Dual-Space Decomposition of 2D Complex Shapes

While techniques that segment shapes into visually meaningful parts have generated impressive results, these techniques also have only focused on relatively simple shapes, such as those composed of a single object either without holes or with few simple holes. In many applications, shapes created from images can contain many overlapping objects and holes. These holes may come from sensor noise, may have important parts of the shape or may be arbitrarily complex. These complexities that appear in real-world 2D shapes can pose grand challenges to the existing part segmentation methods. In this paper, we propose a new decomposition method, called Dual-space Decomposition that handles complex 2D shapes by recognizing the importance of holes and classifying holes as either topological noise or structurally important features. Our method creates a nearly convex decomposition of a given shape by segmenting both the polygon itself and its complementary. We compare our results to segmentation produced by nonexpert human subjects. Based on two evaluation methods, we show that this new decomposition method creates statistically similar to those produced by human subjects.