A fuzzy medial axis transformation based on fuzzy disks

Pal, S.K. and A. Rosenfeld, A fuzzy medial axis transformation based on fuzzy disks, Pattern Recognition Letters 12 (1991) 585-590. A fuzzy disk with cenler P is a fuzzy set in which membership depends only on distance from P. For any fuzzy set 1. there is a maximal fuzzy disk g~ ~j centered al every point P, and j is the sup of the g~'s. (Moreover, if j is fuzzy convex, so is every g~, bUI nOl conversely.) We call a set Sj of poinrsj-sufficient if every g~~g6 for some Q iu Sj; evidently j is lhen the sup of the g6's. In particular, in a digital image, the sel of Q's at which g.f is a (nonstrict) local maximum isj-sufficient. This set is called the juzzy medial axis of j, and die set of gb's is called (he fuzzy medial axis uansformatiOIl (FMAT) of j. These definitions evidenlly reduce to lhe standard one if jis a crisp set. Unfortunately, for an arbitrary j, specifying the FMAT may require more storage space than specifying j ilselL