Fire Detection Algorithms Using Multimodal ... - Bilkent University

LIST OF FIGURESxvii6.2 Markov model λ 1 corresponding to wildfire smoke (left) and theMarkov model λ 2 of clouds (right). Transition probabilities a ijand b ij are estimated off-line. . . . . . . . . . . . . . . . . . . . . 886.3 Orthogonal Projection: Find the vector w(n+1) on the hyperplaney(x, n) = D T (x, n)w minimizing the distance between w(n) andthe hyperplane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956.4 Geometric interpretation: Weight vectors corresponding to decisionfunctions at each frame are updated as to satisfy the hyperplaneequations defined by the oracle’s decision y(x, n) and thedecision vector D(x, n). Lines in the figure represent hyperplanesin R M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976.5 The pseudo-code for the active decision fusion algorithm . . . . . 996.6 The pseudo-code for the universal predictor . . . . . . . . . . . . 1006.7 The pseudo-code for the Weighted Majority Algorithm . . . . . . 1016.8 Sequence of frames excerpted from clip V 15. Within 18 secondsof time, cloud shadows cover forestal area which results in a falsealarm in an untrained algorithm with decision weights equal to14depicted as a bounding box. The proposed algorithm does notproduce a false alarm in this video. . . . . . . . . . . . . . . . . . 1036.9 The average error curves for the LMS, universal predictor, andthe WMA based adaptation algorithms in clip V 13.All of thealgorithms converge to the same average error value in this case,however the convergence rate of the LMS algorithm is faster thanboth the universal predictor and the WMA algorithm. . . . . . . . 105