Some further results of three stage ML classification applied to remotely sensed images

Abstract

Recently, a three stage Maximum Likelihood (TSML) classifier (N.B. Venkateswarlu and P. S. V. S. K. Raju, Pattern Recognition 24, 1113–1116 (1991)) has been proposed to reduce the computational requirements of the ML classification rule. Some modifications are proposed here further to improve this fast algorithm. The Winograd method is proposed for use with range calculations, and is also used with Lower Triangular and Unitary canonical form approaches (W. Eppler, IEEE Trans. Geoscience Electronics 14(1), 26–33 (1976)) in calculating quadratic forms. New types of range are derived by expanding the discriminant function which are then used with a TSML algorithm to identify their usefulness in eliminating groups at stages I and II. The use of pre-calculated values is proposed to obviate some multiplications while calculating the ranges. Further, threshold logic (A. H. Feiveson, IEEE Trans. Pattern Analysis Mach. Intell. 5(1), 48–54 (1983)) is used with an old and a modified TSML classifier and its effectiveness observed in further reducing computation time. Performance of the old and the modified TSML algorithms is studied in detail by varying the dimensionality and number of samples. For the purpose of experiment, 6 channel thematic mapper (TM) and randomly generated 12 dimensional data sets are used. A maximum speed-up factor of 4–8 is observed with these data sets. These experiments are also repeated with modified maximum likelihood and Mahalanobis distance classifiers to inspect CPU time requirements.