Anisotropic Laplace-Beltrami Operators for Non-Rigid 3D Shape Retrieval

Anisotropic diffusion has been used as an effective approach for mesh processing. Traditional Laplace-Beltrami operator is based on the diffusion theory, but it does not reflect the anisotropic diffusion. In addition, most methods are based on the Laplace-Beltrami operator(LBO) when calculating point descriptor in many non-rigid 3D shape analysis and retrieval tasks. In order to overcome these limitations, in this paper, we propose nonlinear anisotropic Laplace-Beltrami operators(NALBO) which can be used for applications such as non-rigid 3D shape analysis and retrieval. First of all, we propose the new tensor and incorporate extrinsic information into it. Based on the new tensor, we can transform the gradient domain from one space to another. It can improve the accuracy of point signature. Then, We established the discretization scheme of the anisotropic Laplace-Beltrami operators. Finally, our anisotropic Laplace-Beltrami operator is applied to the non-rigid 3D shape retrieval task. The experimental results turn out that our anisotropic Laplace-Beltrami operator is feasible and efficient for tasks such as non-rigid 3D shape matching and retrieval, etc.