Mesh Segmentation via Spectral Embedding and Contour Analysis

We propose a mesh segmentation algorithm via recursive bisection where at each step, a sub‐mesh embedded in 3D is first spectrally projected into the plane and then a contour is extracted from the planar embedding. We rely on two operators to compute the projection: the well‐known graph Laplacian and a geometric operator designed to emphasize concavity. The two embeddings reveal distinctive shape semantics of the 3D model and complement each other in capturing the structural or geometrical aspect of a segmentation. Transforming the shape analysis problem to the 2D domain also facilitates our segmentability analysis and sampling tasks. We propose a novel measure of the segmentability of a shape, which is used as the stopping criterionfor our segmentation. The measure is derived from simple area‐ and perimeter‐based convexity measures. We achieve invariance to shape bending through multi‐dimensional scaling (MDS) based on the notion of inner distance. We also utilize inner distances to develop a novel sampling scheme to extract two samples along a contour which correspond to two vertices residing on different parts of the sub‐mesh. The two samples are used to derive a spectral linear ordering of the mesh faces. We obtain a final cut via a linear search over the face sequence based on part salience, where a choice of weights for different factors of part salience is guided by the result from segmentability analysis.