Detail-Preserving Mesh Unfolding for Nonrigid Shape Retrieval

Abstract

We present a shape deformation algorithm that unfolds any given 3D shape into a canonical pose that is invariant to nonrigid transformations. Unlike classical approaches, such as least-squares multidimensional scaling, we preserve the geometric details of the input shape in the resulting shape, which in turn leads to a content-based nonrigid shape retrieval application with higher accuracy. Our optimization framework, fed with a triangular or a tetrahedral mesh in 3D, tries to move each vertex as far away from each other as possible subject to finite element regularization constraints. Intuitively this effort minimizes the bending over the shape while preserving the details. Avoiding geodesic distances in our computation renders the method robust to topological noise. Compared to state-of-the-art approaches, our method is simpler to implement, faster, more accurate in shape retrieval, and less sensitive to topological errors.