Two-dimensional shape retrieval using the distribution of extrema of Laplacian eigenfunctions

Abstract

We propose a new method using the distribution of extrema of Laplacian eigenfunctions for two-dimensional (2D) shape description and matching. We construct a weighted directed graph, which we call signed natural neighbor graph, to represent a Laplacian eigenfunction of a shape. The nodes of this sparse graph are the extrema of the corresponding eigenfunction, and the edge weights are defined by signed natural neighbor coordinates derived from the local spatial arrangement of extrema. We construct the signed natural neighbor graphs defined by a small number of low-frequency Laplacian eigenfunctions of a shape to describe it. This shape descriptor is invariant under rigid transformations and uniform scaling, and is also insensitive to minor boundary deformations. When using our shape descriptor for matching two shapes, we determine their similarity by comparing the graphs induced by corresponding Laplacian eigenfunctions of the two shapes. Our experimental shape-matching results demonstrate that our method is effective for 2D shape retrieval.