Shape signature using the edge-based Laplacian

This paper presents a novel analysis and application of the eigensystem of the edge-based Laplacian of a graph. The advantage of using the edge-based Laplacian over its vertex-based counterpart is that it significantly expands the set of differential operators that can be implemented in the graph domain. We use the analysis to develop a novel method for defining pose-invariant signatures for non-rigid three-dimensional shapes based on the edge-based heat kernel. The signature proves useful for both shape segmentation and feature point correspondence. To illustrate the utility of our method, we apply it to segmenting and classifying non-rigid three-dimensional shapes represented in terms of meshes.