Fast homotopy-preserving skeletons using mathematical morphology

Two algorithms for skeletonization of 2-D binary images, each of which explicitly separates the two major aspects of skeletonization are described: the identification of points critical to shape representation, and the identification of further points necessary to preserve homotopy. Sets of points critical to shape representation are found by eroding the original image I with a nested sequence of structuring elements E_i. By choosing appropriate { E_i} and D, a structuring element, either algorithm is capable of producing a variety of skeletons corresponding to different distance functions. A sufficient condition is given for the original image to be reconstructed from the skeleton. In the case of the first algorithm, there are few restrictions on the set of structuring elements. It uses a simple search strategy to find points whose removal would alter homotopy. The second, faster, algorithm has a more constructional approach to finding points necessary for preserving homotopy, which limits it to a more restricted set of structuring elements than the first algorithm. However, it may still be used with a variety of distance functions