Sparsity-Aided Variational Mesh Restoration

• Published in: Scale Space and Variational Methods in Computer Vision pp. 437 - 449
• Main Authors: Huska, Martin, Morigi, Serena, Recupero, Giuseppe Antonio
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Non-convex optimization; Sparse variational formulation; Surface denoising
• ISBN: 3030755487; 9783030755485
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-75549-2_35

We propose a variational method for recovering discrete surfaces from noisy observations which promotes sparsity in the normal variation more accurately than ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document} norm (total variation) and ℓ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _0$$\end{document} 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.