Extracting Parts of 2D Shapes Using Local and Global Interactions Simultaneously

Perception research provides strong evidence in favor of part based representation of shapes in human visual system. Despite considerable differences among different theories in terms of how part boundaries are found, there is substantial agreement on that the process depends on many local and global geometric factors. This poses an important challenge from the computational point of view. In the first part of the chapter, I present a novel decomposition method by taking both local and global interactions within the shape domain into account. At the top of the partitioning hierarchy, the shape gets split into two parts capturing, respectively, the gross structure and the peripheral structure. The gross structure may be conceived as the least deformable part of the shape which remains stable under visual transformations. The peripheral structure includes limbs, protrusions, and boundary texture. Such a separation is in accord with the behavior of the artists who start with a gross shape and enrich it with details. The method is particularly interesting from the computational point of view as it does not resort to any geometric notions (e.g. curvature, convexity) explicitly. In the second part of the chapter, I relate the new method to PDE based shape representation schemes.