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26
Feature preserving point set surfaces based on nonlinear kernel regression
, 2009
"... Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smoothout small or sharp features. In this paper, we addre ..."
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Cited by 55 (3 self)
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Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smoothout small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicity of implicit MLS surfaces [SOS04,Kol05] with the strength of robust statistics. To reach this new definition, we review MLS surfaces in terms of local kernel regression, opening the doors to a vast and well established literature from which we utilize robust kernel regression. Our novel representation can handle sparse sampling, generates a continuous surface better preserving fine details, and can naturally handle any kind of sharp features with controllable sharpness. Finally, it combines ease of implementation with performance competing with other nonrobust approaches.
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.
Volume MLS ray casting
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2008
"... The method of Moving Least Squares (MLS) is a popular framework for reconstructing continuous functions from scattered data due to its rich mathematical properties and wellunderstood theoretical foundations. This paper applies MLS to volume rendering, providing a unified mathematical framework fo ..."
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Cited by 18 (1 self)
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The method of Moving Least Squares (MLS) is a popular framework for reconstructing continuous functions from scattered data due to its rich mathematical properties and wellunderstood theoretical foundations. This paper applies MLS to volume rendering, providing a unified mathematical framework for ray casting of scalar data stored over regular as well as irregular grids. We use the MLS reconstruction to render smooth isosurfaces and to compute accurate derivatives for highquality shading effects. We also present a novel, adaptive preintegration scheme to improve the efficiency of the ray casting algorithm by reducing the overall number of function evaluations, and an efficient implementation of our framework exploiting modern graphics hardware. The resulting system enables highquality volume integration and shaded isosurface rendering for regular and irregular volume data.
Robust Voronoibased Curvature and Feature Estimation
 SIAM/ACM JOINT CONFERENCE ON GEOMETRIC AND PHYSICAL MODELING
, 2009
"... Many algorithms for shape analysis and shape processing rely on accurate estimates of di erential information such as normals and curvature. In most settings, however, care must be taken around nonsmooth areas of the shape where these quantities are not easily de ned. This problem is particularly pr ..."
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Cited by 16 (3 self)
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Many algorithms for shape analysis and shape processing rely on accurate estimates of di erential information such as normals and curvature. In most settings, however, care must be taken around nonsmooth areas of the shape where these quantities are not easily de ned. This problem is particularly prominent with pointcloud data, which are discontinuous everywhere. In this paper we present an e cient and robust method for extracting principal curvatures, sharp features and normal directions of a piecewise smooth surface from its point cloud sampling, with theoretical guarantees. Our method is integral in nature and uses convolved covariance matrices of Voronoi cells of the point cloud which makes it provably robust in the presence of noise. We show analytically that our method recovers correct principal curvatures and principal curvature directions in smooth parts of the shape, and correct feature directions and feature angles at the sharp edges of a piecewise smooth surface, with the error bounded by the Hausdor distance between the point cloud and the underlying surface. Using the same analysis we provide theoretical guarantees for a modi cation of a previously proposed normal estimation technique. We illustrate the correctness of both principal curvature information and feature extraction in the presence of varying levels of noise and sampling density on a variety of models.
Feature preserving mesh generation from 3d point clouds
 Computer Graphics Forum
"... We address the problem of generating quality surface triangle meshes from 3D point clouds sampled on piecewise smooth surfaces. Using a feature detection process based on the covariance matrices of Voronoi cells, we first extract from the point cloud a set of sharp features. Our algorithm also runs ..."
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Cited by 11 (0 self)
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We address the problem of generating quality surface triangle meshes from 3D point clouds sampled on piecewise smooth surfaces. Using a feature detection process based on the covariance matrices of Voronoi cells, we first extract from the point cloud a set of sharp features. Our algorithm also runs on the input point cloud a reconstruction process, such as Poisson reconstruction, providing an implicit surface. A feature preserving variant of a Delaunay refinement process is then used to generate a mesh approximating the implicit surface and containing a faithful representation of the extracted sharp edges. Such a mesh provides an enhanced tradeoff between accuracy and mesh complexity. The whole process is robust to noise and made versatile through a small set of parameters which govern the mesh sizing, approximation error and shape of the elements. We demonstrate the effectiveness of our method on a variety of models including laser scanned datasets ranging from indoor to outdoor scenes. Categories and Subject Descriptors (according to ACM CCS): [Computational Geometry and Object Modeling] [I.3.5]: Curve, surface, solid, and object representations—
Highly Parallel Surface Reconstruction
"... We present a 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 extract ..."
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Cited by 10 (0 self)
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We present a 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.
PatchGraph Reconstruction for Piecewise Smooth Surfaces
 VMV 2008
, 2008
"... In this paper we present a new surface reconstruction technique for piecewise smooth surfaces from point clouds, such as scans of architectural sites or manmade artifacts. The technique operates in three conceptual steps: First, a graph of local surface patches, each consisting of a set of basis fu ..."
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Cited by 10 (0 self)
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In this paper we present a new surface reconstruction technique for piecewise smooth surfaces from point clouds, such as scans of architectural sites or manmade artifacts. The technique operates in three conceptual steps: First, a graph of local surface patches, each consisting of a set of basis functions, is assembled. Second, we establish topological connectivity among the nodes that respects sharp features. Third, we find optimal coefficients for the basis functions in each node by solving a sparse optimization problem. Our final representation allows for robust finding of crease and border edges which separate the piecewise smooth parts. As output of our approach, we extract a clean, manifold surface mesh which preserves and even aggravates feature lines. The main benefit of our new proposal in comparison to previous work is its robustness and efficiency, which we examine by applying the algorithm to a variety of different synthetic and realword data sets.
State of the Art in Surface Reconstruction from Point Clouds
 IN PROC. EUROGRAPHICS 2014
, 2014
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FeaturePreserving Surface Reconstruction and Simplification from DefectLaden Point Sets
, 2012
"... We introduce a robust and featurecapturing surface reconstruction and simplification method that turns an input point set into a low trianglecount simplicial complex. Our approach starts with a (possibly nonmanifold) simplicial complex filtered from a 3D Delaunay triangulation of the input point ..."
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Cited by 8 (1 self)
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We introduce a robust and featurecapturing surface reconstruction and simplification method that turns an input point set into a low trianglecount simplicial complex. Our approach starts with a (possibly nonmanifold) simplicial complex filtered from a 3D Delaunay triangulation of the input points. This initial approximation is iteratively simplified based on an error metric that measures, through optimal transport, the distance between the input points and the current simplicial complex—both seen as mass distributions. Our approach is shown to exhibit both robustness to noise and outliers, as well as preservation of sharp features and boundaries. Our new featuresensitive metric between point sets and triangle meshes can also be used as a postprocessing tool that, from the smooth output of a reconstruction method, recovers sharp features and boundaries present in the initial point set.
A Survey of Methods for Moving Least Squares Surfaces
, 2008
"... Moving least squares (MLS) surfaces representation directly defines smooth surfaces from point cloud data, on which the differential geometric properties of point set can be conveniently estimated. Nowadays, the MLS surfaces have been widely applied in the processing and rendering of pointsampled m ..."
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Cited by 8 (0 self)
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Moving least squares (MLS) surfaces representation directly defines smooth surfaces from point cloud data, on which the differential geometric properties of point set can be conveniently estimated. Nowadays, the MLS surfaces have been widely applied in the processing and rendering of pointsampled models and increasingly adopted as the standard definition of point set surfaces. We classify the MLS surface algorithms into two types: projection MLS surfaces and implicit MLS surfaces, according to employing a stationary projection or a scalar field in their definitions. Then, the properties and constrains of the MLS surfaces are analyzed. After presenting its applications, we summarize the MLS surfaces definitions in a generic form and give the outlook of the future work at last.