Results 1  10
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123
ExampleBased 3D Scan Completion
 EUROGRAPHICS SYMPOSIUM ON GEOMETRY PROCESSING
, 2005
"... Optical acquisition devices often produce noisy and incomplete data sets, due to occlusion, unfavorable surface reflectance properties, or geometric restrictions in the scanner setup. We present a novel approach for obtaining a complete and consistent 3D model representation from such incomplete sur ..."
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Cited by 85 (23 self)
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Optical acquisition devices often produce noisy and incomplete data sets, due to occlusion, unfavorable surface reflectance properties, or geometric restrictions in the scanner setup. We present a novel approach for obtaining a complete and consistent 3D model representation from such incomplete surface scans, using a database of 3D shapes to provide geometric priors for regions of missing data. Our method retrieves suitable context models from the database, warps the retrieved models to conform with the input data, and consistently blends the warped models to obtain the final consolidated 3D shape. We define a shape matching penalty function and corresponding optimization scheme for computing the nonrigid alignment of the context models with the input data. This allows a quantitative evaluation and comparison of the quality of the shape extrapolation provided by each model. Our algorithms are explicitly designed to accommodate uncertain data and can thus be applied directly to raw scanner output. We show on a variety of real data sets how consistent models can be obtained from highly incomplete input. The information gained during the shape completion process can be utilized for future scans, thus continuously simplifying the creation of complex 3D models.
Spectral Surface Reconstruction from Noisy Point Clouds
, 2004
"... We introduce a noiseresistant algorithm for reconstructing a watertight surface from point cloud data. It forms a
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Cited by 81 (1 self)
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We introduce a noiseresistant algorithm for reconstructing a watertight surface from point cloud data. It forms a
Approximating and Intersecting Surfaces from Points
, 2003
"... Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each poin ..."
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Cited by 73 (3 self)
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Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each point on a ray, a local normal direction is estimated as the direction of smallest weighted covariances of the points. The normal direction is used to build a local polynomial approximation to the surface, which is then intersected with the ray. The distance to the polynomials essentially defines a distance field, whose zeroset is computed by repeated ray intersection. Requiring the distance field to be smooth leads to an intuitive and natural sampling criterion, namely, that normals derived from the weighted covariances are well defined in a tubular neighborhood of the surface. For certain, wellchosen weight functions we can show that wellsampled surfaces lead to smooth distance fields with nonzero gradients and, thus, the surface is a continuously differentiable manifold. We detail spatial data structures and efficient algorithms to compute raysurface intersections for fast ray casting and ray tracing of the surface.
Robust Reconstruction of Watertight 3D Models from Nonuniformly Sampled Point Clouds Without Normal Information
, 2006
"... We present a new volumetric method for reconstructing watertight triangle meshes from arbitrary, unoriented point clouds. While previous techniques usually reconstruct surfaces as the zero levelset of a signed distance function, our method uses an unsigned distance function and hence does not requi ..."
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Cited by 46 (0 self)
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We present a new volumetric method for reconstructing watertight triangle meshes from arbitrary, unoriented point clouds. While previous techniques usually reconstruct surfaces as the zero levelset of a signed distance function, our method uses an unsigned distance function and hence does not require any information about the local surface orientation. Our algorithm estimates local surface confidence values within a dilated crust around the input samples. The surface which maximizes the global confidence is then extracted by computing the minimum cut of a weighted spatial graph structure. We present an algorithm, which efficiently converts this cut into a closed, manifold triangle mesh with a minimal number of vertices. The use of an unsigned distance function avoids the topological noise artifacts caused by misalignment of 3D scans, which are common to most volumetric reconstruction techniques. Due to a hierarchical approach our method efficiently produces solid models of low genus even for noisy and highly irregular data containing large holes, without loosing fine details in densely sampled regions. We show several examples for different application settings such as model generation from raw laserscanned data, imagebased 3D reconstruction, and mesh repair.
Provably good sampling and meshing of surfaces
 Graphical Models
, 2005
"... The notion of εsample, introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an εsample of a C2continuous surface S for a sufficiently small ε, then the Delaunay triangulation of E restricted to S is a goo ..."
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Cited by 37 (9 self)
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The notion of εsample, introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an εsample of a C2continuous surface S for a sufficiently small ε, then the Delaunay triangulation of E restricted to S is a good approximation of S, both in a topological and in a geometric sense. Hence, if one can construct an εsample, one also gets a good approximation of the surface. Moreover, correct reconstruction is ensured by various algorithms. In this paper, we introduce the notion of loose εsample. We show that the set of loose εsamples contains and is asymptotically identical to the set of εsamples. The main advantage of loose εsamples over εsamples is that they are easier to check and to construct. We also present a simple algorithm that constructs provably good surface samples and meshes. Given a C2continuous surface S without boundary, the algorithm generates a sparse εsample E and at the same time a triangulated surface DelS(E). The triangulated surface has the same topological type as S, is close to S for the Hausdorff distance and can provide good approximations of normals, areas and curvatures. A notable feature of the algorithm is that the surface needs only to be known through an oracle that, given a line segment, detects whether the segment intersects the surface and, in the affirmative, returns the intersection points. This makes the algorithm useful in a wide variety of contexts and for a large class of surfaces. Keywords: Surface mesh generation, εsampling, surface approximation, restricted Delaunay triangulation, mesh refinement
On Fast Surface Reconstruction Methods for Large and Noisy Datasets
 in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA
, 2009
"... Abstract — In this paper we present a method for fast surface reconstruction from large noisy datasets. Given an unorganized 3D point cloud, our algorithm recreates the underlying surface’s geometrical properties using data resampling and a robust triangulation algorithm in near realtime. For result ..."
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Cited by 34 (9 self)
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Abstract — In this paper we present a method for fast surface reconstruction from large noisy datasets. Given an unorganized 3D point cloud, our algorithm recreates the underlying surface’s geometrical properties using data resampling and a robust triangulation algorithm in near realtime. For resulting smooth surfaces, the data is resampled with variable densities according to previously estimated surface curvatures. Incremental scans are easily incorporated into an existing surface mesh, by determining the respective overlapping area and reconstructing only the updated part of the surface mesh. The proposed framework is flexible enough to be integrated with additional point label information, where groups of points sharing the same label are clustered together and can be reconstructed separately, thus allowing fast updates via triangular mesh decoupling. To validate our approach, we present results obtained from laser scans acquired in both indoor and outdoor environments. I.
Curve and Surface Reconstruction
, 2004
"... The problem of reconstructing a shape from its sample appears in many scientific and engineering applications. Because of the variety in shapes and applications, many algorithms have been proposed over the last two decades, some of which exploit applicationspecific information and some of which are ..."
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Cited by 23 (0 self)
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The problem of reconstructing a shape from its sample appears in many scientific and engineering applications. Because of the variety in shapes and applications, many algorithms have been proposed over the last two decades, some of which exploit applicationspecific information and some of which are more general. We will concentrate on techniques that apply to the general setting and have proved to provide some guarantees on the quality of reconstruction.
Topology guaranteeing manifold reconstruction using distance function to noisy data, Research Report 429 (2005), available at http://math.ubourgogne.fr/topo/chazal/publications.htm
"... Given a smooth compact codimension one submanifold S of R k and a compact approximation K of S, we prove that it is possible to reconstruct S and to approximate the medial axis of S with topological guarantees using unions of balls centered on K. We consider two notions of noisyapproximation that g ..."
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Cited by 22 (4 self)
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Given a smooth compact codimension one submanifold S of R k and a compact approximation K of S, we prove that it is possible to reconstruct S and to approximate the medial axis of S with topological guarantees using unions of balls centered on K. We consider two notions of noisyapproximation that generalize sampling conditions introduced by Amenta & al. and Dey & al. Our results are based upon critical point theory for distance functions. For the two approximation conditions, we prove that the connected components of the boundary of unions of balls centered on K are isotopic to S. Our results allow to consider balls of different radii. For the first approximation condition, we also prove that a subset (known as the λmedial axis) of the medial axis of R k \ K is homotopy equivalent to the medial axis of S. We obtain similar results for smooth compact submanifolds S of R k of any codimension.