ABSTRACT
This chapter discusses with shape descriptors that are complete, that is, they contain enough information to fully reconstitute the original shape and are therefore unique. For nearly 40 years the medial axis transform (MAT) has been an intriguing tool for analyzing and computing with form, but it is one that is notoriously difficult to apply in a robust and stable way. Once a distance map has been constructed, the MAT is extracted from it and the interpretation of nonredundant points is carried out as for the circles. Unfortunately, there is no shortcut method for locating the nonredundant points, and an exhaustive search is the only sure approach. The practical difficulties of finding isomorphisms in graphs are reduced somewhat by constructing a directed graph from the MAT. The medial axis transform as described encodes complete information about the topology of an object and its local shape.
