Algorithms for Fuzzy Segmentation

Abstract

Segmentation is the process of recognizing an object of interest in a picture. Thresholding is not an appropriate method of segmentation if there is some nonuniform shading in the picture or if what distinguishes the object of interest is not the exact values assigned to the individual pixels but rather some textural property. In such cases one can usefully apply fuzzy segmentation. We call a sequence of pixels in which consecutive pixels are adjacent a chain, and a pair of adjacent pixels a link. In fuzzy segmentation, the strength of any link is automatically defined based on statistical properties of the links within regions identified by the user as belonging to the object of interest. The strength of a chain is the strength of its weakest link. The fuzzy connectedness between any pair of pixels is the strength of the strongest chain between them. The fuzzy object containing a given pixel at a particular threshold is the set of all those pixels whose fuzzy connectedness to the given one exceeds or equals the threshold. A potentially time-consuming step in fuzzy segmentation is the calculation of the fuzzy connectedness of all other pixels to the given one. Previously this was done by a dynamic programming technique. We investigate the usefulness of replacing this by either of two greedy algorithms that have asymptotically better worst-case running times. We experimentally demonstrate that, even on quite small pictures, the greedy algorithms are many times faster than the dynamic programming technique.