Convexity rule for shape decomposition based on discrete contour evolution

We concentrate here on decomposition of 2D objects into meaningful parts of visual form, or visual parts. It is a simple observation that convex parts of objects determine visual parts, However, the problem is that many signi ficant visual parts are not convex, since a visual part may have concavitie s. We solve this problem by identifying convex parts at different stages of a proposed contour evolution method in which significant visual parts will become convex object parts at higher stages of the evolution, We obtain a novel rule for decomposition of 2D objects into visual parts, called the hi erarchical convexity rule, which states that visual parts are enclosed by m aximal convex (with respect to the object) boundary arcs at different stage s of the contour evolution. This rule determines not only parts of boundary curves but directly the visual parts of objects. Moreover, the stages of t he evolution hierarchy induce a hierarchical structure of the visual parts. The more advanced the stage of contour evolution, the more significant is the shape contribution of the obtained visual parts. (C) 1999 Academic Pres s.