4,049 research outputs found
Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement
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
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
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
-minimization algorithm by adaptively estimating the 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
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
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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