Simultaneous Fuzzy Segmentation of Multiple Objects

Fuzzy segmentation is a technique that assigns to each element in an image (corrupted by noise and/or shading) a grade of membership in an object (which is believed to be contained in the image). In an earlier work the first two authors extended this concept by presenting and illustrating an algorithm which simultaneously assigns to each element in an image a grade of membership in each one of a number of objects (which are believed to be contained in the image). In this paper we establish the correctness of this algorithm (in the sense of producing an output that is uniquely specified by a desirable mathematical property) and present a further example of its use in medical imaging. We also compare our method with two recently published related methods.