Sparsity-Aided Variational Mesh Restoration.

We propose a variational method for recovering discrete surfaces from noisy observations which promotes sparsity in the normal variation more accurately than \(\ell _1\) norm (total variation) and \(\ell _0\) pseudo-norm regularization methods by incorporating a parameterized non-convex penalty function. This results in denoised surfaces with enhanced flat regions and maximally preserved sharp features, including edges and corners. Unlike the classical two-steps mesh denoising approaches, we propose a unique, effective optimization model which is efficiently solved by an instance of Alternating Direction Method of Multipliers. Experiments are presented which strongly indicate that using the sparsity-aided formulation holds the potential for accurate restorations even in the presence of high noise.