Parts-based 2D shape decomposition by convex hull

Parts-based 2D shape decomposition is important to shape analysis and recognition. Much research in psychology has shown that the human visual system tends to segment complex objects at regions of deep concavities, so concavity measurement is very important to shape decompositions, but it still has not a well accepted definition. In this paper, we propose a method for measuring concavities and segmenting a 2D shape without holes by 2D convex hulls. The primary motivation for using 2D convex hull in our SLA-concavity (straight line and angle concavity) is to grasp global variation trends of the polygon boundary, and furthermore, determine concave vertexes before computing interior angles for representing local attribute. SLA-concavity is invariant despite the presence of arbitrary translations, rotations and scales after normalizing the polygon by its area. For dealing with over-segmentation, we introduce a decomposition method in order of decreasing concavities, avoiding connection of two vertexes in the same pocket generated by a convex hull. Experimental results show that our approach has good performance.