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Salient critical points for meshes

A novel method for extracting the salient critical points of meshes, possibly with noise, is presented by combining mesh saliency with Morse theory. In this paper, we use the idea of mesh saliency as a measure of regional importance for meshes. The proposed method defines the salient critical points in a scalar function space using a center-surround filter operator on Gaussian-weighted average of the scalar of vertices. Compared to using a purely geometric measure of shape, such as curvature, our method yields more satisfactory results with the lower number of critical points. We demonstrate the effectiveness of this approach by comparing our results with the results of the conventional approaches in a number of examples. Furthermore, this work has a variety of potential applications. We give a direct application to the hierarchical topological representation for meshes by combining the salient critical points with the Morse-Smale complex.