Computation of geometric properties from the medial axis transform in (O(nlogn) time

Abstract The digital medial axis transform (MAT) represents an image subset S as the union of maximal upright squares contained in S . Brute-force algorithms for computing geometric properties of S from its MAT require time O(n 2 ) , where n is the number of squares. Over the past few years, however, algorithms have been developed that compute properties for a union of upright rectangles in time O(n log n) , which makes the use of the MAT much more attractive. We review these algorithms and also present efficient algorithms for computing union-of-rectangle representations of derived sets (union, intersection, complement) and for conversion between the union of rectangles and other representations of a subset.