Dictionary Learning-based Inpainting on Triangular Meshes

The problem of inpainting consists of filling missing or damaged regions in images and videos in such a way that the filling pattern does not produce artifacts that deviate from the original data. In addition to restoring the missing data, the inpainting technique can also be used to remove undesired objects. In this work, we address the problem of inpainting on surfaces through a new method based on dictionary learning and sparse coding. Our method learns the dictionary through the subdivision of the mesh into patches and rebuilds the mesh via a method of reconstruction inspired by the Non-local Means method on the computed sparse codes. One of the advantages of our method is that it is capable of filling the missing regions and simultaneously removes noise and enhances important features of the mesh. Moreover, the inpainting result is globally coherent as the representation based on the dictionaries captures all the geometric information in the transformed domain. We present two variations of the method: a direct one, in which the model is reconstructed and restored directly from the representation in the transformed domain and a second one, adaptive, in which the missing regions are recreated iteratively through the successive propagation of the sparse code computed in the hole boundaries, which guides the local reconstructions. The second method produces better results for large regions because the sparse codes of the patches are adapted according to the sparse codes of the boundary patches. Finally, we present and analyze experimental results that demonstrate the performance of our method compared to the literature

A comparison of hole-filling methods in 3D

This paper presents a review of the most relevant current techniques that deal with hole-filling in 3D models. Contrary to earlier reports, which approach mesh repairing in a sparse and global manner, the objective of this review is twofold. First, a specific and comprehensive review of hole-filling techniques (as a relevant part in the field of mesh repairing) is carried out. We present a brief summary of each technique with attention paid to its algorithmic essence, main contributions and limitations. Second, a solid comparison between 34 methods is established. To do this, we define 19 possible meaningful features and properties that can be found in a generic hole-filling process. Then, we use these features to assess the virtues and deficiencies of the method and to build comparative tables. The purpose of this review is to make a comparative hole-filling state-of-the-art available to researchers, showing pros and cons in a common framework.• Ministerio de Economía y Competitividad: Proyecto DPI2013-43344-R (I+D+i) • Gobierno de Castilla-La Mancha: Proyecto PEII-2014-017-PpeerReviewe

Heritage Reproduction in the Age of High-Resolution Scanning:A Critical Evaluation of Digital Infilling Methods for Historic Preservation

High-definition digital scanning has established itself as a useful tool for documenting cultural heritage in the twenty-first century. Proponents of surveying technology are hailing the use of digital fact-based 3D models as valuable tools for recording, analyzing and safeguarding items of cultural importance. Methods for digitally filling holes have not yet been considered through the lens of historic preservation. No modeling technique is error-free and understanding how heritage professionals are addressing lacunae is vital for understanding digital heritage objects resulting from 3D scanning hardware. Frameworks exist for working with scanned data, but they define general principles for a broad range of applications and do not provide any guidelines or strategies of how to comply with them practically. This thesis is a comparative evaluation of current practices of in-filling digital lacunae that attempts to establish which methods are best suited to the following historic preservation practices: documentation, Interpretation graphics, Long-term monitoring, digital restoration, physical fabrication

Surface Reconstruction from Unorganized Point Cloud Data via Progressive Local Mesh Matching

This thesis presents an integrated triangle mesh processing framework for surface reconstruction based on Delaunay triangulation. It features an innovative multi-level inheritance priority queuing mechanism for seeking and updating the optimum local manifold mesh at each data point. The proposed algorithms aim at generating a watertight triangle mesh interpolating all the input points data when all the fully matched local manifold meshes (umbrellas) are found. Compared to existing reconstruction algorithms, the proposed algorithms can automatically reconstruct watertight interpolation triangle mesh without additional hole-filling or manifold post-processing. The resulting surface can effectively recover the sharp features in the scanned physical object and capture their correct topology and geometric shapes reliably. The main Umbrella Facet Matching (UFM) algorithm and its two extended algorithms are documented in detail in the thesis. The UFM algorithm accomplishes and implements the core surface reconstruction framework based on a multi-level inheritance priority queuing mechanism according to the progressive matching results of local meshes. The first extended algorithm presents a new normal vector combinatorial estimation method for point cloud data depending on local mesh matching results, which is benefit to sharp features reconstruction. The second extended algorithm addresses the sharp-feature preservation issue in surface reconstruction by the proposed normal vector cone (NVC) filtering. The effectiveness of these algorithms has been demonstrated using both simulated and real-world point cloud data sets. For each algorithm, multiple case studies are performed and analyzed to validate its performance

Fitting and filling of 3D datasets with volume constraints using radial basis functions under tension

Acknowledgments This work was supported by FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (Research Project A-FQM-76-UGR20, University of Granada) and by the Junta de Andalucía (Research Groups FQM-191 and TEP-190). Funding for open access charge: Universidad de Granada / CBUA.Given a dataset of 3D points in which there is a hole, i.e., a region with a lack of information, we develop a method providing a surface that fits the dataset and fills the hole. The filling patch is required to fulfill a prescribed volume condition. The fitting–filling function consists of a radial basis functions that minimizes an energy functional involving both, the fitting of the dataset and the volume constraint of the filling patch, as well as the fairness of the function. We give a convergence result and we present some graphical and numerical examples.FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (Research Project A-FQM-76-UGR20, University of Granada)Junta de Andalucía (Research Groups FQM-191 and TEP-190)Funding for open access charge: Universidad de Granada / CBU

hole˙filling˙journal Filling Holes in Triangular Meshes Using Digital Images by Curve Unfolding ∗

We propose a novel approach to automatically fill holes in triangulated models. Each hole is filled using a minimum energy surface that is obtained in three steps. First, we unfold the hole boundary onto a plane using energy minimization. Second, we triangulate the unfolded hole using a constrained Delaunay triangulation. Third, we embed the triangular mesh as a minimum energy surface in R 3. When embedding the triangular mesh, any energy function can be used to estimate the missing data. We use a variational multi-view approach to estimate the missing data. The running time of the method depends primarily on the size of the hole boundary and not on the size of the model, thereby makin

Smooth parametric surfaces and n-sided patches

The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed

An Automated Process for 2D and 3D Finite Element Overclosure and Gap Adjustment using Radial Basis Function Networks

In biomechanics, geometries representing complicated organic structures are consistently segmented from sparse volumetric data or morphed from template geometries resulting in initial overclosure between adjacent geometries. In FEA, these overclosures result in numerical instability and inaccuracy as part of contact analysis. Several techniques exist to fix overclosures, but most suffer from several drawbacks. This work introduces a novel automated algorithm in an iterative process to remove overclosure and create a desired minimum gap for 2D and 3D finite element models. The RBF Network algorithm was introduced by its four major steps to remove the initial overclosure. Additionally, the algorithm was validated using two test cases against conventional nodal adjustment. The first case compared the ability of each algorithm to remove differing levels of overclosure between two deformable muscles and the effects on mesh quality. The second case used a non-deformable femur and deformable distal femoral cartilage geometry with initial overclosure to test both algorithms and observe the effects on the resulting contact FEA. The RBF Network in the first case study was successfully able to remove all overclosures. In the second case, the nodal adjustment method failed to create a usable FEA model, while the RBF Network had no such issue. This work proposed an algorithm to remove initial overclosures prior to FEA that has improved performance over conventional nodal adjustment, especially in complicated situations and those involving 3D elements. The work can be included in existing FEA modeling workflows to improve FEA results in situations involving sparse volumetric segmentation and mesh morphing. This algorithm has been implemented in MATLAB, and the source code is publicly available to download at the following GitHub repository: https://github.com/thor-andreassen/femorsComment: 26 Pages, 5 Figures, 2 Table

CAD-Based Porous Scaffold Design of Intervertebral Discs in Tissue Engineering

With the development and maturity of three-dimensional (3D) printing technology over the past decade, 3D printing has been widely investigated and applied in the field of tissue engineering to repair damaged tissues or organs, such as muscles, skin, and bones, Although a number of automated fabrication methods have been developed to create superior bio-scaffolds with specific surface properties and porosity, the major challenges still focus on how to fabricate 3D natural biodegradable scaffolds that have tailor properties such as intricate architecture, porosity, and interconnectivity in order to provide the needed structural integrity, strength, transport, and ideal microenvironment for cell- and tissue-growth. In this dissertation, a robust pipeline of fabricating bio-functional porous scaffolds of intervertebral discs based on different innovative porous design methodologies is illustrated. Firstly, a triply periodic minimal surface (TPMS) based parameterization method, which has overcome the integrity problem of traditional TPMS method, is presented in Chapter 3. Then, an implicit surface modeling (ISM) approach using tetrahedral implicit surface (TIS) is demonstrated and compared with the TPMS method in Chapter 4. In Chapter 5, we present an advanced porous design method with higher flexibility using anisotropic radial basis function (ARBF) and volumetric meshes. Based on all these advanced porous design methods, the 3D model of a bio-functional porous intervertebral disc scaffold can be easily designed and its physical model can also be manufactured through 3D printing. However, due to the unique shape of each intervertebral disc and the intricate topological relationship between the intervertebral discs and the spine, the accurate localization and segmentation of dysfunctional discs are regarded as another obstacle to fabricating porous 3D disc models. To that end, we discuss in Chapter 6 a segmentation technique of intervertebral discs from CT-scanned medical images by using deep convolutional neural networks. Additionally, some examples of applying different porous designs on the segmented intervertebral disc models are demonstrated in Chapter 6