On the computation of the digital convex hull and circular hull of a digital region

Abstract The problems of defining convexity and circularity of a digital region are considered. A new definition of digital convexity, called DL- (digital line) convexity, is proposed. A region is DL-convex if, for any two pixels belonging to it, there exists a digital straight line between them all of whose pixels belong to the region. DL-convexity is shown to be stronger that two other definitions, T- (triangle) convexity and L- (line) convexity. A digital region is T-convex if it is DL-convex, but the converse is not generally true. This is because a DL-convex region must be connected, but T- and L-convex regions can be disconnected. An algorithm to compute the DL-convex hull of a digital region is described. A related problem, the computation of the circular hull and its application to testing the circularity of a digital region, is also considered, and an algorithm is given that is computationally cheaper than a previous algorithm for testing circularity.