Approximate convex decomposition for 2D shapes based on visibility range

Abstract

Organizing shapes by convex parts is a fundamental procedure for many shape-related applications. However, convexity is sensitive to noise and shape variations. Recent publications in the field concentrated on decomposing shapes into near-convex parts. Although a variety of methods have been presented, there is still a need for a robust and versatile method, especially when a shape possesses long curved branches such as a lizard with a long curved tail. It is difficult to capture the tail as a whole part because its concavity is too high based on classic measures. To address this issue, we propose a ‘Visibility Range’, novel shape signature in this paper. Visibility range reaches low values for points in concave regions and high values in convex regions. Moreover, a novel concavity measure based on visibility range is presented. Compared to previous measures, the novel measure describes long curved branches better. With these, a simple but effective shape decomposition algorithm is designed. The decomposition is formulated as a problem of detecting points with extreme visibility range in a visibility matrix. Extensive experiments have been done on shapes with various kinds of near-convex parts, demonstrating that the proposed method is more robust and effective than the state-of-art methods based on other concave-convex features.