Multidimensional Algorithm for Finding Discontinuities of Signals from Noisy Discrete Data

Algorithms are given for finding discontinuity surfaces of a signal specified with random errors at a regular grid in Rp, p ≥ 1. For each position of a sliding window one arranges points from it in ascending order of the measured values of the signal and divides them into two groups. One group contains points with larger values than the other. The division is made according to the nature of the particular pattern recognition problem. In the case of edge detection these groups have equal number of points. In the case of thin line detection one of the groups have a number of points proportional to the width of a line one is looking for. Then one calculates a functional which measures spatial separation of the above two groups. If the spatial separation is larger than the threshold, a discontinuity is deemed present. The threshold value is computed so that the probability of false alarm equals given parameter . The above approach is generalized to yield a computational scheme applicable for other pattern recognition problems. The consistency of the algorithms is proved. The results of testing of the algorithms are presented.