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

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

Graph Rotation Systems for Physical Construction of Large Structures

In this dissertation, I present an approach for physical construction of large structures. The approach is based on the graph rotation system framework. I propose two kinds of physical structures to represent the shape of design models. I have developed techniques to generate developable panels from any input polygonal mesh, which can be easily assembled to get the shape of the input polygonal mesh. The first structure is called plain woven structures. I have developed the ?projection method? to convert mathematical weaving cycles on any given polygonal mesh to developable strip panels. The width of weaving strips varies so that the surface of the input model can be covered almost completely. When these strip panels are assembled together, resulting shape resembles to a weaving in 3-space. The second structure is called band decomposition structures. I have developed a method to convert any given polygonal mesh into star-like developable elements, which we call vertex panels. Assembling vertex panels results in band decomposition structures. These band decomposition structures correspond to 2D-thickening of graphs embedded on surfaces. These band decompositions are contractible to their original graph. In a 2D-thickening, each vertex thickens to a polygon and each edge thickens to a band. Within the resulting band decomposition, each polygon corresponds to a vertex and each band corresponds to an edge that connects two vertex polygons. Since the approach is based on graph rotation system framework, the two structures do not have restrictions on design models. The input mesh can be of any genus. The faces in the input mesh can be triangle, quadrilateral, and any polygon. The advantages of this kind of large physical structure construction are low-cost material and prefabrication, easy assemble. Our techniques take the digital fabrication in a new direction and create complex and organic 3D forms. Along the theme of architecture this research has great implication for structure design and makes the more difficult task of construction techniques easier to understand for the fabricator. It has implications to the sculpture world as well as architecture

Fast arbitrary geodesic computation on triangular meshes

We propose a method to accelerate the computation of geodesic over triangular meshes. The method is based on a precomputation step that allows to store arbitrary complex distance metrics and a query step where we employ a modified version of the bidirectional A* algorithm. We show how this method is significantly faster then the classical Dijkstra algorithm for the computation of point to point distance. Moreover, as we precompute the exact geodesic, it achieves better accuracy

Surface Patches for 3D Curve Network Based on Its Design Intent

학위논문 (석사)-- 서울대학교 대학원 : 기계항공공학부, 2014. 2. 이건우.최근 스케치 기반 인터페이스를 이용한 자연스러운 기하모델링 방법들이 제시됨에 따라, 스케치를 통해 얻어진 3차원 곡선 네트워크로부터 모델을 생성하는 방법에 대한 다양한 연구가 진행되어왔다. 하지만 3차원 곡선들로부터 곡면 패치를 생성하는 것은 기하학적 정보의 부재로 인해 최적의 해가 존재하기 보다는 다양한 방법으로 해석할 수 있는 모호한 문제이다. 이 논문에서는 3차원 곡선 네트워크로부터 곡면 패치를 생성하는 알고리듬을 제안하며, 문제의 모호성을 해결하기 위해 스케치 특성에 따른 기하 구속조건을 추가적으로 부가한다. 각각의 기하 구속조건들은 곡면의 법선 벡터에 관하여 수식화되며, 최적 해를 찾는 방법으로 디자인 의도를 고려한 곡면의 법선 벡터를 추정한다. 이렇게 추정된 법선 벡터를 이용하여 곡선 네트워크가 이루는 곡면 모델을 생성하게 된다. 제안한 알고리듬은 다양한 곡선 네트워크에 대한 모델 생성을 통해 검증하였으며, 디자인 의도를 충분히 반영하기 위해 곡선에 기하 구속조건을 정의하여 새로운 기하정보를 추정했다는 점에서 기존의 논문들에 비해 시각적으로 합리적인 결과를 얻었다. 이 연구의 3차원 곡선의 기하정보를 추정하는 기술은 스케치를 기반으로 하는 모델링 방식에서 새로운 정보를 추출하기 위한 방법으로 사용될 수 있다. 더 나아가, 곡선 네트워크의 각각의 곡면에서 구한 곡선의 법선 벡터들은 인접 곡면의 법선 벡터 정보와 더해져 사용자 의도에 더욱 가까운 곡면 모델을 얻을 수 있을 것이다. 또한 곡선 네트워크 생성기술과의 결합은 3차원 모델링의 새로운 프레임워크를 제시할 수 있을 것으로 기대된다.초록 목차 그림 목차 표 목차 제 1 장 서론 1 1.1 곡선 네트워크 2 1.2 3차원 곡면 모델 생성 3 1.3 디자인 의도를 고려한 모델 생성 4 제 2 장 관련 연구 6 2.1 스케치 기반 모델링 인터페이스 6 2.2 곡선 네트워크로부터 곡면 패치/모델 생성 8 제 3 장 전체 과정 개괄 12 3.1 곡면 법선 벡터의 추정 12 3.2 곡면 모델 생성 13 제 4 장 기하정보 추정 15 4.1 기하정보 추정을 위한 기준 17 4.1.1 스케치의 연속성 17 4.1.2 곡선의 접선 벡터 조건 17 4.1.3 닫힌곡선 스케치 18 4.1.4 곡면 굽힘 최소화 18 4.2 법선 벡터 추정 20 4.2.1 회전 최소화 프레임 21 4.2.2 회전 최소화 프레임의 경계조건 23 4.2.3 곡면 굽힘 에너지 최소화 24 제 5 장 곡면 모델 생성 27 5.1 초기 메시 생성 27 5.2 메시 Refine 28 5.3 추정 법선 벡터 적용 31 제 6 장 결과 36 제 7 장 결론 42 참고문헌 43 Abstract 49Maste

Schnelle Löser für partielle Differentialgleichungen

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