Biharmonic fields and mesh completion

Argudo, Oscar; Brunet, Pere; Chica, Antoni; Vinacua, Àlvar

doi:10.1016/j.gmod.2015.06.010

Cited by 12 publications

(5 citation statements)

References 13 publications

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“…As far as the hole filling or repairing problem is concerned, standard approaches range from fourth-order surface diffusion PDE methods [13], to volumetric approaches mainly based on signed distance functions to implicitly represent the surface [14,15]. Other popular non-polygonal methods rely on Radial Basis Functions implicit interpolations [16], and Moving Least Squares [17].…”

Section: Related Workmentioning

confidence: 99%

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

et al. 2022

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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.

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Section: Related Workmentioning

confidence: 99%

“…where we omitted the constant terms in (15). Due to the separability property of φ(•; a), problem ( 22) is equivalent to n E independent, three-dimensional problems for each t j , j = 1, .…”

Section: Sub-problem For Tmentioning

confidence: 99%

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

et al. 2022

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“…Centin et al [35] employed a Poisson reconstruction step to generate an implicit function for completing the missing parts. Argudo et al [36] presented an adaptive, multigrid algorithm for mesh completion in general and complex cases by using the Bi-Harmonic fields. The main advantage of volume-based methods is its robustness in resolving geometric errors, and the drawback is the loss of geometric detail.…”

Section: Hole-fillingmentioning

confidence: 99%

A Fast Hole-Filling Method for Triangular Mesh in Additive Repair

et al. 2020

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In the triangular meshes obtained in additive repair, it is a challenge to find one single hole-filling method to close all holes and make the filling patches assort with surrounding meshes well with low time complexity, which is mainly caused by the shape complexity and size difference of the various holes, especially in the fields of intelligent manufacturing, 3D measurement, and reverse engineering. Therefore, it is reasonable to adopt different algorithms to fill different types of holes. In this research, a fast hole-filling method for triangular mesh is proposed based on the hole size. First, a group of basic concepts is defined to make them uniform throughout the whole text, followed by the descriptions of hole detection and boundary cleaning. Second, three different algorithms are developed to fill the small-sized, middle-sized, and large-sized holes classified by hole size respectively, which can fill all the detected holes in a fast and proper manner. Finally, two experiments are carried out to verify the efficiency, robustness, and ability to recover the shape of our method. Compared to two state-of-the-art hole-filling methods in the first experiment, the quantitative evaluation results demonstrate that our proposed method is much faster than them with the ability to guarantee the regularity of most filling triangles. The second experiment proves that our method can produce satisfactory filling results by making the filling patches be compatible with surrounding meshes well.

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“…In existing studies, scholars have focused more on the repair of closed holes formed in the reconstruction of point cloud models commonly encountered in industrial design, medical imaging, and the study of cultural relics, such as industrial parts and animal models. There two common kinds of methods for filling holes: voxel-based methods [3][4][5][6][7] and surface-based methods [8][9][10][11]. Methods of the former type, which take point cloud data as their input for processing, can accomplish hole filling via volume diffusion in the distance field by converting the point cloud data into a symbolic distance field, while methods of the latter type, in which the processing input mostly consists of triangular facet data, can achieve hole filling by calculating the normal vector of each facet for surface fitting.…”

Section: Introductionmentioning

confidence: 99%

A Parallel Method for Open Hole Filling in Large-Scale 3D Automatic Modeling Based on Oblique Photography

et al. 2021

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Common methods of filling open holes first reaggregate them into closed holes and then use a closed hole filling method to repair them. These methods have problems such as long calculation times, high memory consumption, and difficulties in filling large-area open holes. Hence, this paper proposes a parallel method for open hole filling in large-scale 3D automatic modeling. First, open holes are automatically identified and divided into two categories (internal and external). Second, the hierarchical relationships between the open holes are calculated in accordance with the adjacency relationships between partitioning cells, and the open holes are filled through propagation from the outer level to the inner level with topological closure and height projection transformation. Finally, the common boundaries between adjacent open holes are smoothed based on the Laplacian algorithm to achieve natural transitions between partitioning cells. Oblique photography data from an area of 28 km2 in Dongying, Shandong, were used for validation. The experimental results reveal the following: (i) Compared to the Han method, the proposed approach has a 12.4% higher filling success rate for internal open holes and increases the filling success rate for external open holes from 0% to 100%. (ii) Concerning filling efficiency, the Han method can achieve hole filling only in a small area, whereas with the proposed method, the size of the reconstruction area is not restricted. The time and memory consumption are improved by factors of approximately 4–5 and 7–21, respectively. (iii) In terms of filling accuracy, the two methods are basically the same.

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Biharmonic fields and mesh completion

Cited by 12 publications

References 13 publications

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

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

A Fast Hole-Filling Method for Triangular Mesh in Additive Repair

A Parallel Method for Open Hole Filling in Large-Scale 3D Automatic Modeling Based on Oblique Photography

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