Skeletonization via dual of shape segmentation

摘要

Curve skeletons of 3D objects are central to many geometry analysis tasks in the field of computer graphics. A desirable skeleton has to meet at least four requirements: (1) topologically homotopic to the primitive shape, (2) truly well-centred, (3) feature preserving and (4) has a reasonable degree of smoothness. There are at least a couple of difficulties with skeletonization. On the one hand, finding the "best" skeleton is related to visual perception, to some extent, and thus hard to be completely solved by a pure geometric technique. On the other hand, how to exactly characterize the centredness of a skeleton, without a pre-computed medial axis surface, still remains challenging. Due to the fact that skeletons are able to encode the overall structure, a skeleton has been used to guide segmentation of a shape, which implies that there exists a dual relationship between segmentation and skeletonization. Based on the underlying duality, we propose to generate skeletons from a reliable segmentation result that is more easily available by deep learning or alternative techniques. In implementation, we first extract a collection of samples and then compute the Voronoi diagram restricted in the volume w.r.t. those samples, followed by transforming the clipped Voronoi diagram into a graph G. We further equip each edge in G with a centredness score. The user-specific segmentation result is then used to decompose G into a set of subgraphs G_(i=1)~k The next task is to compute the Steiner tree for each subgraph while requiring that the Steiner trees of two adjacent parts G_i and G_j must be linked together. The global structure of the final skeleton inherits the proximity configuration of the user-specific segmentation, and thus is topologically homotopic to the primitive shape. At the same time, the centredness of the final skeleton is taken into full consideration by maximizing the overall centredness score. We also integrate the other two requirements carefully into our algorithmic framework. We conduct extensive experiments to evaluate the new approach in terms of the above-mentioned aspects. The experimental results show that our approach has an obvious advantage over the state-of-the-arts. As a by-product of our algorithm, users can obtain skeletons with different levels of details by editing the segmentation configurations.