4,049 research outputs found

    Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

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    The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error {\delta}, minimal interior angle {\theta} and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound {\delta} as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. In this way our optimization framework greedily searches for the coarsest mesh with minimal interior angle above {\theta} and approximation error bounded by {\delta}. Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.Comment: 14 pages, 20 figures. Submitted to IEEE Transactions on Visualization and Computer Graphic

    The Modified Direct Method: an Approach for Smoothing Planar and Surface Meshes

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    The Modified Direct Method (MDM) is an iterative mesh smoothing method for smoothing planar and surface meshes, which is developed from the non-iterative smoothing method originated by Balendran [1]. When smooth planar meshes, the performance of the MDM is effectively identical to that of Laplacian smoothing, for triangular and quadrilateral meshes; however, the MDM outperforms Laplacian smoothing for tri-quad meshes. When smooth surface meshes, for trian-gular, quadrilateral and quad-dominant mixed meshes, the mean quality(MQ) of all mesh elements always increases and the mean square error (MSE) decreases during smoothing; For tri-dominant mixed mesh, the quality of triangles always descends while that of quads ascends. Test examples show that the MDM is convergent for both planar and surface triangular, quadrilateral and tri-quad meshes.Comment: 18 page

    Detail-preserving and Content-aware Variational Multi-view Stereo Reconstruction

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    Accurate recovery of 3D geometrical surfaces from calibrated 2D multi-view images is a fundamental yet active research area in computer vision. Despite the steady progress in multi-view stereo reconstruction, most existing methods are still limited in recovering fine-scale details and sharp features while suppressing noises, and may fail in reconstructing regions with few textures. To address these limitations, this paper presents a Detail-preserving and Content-aware Variational (DCV) multi-view stereo method, which reconstructs the 3D surface by alternating between reprojection error minimization and mesh denoising. In reprojection error minimization, we propose a novel inter-image similarity measure, which is effective to preserve fine-scale details of the reconstructed surface and builds a connection between guided image filtering and image registration. In mesh denoising, we propose a content-aware p\ell_{p}-minimization algorithm by adaptively estimating the pp value and regularization parameters based on the current input. It is much more promising in suppressing noise while preserving sharp features than conventional isotropic mesh smoothing. Experimental results on benchmark datasets demonstrate that our DCV method is capable of recovering more surface details, and obtains cleaner and more accurate reconstructions than state-of-the-art methods. In particular, our method achieves the best results among all published methods on the Middlebury dino ring and dino sparse ring datasets in terms of both completeness and accuracy.Comment: 14 pages,16 figures. Submitted to IEEE Transaction on image processin

    3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

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    Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

    Practical quad mesh simplification

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    In this paper we present an innovative approach to incremental quad mesh simplification, i.e. the task of producing a low complexity quad mesh starting from a high complexity one. The process is based on a novel set of strictly local operations which preserve quad structure. We show how good tessellation quality (e.g. in terms of vertex valencies) can be achieved by pursuing uniform length and canonical proportions of edges and diagonals. The decimation process is interleaved with smoothing in tangent space. The latter strongly contributes to identify a suitable sequence of local modification operations. The method is naturally extended to manage preservation of feature lines (e.g. creases) and varying (e.g. adaptive) tessellation densities. We also present an original Triangle-to-Quad conversion algorithm that behaves well in terms of geometrical complexity and tessellation quality, which we use to obtain the initial quad mesh from a given triangle mesh
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