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

Surface Completion Using Laplacian Transform

Model acquisition process usually produce incomplete surfaces due to the technical constrains. This research presents the algorithm to perform surface completion using the available surface's context. Previous works on surface completions do not handle surfaces with near-regular pattern or irregular patterns well. The main goal of this research is to synthesize surface for hole that will have similar surface's context or geometric details as the hole's surrounding. This research uses multi-resolution approach to decompose the model into low-frequency part and high-frequency part. The low-frequency part is filled smoothly. The high-frequency part are transformed it into the Laplacian coordinate and filled using example-based synthesize approach. The algorithm is tested with planar surfaces and curve surfaces with all kind of relief patterns. The results indicate that the holes can be completed with the geometric detail similar to the surrounding surface

A framework for hull form reverse engineering and geometry integration into numerical simulations

The thesis presents a ship hull form specific reverse engineering and CAD integration framework. The reverse engineering part proposes three alternative suitable reconstruction approaches namely curves network, direct surface fitting, and triangulated surface reconstruction. The CAD integration part includes surface healing, region identification, and domain preparation strategies which used to adapt the CAD model to downstream application requirements. In general, the developed framework bridges a point cloud and a CAD model obtained from IGES and STL file into downstream applications

Robust Surface Reconstruction from Point Clouds

The problem of generating a surface triangulation from a set of points with normal information arises in several mesh processing tasks like surface reconstruction or surface resampling. In this paper we present a surface triangulation approach which is based on local 2d delaunay triangulations in tangent space. Our contribution is the extension of this method to surfaces with sharp corners and creases. We demonstrate the robustness of the method on difficult meshing problems that include nearby sheets, self intersecting non manifold surfaces and noisy point samples

Surface Reconstruction From 3D Point Clouds

The triangulation of a point cloud of a 3D object is a complex problem, since it depends on the complexity of the shape of such object, as well as on the density of points generated by a specific scanner. In the literature, there are essentially two approaches to the reconstruction of surfaces from point clouds: interpolation and approximation. In general, interpolation approaches are associated with simplicial methods; that is, methods that directly generate a triangle mesh from a point cloud. On the other hand, approximation approaches generate a global implicit function — that represents an implicit surface — from local shape functions, then generating a triangulation of such implicit surface. The simplicial methods are divided into two families: Delaunay and mesh growing. Bearing in mind that the first of the methods presented in this dissertation falls under the category of mesh growing methods, let us focus our attention for now on these methods. One of the biggest problems with these methods is that, in general, they are based on the establishment of dihedral angle bounds between adjacent triangles, as needed to make the decision on which triangle to add to the expansion mesh front. Typically, other bounds are also used for the internal angles of each triangle. In the course of this dissertation, we will see how this problem was solved. The second algorithm introduced in this dissertation is also a simplicial method but does not fit into any of the two families mentioned above, which makes us think that we are in the presence of a new family: triangulation based on the atlas of charts or triangle stars. This algorithm generates an atlas of the surface that consists of overlapping stars of triangles, that is, one produces a total surface coverage, thus solving one of the common problems of this family of direct triangulation methods, which is the appearance of holes or incomplete triangulation of the surface. The third algorithm refers to an implicit method, but, unlike other implicit methods, it uses an interpolation approach. That is, the local shape functions interpolate the points of the cloud. It is, perhaps, one of a few implicit methods that we can find in the literature that interpolates all points of the cloud. Therefore, one of the biggest problems of the implicit methods is solved, which has to do with the smoothing of the surface sharp features resulting from the blending of the local functions into the global function. What is common to the three methods is the interpolation approach, either in simple or implicit methods, that is, the linearization of the surface subject to reconstruction. As will be seen, the linearization of the neighborhood of each point allows us to solve several problems posed to the surface reconstruction algorithms, namely: point sub‐sampling, non‐uniform sampling, as well as sharp features.A triangulação de uma nuvem de pontos de um objeto 3D é um problema complexo, uma vez que depende da complexidade da forma desse objeto, assim como da densidade dos pontos extraídos desse objeto através de um scanner 3D particular. Na literatura, existem essencialmente duas abordagens na reconstrução de superfícies a partir de nuvens de pontos: interpolação e aproximação. Em geral, as abordagens de interpolação estão associadas aos métodos simpliciais, ou seja, a métodos que geram diretamente uma malha de triângulos a partir de uma nuvem de pontos. Por outro lado, as abordagens de aproximação estão habitualmente associadas à geração de uma função implícita global —que representa uma superfície implícita— a partir de funções locais de forma, para em seguida gerar uma triangulação da dita superfície implícita. Os métodos simpliciais dividem‐se em duas famílias: triangulação de Delaunay e triangulação baseada em crescimento progressivo da triangulação (i.e., mesh growing). Tendo em conta que o primeiro dos métodos apresentados nesta dissertação se enquadra na categoria de métodos de crescimento progressivo, foquemos a nossa atenção por ora nestes métodos. Um dos maiores problemas destes métodos é que, em geral, se baseiam no estabelecimento de limites de ângulos diédricos (i.e., dihedral angle bounds) entre triângulos adjacentes, para assim tomar a decisão sobre qual triângulo acrescentar à frente de expansão da malha. Tipicamente, também se usam limites para os ângulos internos de cada triângulo. No decorrer desta dissertação veremos como é que este problema foi resolvido. O segundo algoritmo introduzido nesta dissertação também é um método simplicial, mas não se enquadra em nenhuma das duas famílias acima referidas, o que nos faz pensar que estaremos na presença de uma nova família: triangulação baseada em atlas de vizinhanças sobrepostas (i.e., atlas of charts) ou estrelas de triângulos (i.e., triangle star). Este algoritmo gera um atlas da superfície que é constituído por estrelas sobrepostas de triângulos, ou seja, produz‐se a cobertura total da superfície, resolvendo assim um dos problemas comuns desta família de métodos de triangulação direta que é o do surgimento de furos ou de triangulação incompleta da superfície. O terceiro algoritmo refere‐se a um método implícito, mas, ao invés de grande parte dos métodos implícitos, utiliza uma abordagem de interpolação. Ou seja, as funções locais de forma interpolam os pontos da nuvem. É, talvez, um dos poucos métodos implícitos que podemos encontrar na literatura que interpola todos os pontos da nuvem. Desta forma resolve‐se um dos maiores problemas dos métodos implícitos que é o do arredondamento de forma resultante do blending das funções locais que geram a função global, em particular ao longo dos vincos da superfície (i.e., sharp features). O que é comum aos três métodos é a abordagem de interpolação, quer em métodos simpliciais quer em métodos implícitos, ou seja a linearização da superfície sujeita a reconstrução. Como se verá, a linearização da vizinhança de cada ponto permite‐nos resolver vários problemas colocados aos algoritmos de reconstrução de superfícies, nomeadamente: sub‐amostragem de pontos (point sub‐sampling), amostragem não uniforme (non‐uniform sampling), bem como formas vincadas (sharp features)