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Poisson Surface Reconstruction
, 2006
"... We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function ..."
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Cited by 369 (5 self)
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We show that surface reconstruction from oriented points can be cast as a spatial Poisson problem. This Poisson formulation considers all the points at once, without resorting to heuristic spatial partitioning or blending, and is therefore highly resilient to data noise. Unlike radial basis function schemes, our Poisson approach allows a hierarchy of locally supported basis functions, and therefore the solution reduces to a well conditioned sparse linear system. We describe a spatially adaptive multiscale algorithm whose time and space complexities are proportional to the size of the reconstructed model. Experimenting with publicly available scan data, we demonstrate reconstruction of surfaces with greater detail than previously achievable.
NonRigid Spectral Correspondence of Triangle Meshes
, 2006
"... We present an algorithm for finding a meaningful vertextovertex correspondence between two triangle meshes, which is designed to handle general nonrigid transformations. Our algorithm operates on embeddings of the two shapes in the spectral domain so as to normalize them with respect to uniform s ..."
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Cited by 37 (7 self)
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We present an algorithm for finding a meaningful vertextovertex correspondence between two triangle meshes, which is designed to handle general nonrigid transformations. Our algorithm operates on embeddings of the two shapes in the spectral domain so as to normalize them with respect to uniform scaling and rigidbody transformation. Invariance to shape bending is achieved by relying on approximate geodesic point proximities on a mesh to capture its shape. To deal with moderate stretching, we first raise the issue of “eigenmode switching ” and discuss heuristics to bring the eigenmodes to alignment. For additional nonrigid discrepancies in the spectral embeddings, we propose to use nonrigid alignment via thinplate splines. This is combined with a refinement step based on geodesic proximities to improve dense correspondence. We show empirically that our algorithm outperforms previous spectral methods, as well as schemes that compute correspondence in the spatial domain via nonrigid iterative closest points or the use of local shape descriptors, e.g., 3D shape context. Finally, to speed up our algorithm, we examine the effect of using subsampling and Nyström method.
Screened Poisson Surface Reconstruction
"... Poisson surface reconstruction creates watertight surfaces from oriented point sets. In this work we extend the technique to explicitly incorporate the points as interpolation constraints. The extension can be interpreted as a generalization of the underlying mathematical framework to a screened Poi ..."
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Cited by 36 (1 self)
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Poisson surface reconstruction creates watertight surfaces from oriented point sets. In this work we extend the technique to explicitly incorporate the points as interpolation constraints. The extension can be interpreted as a generalization of the underlying mathematical framework to a screened Poisson equation. In contrast to other image and geometry processing techniques, the screening term is defined over a sparse set of points rather than over the full domain. We show that these sparse constraints can nonetheless be integrated efficiently. Because the modified linear system retains the same finiteelement discretization, the sparsity structure is unchanged, and the system can still be solved using a multigrid approach. Moreover we present several algorithmic improvements that together reduce the time complexity of the solver to linear in the number of points, thereby enabling faster, higherquality surface reconstructions.
Triangulating Point Set Surfaces with Bounded Error
, 2005
"... We introduce an algorithm for constructing a highquality triangulation directly from Point Set Surfaces. Our algorithm requires no intermediate representation and no postprocessing of the output, and naturally handles noisy input data, typically in the form of a set of registered range scans. It c ..."
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Cited by 29 (6 self)
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We introduce an algorithm for constructing a highquality triangulation directly from Point Set Surfaces. Our algorithm requires no intermediate representation and no postprocessing of the output, and naturally handles noisy input data, typically in the form of a set of registered range scans. It creates a triangulation where triangle size respects the geometry of the surface rather than the sampling density of the range scans. Our technique does not require normal information, but still produces a consistent orientation of the triangles, assuming the sampled surface is an orientable twomanifold. Our work is based on using Moving LeastSquares (MLS) surfaces as the underlying representation. Our technique is a novel advancing front algorithm, that bounds the Hausdorff distance to within a userspecified limit. Specifically, we introduce a way of augmenting advancing front algorithms with global information, so that triangle size adapts gracefully even when there are large changes in surface curvature. Our results show that our technique generates highquality triangulations where other techniques fail to reconstruct the correct surface due to irregular sampling on the point cloud, noise, registration artifacts, and underlying geometric features, such as regions with high curvature gradients.
Spectral Methods for Mesh Processing and Analysis
 EUROGRAPHICS 2007
, 2007
"... Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. Early works in this area can be traced back to the seminal paper by Taubin in 1995, where spectral analysis ..."
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Cited by 29 (0 self)
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Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. Early works in this area can be traced back to the seminal paper by Taubin in 1995, where spectral analysis of mesh geometry based on a combinatorial Laplacian aids our understanding of the lowpass filtering approach to mesh smoothing. Over the past ten years or so, the list of applications in the area of geometry processing which utilize the eigenstructures of a variety of mesh operators in different manners have been growing steadily. Many works presented so far draw parallels from developments in fields such as graph theory, computer vision, machine learning, graph drawing, numerical linear algebra, and highperformance computing. This stateoftheart report aims to provide a comprehensive survey on the spectral approach, focusing on its power and versatility in solving geometry processing problems and attempting to bridge the gap between relevant research in computer graphics and other fields. Necessary theoretical background will be provided and existing works will be classified according to different criteria — the operators or eigenstructures employed, application domains, or the dimensionality of the spectral embeddings used — and described in adequate length. Finally, despite much empirical success, there still remain many open questions pertaining to the spectral approach, which we will discuss in the report as well.
DataParallel Octrees for Surface Reconstruction
 IEEE TRANSACTIONS ON VISUALIZATION & COMPUTER GRAPHICS
"... We present the first parallel surface reconstruction algorithm that runs entirely on the GPU. Like existing implicit surface reconstruction methods, our algorithm first builds an octree for the given set of oriented points, then computes an implicit function over the space of the octree, and finally ..."
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Cited by 23 (0 self)
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We present the first parallel surface reconstruction algorithm that runs entirely on the GPU. Like existing implicit surface reconstruction methods, our algorithm first builds an octree for the given set of oriented points, then computes an implicit function over the space of the octree, and finally extracts an isosurface as a watertight triangle mesh. A key component of our algorithm is a novel technique for octree construction on the GPU. This technique builds octrees in realtime and uses levelorder traversals to exploit the finegrained parallelism of the GPU. Moreover, the technique produces octrees that provide fast access to the neighborhood information of each octree node, which is critical for fast GPU surface reconstruction. With an octree so constructed, our GPU algorithm performs Poisson surface reconstruction, which produces high quality surfaces through a global optimization. Given a set of 500K points, our algorithm runs at the rate of about five frames per second, which is over two orders of magnitude faster than previous CPU algorithms. To demonstrate the potential of our algorithm, we propose a userguided surface reconstruction technique which reduces the topological ambiguity and improves reconstruction results for imperfect scan data. We also show how to use our algorithm to perform onthefly conversion from dynamic point clouds to surfaces as well as to reconstruct fluid surfaces for realtime fluid simulation.
Pointcloudxplore: Visual analysis of 3d gene expression data using physical views and parallel coordinates
 In Proceedings of the Eighth Joint Eurographics / IEEE VGTC Conference on Visualization, EUROVIS’06
, 2006
"... To allow a more rigorous understanding of animal gene regulatory networks, the Berkeley Drosophila Transcription Network Project (BDTNP) has developed a suite of methods that support quantitative, computational analysis of threedimensional (3D) gene expression patterns with cellular resolution in ..."
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Cited by 17 (6 self)
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To allow a more rigorous understanding of animal gene regulatory networks, the Berkeley Drosophila Transcription Network Project (BDTNP) has developed a suite of methods that support quantitative, computational analysis of threedimensional (3D) gene expression patterns with cellular resolution in early Drosophila embryos. Here we report the first components of a visualization tool, PointCloudXplore, that allows the relationships between different gene’s expression to be analyzed using the BDTNP’s datasets. PointCloudXplore uses the established visualization techniques of multiple views, brushing, and linking to support the analysis of highdimensional datasets that describe many genes ’ expression. Each of the views in PointCloudXplore shows a different gene expression data property. Brushing is used to select and emphasize data associated with defined subsets of embryo cells within a view. Linking is used to show in additional views the expression data for a group of cells that have first been highlighted as a brush in a single view, allowing further data subset properties to be determined. In PointCloudXplore, physical views of the data are linked to parallel coordinates. Physical views show the spatial relationships between different genes ’ expression patterns within the embryo. Parallel coordinates, on the other hand, show only some features of each gene’s expression, but allow simultaneous analysis of data for many more genes than would be possible in a physical view. We have developed several extensions to
An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes
, 2011
"... We propose a robust 2D shape reconstruction and simplification algorithm which takes as input a defectladen point set with noise and outliers. We introduce an optimaltransport driven approach where the input point set, considered as a sum of Dirac measures, is approximated by a simplicial complex ..."
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Cited by 11 (3 self)
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We propose a robust 2D shape reconstruction and simplification algorithm which takes as input a defectladen point set with noise and outliers. We introduce an optimaltransport driven approach where the input point set, considered as a sum of Dirac measures, is approximated by a simplicial complex considered as a sum of uniform measures on 0 and 1simplices. A finetocoarse scheme is devised to construct the resulting simplicial complex through greedy decimation of a Delaunay triangulation of the input point set. Our method performs well on a variety of examples ranging from line drawings to grayscale images, with or without noise, features, and boundaries.
Spectral Mesh Processing
"... Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. Early work in this area can be traced back to the seminal paper by Taubin in 1995, where spectral analysis ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
(Show Context)
Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. Early work in this area can be traced back to the seminal paper by Taubin in 1995, where spectral analysis of mesh geometry based on a combinatorial Laplacian aids our understanding of the lowpass filtering approach to mesh smoothing. Over the past fifteen years, the list of applications in the area of geometry processing which utilize the eigenstructures of a variety of mesh operators in different manners have been growing steadily. Many works presented so far draw parallels from developments in fields such as graph theory, computer vision, machine learning, graph drawing, numerical linear algebra, and highperformance computing. This paper aims to provide a comprehensive survey on the spectral approach, focusing on its power and versatility in solving geometry processing problems and attempting to bridge the gap between relevant research in computer graphics and other fields. Necessary theoretical background is provided. Existing works covered are classified according to different criteria: the operators or eigenstructures employed, application domains, or the dimensionality of the spectral embeddings used. Despite much empirical success, there still remain many open questions pertaining to the spectral approach. These are discussed as we conclude the survey and provide our perspective on possible future research.