A sequential learning method for boundary detection

摘要

In various fields digitized pictures are sometimes analysed, where it is desired to find the boundary of a figure on a background, when the background level is not strictly uniform but may be subject to very slow spatial variations of a certain importance with respect to the figure-background contrast. Moreover, the demarcation between the regions “figure” and “background” is at times characterized by a more or less sharp discontinuity of the gradient, rather than a level discontinuity. As is known, in such cases the boundary detection is frequently rather critical, if the image is blurred by a superimposed noise.In this work we propose a sequential learning method for boundary detection, which is particularly efficient in such critical cases. This method is based on using the information supplied by the pixels while they are been classified “on the boundary”, to obtain a Bayesian updating of the information on the two classes “figure” and “background”. This updating allows the decision rule to “learn” slow variations of both the background level and the gradient near the boundary in the “figure” region.This method works sequentially, since at each step it determines a new boundary pixel, referring to the likelihood of all the neighbours of the previous boundary pixel, by minimizing the “a posteriori” probability of error.