Fuzzy medial axis transformation (FMAT): practical feasibility

Abstract

The Fuzzy Medial Axis Transformation (FMAT) of a fuzzy set f is a set of fuzzy disks whose sup is f. Unfortunately, specifying the FMAT sometimes requires more storage space than specifying f itself. The present paper describes some techniques to improve the compact representation of FMAT; thereby making it practically feasible and useful. The algorithms involve reduction of redundancy in FMAT, its approximation, and reduction of the searching spaces for its computation. The computational aspects for the convenience of writing an efficient program have also been described. A concept of 'sponsoring capability' of a pixel is described in order to view the principle of removing redundancy in FMAT and to generate its approximation. Two kinds of approximations are made, namely, distributed approximation and optimum fuzzy compactness. The aforesaid features have been demonstrated on a gray image.