A fuzzy medial axis transformation based on fuzzy disks

Abstract A fuzzy disk with center P is a fuzzy set in which membership depends only on distance from P. For any fuzzy set ƒ , there is a maximal fuzzy disk gpƒ ⩽ ƒ centered at every point P, and ƒ is the sup of the gpƒ's. (Moreover, if ƒ is fuzzy convex, so is every gpƒ, but not conversely.) We call a set S ƒ of points ƒ -sufficient if every gpƒ ⩽ gQƒ for some Q in S ƒ ; evidently ƒ is then the sup of the gQƒ's. In particular, in a digital image, the set of Q's at which g ƒ is a (nonstrict) local maximum is ƒ -sufficient. This set is called the fuzzy medial axis of ƒ , and the set of g Q ƒ 's is called the fuzzy medial axis transformation (FMAT) of ƒ . These definitions evidently reduce to the standard one if ƒ is a crisp set. Unfortunately, for an arbitrary ƒ , specifying the FMAT may require more storage space than specifying ƒ itself.

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