Algorithms for testing convexity of digital polygons

Abstract A simple approach based on Shoenberg's theorem is described to test whether a set of border points of a simply 4-connected digital picture is convex. The sequential implementation of this method is linear inthe number of points; the parallel algorithm needs constant time only, using bitwise parallel Boolean operations and shifts on binary matrices. Suitable modifications of this approach can be used for decomposing two-dimensional objects into convex sets and for filling concavities.