Convexity Verification, Block-Chords, and Digital Straight Lines

Convexity is an important pictorial property of an object, or a region in a picture. Beginning from the definition of convexity in the real plane we consider the effect of digitization and develop a general sequential algorithm capable of determining any concavity in a digitized picture. The algorithm employed is sequential, global, and has no adjustable parameters (diameters); it is thus capable of discovering localized as well as smooth (gentle) concavities within the extreme limits of sampling. By developing a similar point of view for digitized straight lines or edges we can deduce important properties of these patterns.