Three-Dimensional Bilateral Symmetry Plane Estimation in the Phase Domain

We show that bilateral symmetry plane estimation for three-dimensional (3-D) shapes may be carried out accurately, and efficiently, in the spherical harmonic domain. Our methods are valuable for applications where spherical harmonic expansion is already employed, such as 3-D shape registration, morphometry, and retrieval. We show that the presence of bilateral symmetry in the 3-D shape is equivalent to a linear phase structure in the corresponding spherical harmonic coefficients, and provide algorithms for estimating the orientation of the symmetry plane. The benefit of using spherical harmonic phase is that symmetry estimation reduces to matching a compact set of descriptors, without the need to solve a correspondence problem. Our methods work on point clouds as well as large-scale mesh models of 3-D shapes.