Section: New Results

3D Shape Decomposition and Sub-parts Classification

Figure 5. 3D Shape Decomposition and Sub-parts Classification. Starting from a 3D shape and its curve skeleton, we compute a new measure called WEDF on the curve skeleton (a) and, by clustering WEDF values, we decompose the skeleton into hierarchical parts (b). To each connected part on the skeleton –shown with a different color (c)– a connected region of the surface mesh is assigned (d). Then, a salience value according to the hierarchy is assigned to each corresponding surface part (e) –parts of same importance get a similar color.

This paper (illustrated in Fig. 5) introduces a measure of significance on a curve skeleton of a 3D piecewise linear shape mesh, allowing the computation of both the shape’s parts and their saliency. We begin by reformulating three existing pruning measures into a non-linear PCA along the skeleton. From this PCA, we then derive a volume-based salience measure, the 3D WEDF, that determines the relative importance to the global shape of the shape part associated to a point of the skeleton. First, we provide robust algorithms for computing the 3D WEDF on a curve skeleton, independent on the number of skeleton branches. Then, we cluster the WEDF values to partition the curve skeleton, and coherently map the decomposition to the associated surface mesh. Thus, we develop an unsupervised hierarchical decomposition of the mesh faces into visually meaningful shape regions that are ordered according to their degree of perceptual salience. The shape analysis tools introduced in this paper are important for many applications including shape comparison, editing, and compression.