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

Autor: Luca Calatroni, Martin Huska, Serena Morigi, Giuseppe Antonio Recupero
Přispěvatelé: Calatroni, Luca, Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Matematica [Bologna], Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Calatroni L., Huska M., Morigi S., Recupero G.A.
Rok vydání: 2022
Předmět:
Willmore energy
Statistics and Probability
Surface inpainting
sparse non-convex optimization
Applied Mathematics
Context-aware mesh completion
[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]
[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]
Condensed Matter Physics
Surface denoising
[INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV]
Variational surface restoration
[INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]
Modeling and Simulation
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Geometry and Topology
Computer Vision and Pattern Recognition
[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Zdroj: Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision, 2022
ISSN: 1573-7683
0924-9907
DOI: 10.1007/s10851-022-01107-w
Popis: 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 $$\ell _0$$ 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.
Databáze: OpenAIRE
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