A Comparative Study on Polygonal Mesh Simplification Algorithms

Polygonal meshes are a common way of representing three dimensional surface models in many different areas of computer graphics and geometry processing. However, with the evolution of the technology, polygonal models are becoming more and more complex. As the complexity of the models increase, the visual approximation to the real world objects get better but there is a trade-off between the cost of processing these models and better visual approximation. In order to reduce this cost, the number of polygons in a model can be reduced by mesh simplification algorithms. These algorithms are widely used such that nearly all of the popular mesh editing libraries include at least one of them. In this work, polygonal simplification algorithms that are embedded in open source libraries: CGAL, VTK and OpenMesh are compared with the Metro geometric error measuring tool. By this way we try to supply a guidance for developers for publicly available mesh libraries in order to implement polygonal mesh simplification

3D RECONSTRUCTION USING MULTI-VIEW IMAGING SYSTEM

This thesis presents a new system that reconstructs the 3D representation of dental casts. To maintain the integrity of the 3D representation, a standard model is built to cover the blind spots that the camera cannot reach. The standard model is obtained by scanning a real human mouth model with a laser scanner. Then the model is simplified by an algorithm which is based on iterative contraction of vertex pairs. The simplified standard model uses a local parametrization method to obtain the curvature information. The system uses a digital camera and a square tube mirror in front of the camera to capture multi-view images. The mirror is made of stainless steel in order to avoid double reflections. The reflected areas of the image are considered as images taken by the virtual cameras. Only one camera calibration is needed since the virtual cameras have the same intrinsic parameters as the real camera. Depth is computed by a simple and accurate geometry based method once the corresponding points are identified. Correspondences are selected using a feature point based stereo matching process, including fast normalized cross-correlation and simulated annealing

Surface Networks

We study data-driven representations for three-dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants, which learn from the local metric tensor via the Laplacian operator. Despite offering excellent sample complexity and built-in invariances, intrinsic geometry alone is invariant to isometric deformations, making it unsuitable for many applications. To overcome this limitation, we propose several upgrades to GNNs to leverage extrinsic differential geometry properties of three-dimensional surfaces, increasing its modeling power. In particular, we propose to exploit the Dirac operator, whose spectrum detects principal curvature directions --- this is in stark contrast with the classical Laplace operator, which directly measures mean curvature. We coin the resulting models \emph{Surface Networks (SN)}. We prove that these models define shape representations that are stable to deformation and to discretization, and we demonstrate the efficiency and versatility of SNs on two challenging tasks: temporal prediction of mesh deformations under non-linear dynamics and generative models using a variational autoencoder framework with encoders/decoders given by SNs

Mesh-MLP: An all-MLP Architecture for Mesh Classification and Semantic Segmentation

With the rapid development of geometric deep learning techniques, many mesh-based convolutional operators have been proposed to bridge irregular mesh structures and popular backbone networks. In this paper, we show that while convolutions are helpful, a simple architecture based exclusively on multi-layer perceptrons (MLPs) is competent enough to deal with mesh classification and semantic segmentation. Our new network architecture, named Mesh-MLP, takes mesh vertices equipped with the heat kernel signature (HKS) and dihedral angles as the input, replaces the convolution module of a ResNet with Multi-layer Perceptron (MLP), and utilizes layer normalization (LN) to perform the normalization of the layers. The all-MLP architecture operates in an end-to-end fashion and does not include a pooling module. Extensive experimental results on the mesh classification/segmentation tasks validate the effectiveness of the all-MLP architecture.Comment: 8 pages, 6 figure

Comportamento mecânico de espumas de ligas de alumínio modeladas com recurso a micro-tomografia computorizada de raios-X

In recent years, there has been an increase in interest in cellular materials for structural applications, especially cellular metals (e.g., metal foams made of aluminium and its alloys). These closed-cell and open-cell foams usually have complex cellular structures resulting from the foaming process and their mechanical properties are governed by their cellular structures and by the properties of the base material. However, their mechanical characterization is difficult and most of the times can result in the destruction of the foam specimen. In this study, X-ray microcomputed tomography (µCT) was used together with finite element modelling to develop numerical models to estimate the elastic moduli and evaluate the effects of processing of the information obtained with the µCT scans in the final results. Such a technique complements experimental testing and brings great versatility. In order to accomplish this task, different thresholding techniques (segmentation) were applied to the 2D slices, which are the result of µCT scans, with special focus on a manual global technique with the mass as a quality indicator. Then, some reconstruction algorithms (e.g. Marching Cubes 33) were used to create 3D tessellated models in the STL format, which were oversampled (excessive number of faces) and with errors. Therefore, a simplification/clean-up procedure was applied to solve those issues, being analysed in terms of mass maintenance, shape maintenance with the Hausdorff algorithm and face quality, i.e., face aspect ratio. Two different procedures were evaluated, with and without small structural imperfections, so that the impact of the procedures could be analysed as well as the effect of the presence of small defects. The results obtained were evaluated and compared to several analytical and theoretical models, models based on representative unit-cells and experimental results in terms of the relation between the relative density and the relative Young’s modulus. Results demonstrated that the developed procedures were very good at minimizing changes in mass and shape of the geometries while providing good face quality, i.e., face aspect ratio. The models were also shown to be able to predict the properties of metallic foams in accordance with the findings of other researchers. In addition, the process of obtaining the models and the presence of small structural imperfections were shown to have a great impact on the final results.Nos últimos anos, tem-se verificado um aumento do interesse na área dos materiais celulares, mais especificamente metais celulares, para aplicações estruturais (por exemplo, espumas metálicas de alumínios e as suas ligas). Estas espumas de célula aberta e fechada têm, normalmente, uma estrutura celular complexa resultante do processo de espumação e as suas propriedades mecânicas dependem das suas estruturas celulares e das propriedades do material base. No entanto, a caracterização mecânicas destes materiais é difícil e resulta, regularmente, na destruição dos specimens de espuma. Neste estudo, Micro-Tomografia Computorizada de Raios-X (µCT) foi aplicada juntamente com modelação por elementos finitos para desenvolver modelos numéricos que conseguem estimar os módulos de elasticidade e avaliar os efeitos do processamento da informação obtida pelos scans de µCT nos resultados finais. Esta técnica complementa os procedimentos experimentais e traz uma grande versatilidade. Para se completar a tarefa proposta, diferentes métodos de segmentação foram aplicados às fatias 2D, que são resultantes dos scans de µCT, com especial atenção num método de segmentação manual global que utiliza a massa como indicador de qualidade. Depois disso, alguns algoritmos de reconstrução, por exemplo, Marching Cubes 33, foram aplicados para criar modelos 3D de faces triangulares no formato STL que demonstram sobreamostragem (excessiva quantidade de faces) e alguns erros. Por essa razão, um procedimento de simplificação/limpeza foi aplicado para resolver estes problemas, sendo analisados em termos de preservação de massa, preservação de forma com o algoritmo de Hausdorff e qualidade das faces, ou seja, razão de proporção. Dois procedimentos diferentes foram avaliados, um com e outro sem pequenos defeitos estruturais para que se consiga analisar não só o impacto do processamento dos modelos assim como o efeito da presença de pequenos defeitos. Os resultados obtidos foram comparados com vários modelos analíticos e teóricos, modelos baseados em células unitárias representativas e resultados experimentais com base na relação entre a densidade relativa e o modulo de Young relativo. Os resultados demonstraram que os procedimentos desenvolvidos são bons a preservar a massa e forma das geometrias deixando as faces com boa qualidade. Verificou-se também que os modelos foram capazes de prever as propriedades das espumas metálicas em concordância com o trabalho de outros investigadores. Adicionalmente, mostrou-se que o processo de obtenção dos modelos e a presença de pequenas imperfeiçoes estruturais tem um impacto relevante nos resultados finais.Mestrado em Engenharia Mecânic