Semi-sparsity for Triangular Mesh Denoising

We propose a novel semi-sparsity model for denoising 3D triangular meshes, inspired by the successful application of semi-sparsity regularization in image processing. Firstly, the differential operators defined on the piecewise constant function spaces are introduced for triangular meshes, and the semi-sparsity model is then extended to meshes denoising application. To solve the proposed model efficiently, we also propose an efficient iterative algorithm based on the alternating direction method of multipliers (ADMM) technique. We demonstrate that the semi-sparsity regularization can also be effectively applied to graphic processing tasks, yielding similar simultaneous-fitting outcomes in preserving sharp features and achieving piecewise smoothing surfaces.