The Generalized Shape Distributions for shape matching and analysis

This paper presents a novel 3D shape descriptor "The Generalized Shape Distributions" for effective shape matching and analysis, by taking advantage of both local and global shape signatures. We start this process by generating spin images on meshes. These local shape descriptors are then quantized via k-means clustering. The key contribution of this paper is to represent a global 3D shape as the spatial configuration of a set of specific local shapes. We achieve this goal by computing the distributions of the Euclidean distance of pairs of local shape clusters. Because of the spatial, sparse distribution of local shapes defined over a 3D model, an indexing data structure is adopted to reduce the space complexity of the proposed shape descriptor. The technical merits of our new approach are at least two-fold: (1) It is robust to non-trivial shape occlusions and deformations, since there are statistically a large number of chances that some local shape signatures and their spatial layouts are unchanged and users can easily identify those unchanged parts; (2) It is more discriminative than a simple collection of local shape signatures, since the spatial layouts of a global shape are explicitly computed. Our preliminary experiments have shown the effectiveness of this new approach for shape comparison and analysis.