A Unified Surface Geometric Framework for Feature-Aware Denoising, Hole Filling and Context-Aware Completion

• Published in: Journal of mathematical imaging and vision Vol. 65; no. 1; pp. 82 - 98
• Main Authors: Calatroni, Luca, Huska, Martin, Morigi, Serena, Recupero, Giuseppe Antonio
• Format: Journal Article
• Language: English
• Published: New York Springer US 2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Approximation; Computational geometry; Computer Science; Context; Convexity; Data acquisition; Image Processing and Computer Vision; Mathematical analysis; Mathematical Methods in Physics; Noise reduction; Numerical methods; Optimization; Parameterization; Random noise; Regularization; Robustness (mathematics); Signal,Image and Speech Processing; Three dimensional printing; Willmore energy; Sparse non-convex optimization; Surface denoising; Context-aware mesh completion; Surface inpainting; Variational surface restoration
• ISSN: 0924-9907; 1573-7683
• DOI: 10.1007/s10851-022-01107-w

Technologies for 3D data acquisition and 3D printing have enormously developed in the past few years, and, consequently, the demand for 3D virtual twins of the original scanned objects has increased. In this context, feature-aware denoising, hole filling and context-aware completion are three essential (but far from trivial) tasks. In this work, they are integrated within a geometric framework and realized through a unified variational model aiming at recovering triangulated surfaces from scanned, damaged and possibly incomplete noisy observations. The underlying non-convex optimization problem incorporates two regularisation terms: a discrete approximation of the Willmore energy forcing local sphericity and suited for the recovery of rounded features, and an approximation of the ℓ 0 pseudo-norm penalty favouring sparsity in the normal variation. The proposed numerical method solving the model is parameterization-free, avoids expensive implicit volume-based computations and based on the efficient use of the Alternating Direction Method of Multipliers. Experiments show how the proposed framework can provide a robust and elegant solution suited for accurate restorations even in the presence of severe random noise and large damaged areas.