h 02 )[(h 30 + h 12 ) 2 - (h 21 + h 03 ) 2 ]+ 4h 11 (h 30 + h 12 )(h 21 + h 03 ) • f 7 = (3h 21 - h 03 )(h 30 + h 12 )[(h 30 + h 12 ) 2 - 3(h 21 + h 03 ) 2 ] + • (3h 12 - h 30 )(h 21 + h 03 ) [3(h 30 + h 12 ) 2 - (h 21 + h 30 ) 2 ]

CLUSTERING • Clustering is unsupervised Classification. • VECTOR QUANTIZATION IS A COST FUNCTION BASED CLUSTERING.

STEPS IN CLUSTERING TASK • FEATURE SELECTION • PROXIMITY MEASURES • CLUSTERING CRITERION • CLUSTERING ALGORITHM • VALIDATION OF RESULTS

RESULTS Ф i Original Scaled Rotated Image Image Image Φ 1 6.500 6.500 6.500 Φ 2 16.3201 16.3200 16.3201 Φ 3 25.5669 25.5669 25.5669 Φ 4 25.8880 25.8880 25.8880 Φ 5 43.3000 43.3001 43.3000 Φ 6 34.0960 34.0960 34.0961 Φ 7 47.395 47.395 47.395

INVARIANT MOMENTS FOR 10 AIRCRAFTS Ф 1 Ф 2 Ф 3 Ф 4 Ф 5 Ф 6 Ф 7 Aircraft Image Apache 7.1729 16.6723 19.7413 21.8784 42.8038 30.2146 47.1336 1 A5 7.1487 20.2793 22.4129 24.4962 48.0614 34.6401 50.1980 2 C5 7.0341 16.2207 18.1325 20.3399 39.7008 28.6312 45.6856 3 Mig23 7.1921 17.7858 19.5198 21.7067 42.4404 30.7621 44.8716 4 A-4 SKYHAWK 5.1226 15.9883 11.9615 14.1234 27.4048 22.3531 28.3778 5 A-10 A 5.6575 17.9239 19.3685 21.0637 41.5321 30.3261 42.2122 6 THUNDER BOL TII A-6 INTRUDER 5.0326 16.9623 15.3296 17.1987 36.6321 26.7596 33.8529 7 A-7 CORSAIRII 5.7388 15.3942 16.9992 19.1147 37.6194 27.1467 38.3100 8 ALPHA 4.9672 15.3168 12.4693 14.6741 28.4333 22.5569 29.9875 9 JET AMX 7.2238 16.5452 18.3967 20.5945 40.2130 29.0375 45.2979 10

TEST IMAGE FEATURES Ф 1 Ф 2 Ф 3 Ф 4 Ф 5 Ф 6 Ф 7 Aircraft Image Sample 6.1939 16.1073 21.7588 23.2762 45.8489 33.3117 46.4124

POSTERIOR PROBABILITIES 10 AIRCRAFTS Posterior p(Ф1)/C i p(Ф2)/C i p(Ф3)/C i p(Ф4)/C i p(Ф5)/C i p(Ф6)/C i p(Ф7)/C i probabilitie s AIRCRAFT 0.53010155 0.239142429 0.128713538 0.130153337 0.066254708 0.113322114 0.055174814 8.79767E-07 Apache 1 0.540385913 0.025736543 0.04331936 0.044934173 0.022337103 0.027296774 0.037127917 6.12847E-10 A5 2 0.580429962 0.237774382 0.150376929 0.151342242 0.076931454 0.121520153 0.062799134 1.84401E-06 DELTA 3 WING 0.521569992 0.198120308 0.134533841 0.134759936 0.068735317 0.104895961 0.063198026 8.53643E-07 Mig23 4 0.020378607 0.215134605 0.008885482 0.008545815 0.004052047 0.015835887 0.003047201 6.50934E-14 A-4 5 SKYHAWK 0.123731866 0.187618545 0.13809907 0.147746366 0.073731031 0.111805648 0.062535275 2.44177E-07 A-10 A 6 THUNDER BOL TII 0.014081437 0.237710062 0.08224835 0.071969767 0.063053236 0.096938093 0.018266329 2.2122E-09 A-6 7 INTRUDER 0.153442028 0.171167628 0.135409074 0.135027707 0.069972999 0.104256364 0.044140037 1.54633E-07 A-7 8 CORSAIRII 0.010636652 0.164596904 0.013795254 0.013853378 0.006447256 0.017920509 0.00559365 2.16238E-13 ALPHA 9 JET 0.506820616 0.237494915 0.151036155 0.152098166 0.077253421 0.121735458 0.062231457 1.6183E-06 AMX 10

K-MEANS CLUSTERING AIRCRAFT 5 CLUSTERS 10 CLUSTERS 1 123 RF 1 1 2 CAW4F62P 5 9 3 CA8Q39AI 1 1 4 CAXF7IYK 3 6 5 CAORC6ZQ 3 6 6 B2 4 5 7 DELTA WING 1 1 8 F15 5 9 9 F35A 1 4 10 SAMPLE 1 1 AIRCRAFT

CLUSTER ANALYSIS CLUSTER CENTROIDS DATA No. NAME C 1 6 7.0183 18.9995 21.5296 23.5403 46.1832 33.3138 49.5230 C 2 6 7.0351 16.7412 18.6322 20.7872 40.6296 29.3285 44.8721 7.2015 17.1527 19.6870 21.9202 42.8392 30.6037 48.7196 C 3 7 C 4 7 6.6613 15.7419 16.9512 19.1145 37.5655 27.2579 39.7862 5.4466 14.1287 12.2083 14.4152 27.9367 21.8117 29.7311 C 5 6

CONCLUSION • Invariant moments feature extraction combined with Bayesian classifiers has been successful in classifier design: given a training set of patterns of known class, and a test pattern, a classifier has been designed that is optimal for the expected operating conditions.

REFERENCES • [1] Felix O. Owalla,Elijah Mwangi, “ A Robust Image Watermarking Scheme Invariant to Rotation,Scaling and Translation Attacks”, 16th IEEE Mediterranean Electrotechnical Conference, March , 2012. • [2] Dickson G. Wambaa,Elijah Mwangi, “ Aircrafts identification using moments invariants feature extraction and Bayesian Decision Theory Classification”, IEK Conference May, 2012. • [3] R. O. Duda,P. E. Hart and D. G. Stork, John Wiley & Sons, Pattern Classification ( 2 nd ed ) 2000

REFERENCES • [4] William K. Pratt. Digital image processing 4 th edition John Wiley,US,2007 • [5] M.- K. Hu, “Visual pattern recognition by moment invariants,” IRE Trans. Information Theory , vol. IT-8, pp. 179- 187, 1962. • [6] Richard O. Duda,Peter E. Hart and David G.Stork.Pattern Classification 2 nd edition John Wiley and Sons,US,2007 • [7] Rafael C. Gonzalez,Richard E. Woods and Steven L. Eddins . Digital image processing using matlab 2nd edition Pearson/Prentice Hall,US,2004

REFERENCES • [8] Dickson G. Wambaa,Elijah Mwangi, “ Aircrafts identification using moments invariants feature extraction and Bayesian Decision Theory Classification”, SAICSIT 2012 Masters and Doctoral Symposium 1 October 2012 Irene Country Lodge, Centurion South Africa.