Robust and effective mesh denoising using L₀ sparse regularization

Mesh denoising is of great practical importance in geometric analysis and processing. In this paper we develop a novel L₀ sparse regularization method to robustly and reliably eliminate noises while preserving features with theoretic guarantee, and our assumption is that, local regions of a noise-free shape should be smooth unless they contain geometric features. Both vertex positions and facet normals are integrated into the L₀ norm to measure the sparsity of geometric features, and are then optimized in a sparsity-controllable fashion. We design an improved alternating optimization strategy to solve the L₀ minimization problem, which is proved to be both convergent and stable. As a result, our sparse regularization exhibits its advantage to distinguish features from noises. To further improve the computational performance, we propose a multi-layer approach based on joint bilateral upsampling to handle large and complicated meshes. Moreover, the aforementioned framework is naturally accommodating the need of denoising time-varying mesh sequences. Both theoretical analysis and various experimental results on synthetic and natural noises have demonstrated that, our method can robustly recover multifarious features and smooth regions of 3D shapes even with severe noise corruption, and outperform the state-of-the-art methods.