Near-convex decomposition of 2D shape using visibility range

Abstract

Part-based representation plays an important role in many shape related applications, including segmentation, recognition, editing and animation. An issue of particular interest in recent research is decomposing shapes into near-convex parts. However, it is usually challenging for existing methods to handle such heterogeneous real world shapes, especially when they possess long curved branches such as a lizard with a long curved tail. In this study, we propose a novel shape signature named visibility range, and a concavity measure based on this signature to describe the long curved branches. The visibility range reaches low values for points in concave regions and high values in convex regions, acting as the electrical charge distribution on the shape. Using these techniques, we present a coarse-to-fine approximate convex shape decomposition method, which separates the salient parts from the shape first and then refines the decomposition of the remaining main body of the shape by a visibility graph cut process. Qualitative and quantitative experiments have been conducted on shapes with various kinds of near-convex parts, demonstrating that our method captures the long curved branches as contiguous segments and outperforms the state-of-the-art methods that are based on other concave–convex features.