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106
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.
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.
Visualization of Wormholes in Sensor Networks
, 2004
"... Several protocols have been proposed to defend against wormholes in ad hoc networks by adopting positioning devices, synchronized clocks, or directional antennas. In this paper, we propose a mechanism, MDSVOW, to detect wormholes in a sensor network. MDSVOW first reconstructs the layout of the sen ..."
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Cited by 71 (3 self)
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Several protocols have been proposed to defend against wormholes in ad hoc networks by adopting positioning devices, synchronized clocks, or directional antennas. In this paper, we propose a mechanism, MDSVOW, to detect wormholes in a sensor network. MDSVOW first reconstructs the layout of the sensors using multidimensional scaling. To compensate the distortions caused by distance measurement errors, a surface smoothing scheme is adopted. MDSVOW then detects the wormhole by visualizing the anomalies introduced by the attack. The anomalies, which are caused by the fake connections through the wormhole, bend the reconstructed surface to pull the sensors that are faraway to each other. Through detecting the bending feature, the wormhole is located and the fake connections are identified. The contributions of MDSVOW are: (1) it does not require the sensors to be equipped with special hardware, (2) it adopts and combines the techniques from social science, computer graphics, and scientific visualization to attack the problem in network security. We examine the accuracy of the proposed mechanism when the sensors are deployed in a circle area and one wormhole exists in the network. The results show that MDSVOW has a low false alarm ratio when the distance measurement errors are not large.
Registration of Point Cloud Data from a Geometric Optimization Perspective
, 2004
"... We propose a framework for pairwise registration of shapes represented by point cloud data (PCD). We assume that the points are sampled from a surface and formulate the problem of aligning two PCDs as a minimization of the squared distance between the underlying surfaces. Local quadratic approximant ..."
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Cited by 59 (13 self)
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We propose a framework for pairwise registration of shapes represented by point cloud data (PCD). We assume that the points are sampled from a surface and formulate the problem of aligning two PCDs as a minimization of the squared distance between the underlying surfaces. Local quadratic approximants of the squared distance function are used to develop a linear system whose solution gives the best aligning rigid transform for the given pair of point clouds. The rigid transform is applied and the linear system corresponding to the new orientation is build. This process is iterated until it converges. The pointtopoint and the pointtoplane Iterated Closest Point (ICP) algorithms can be treated as special cases in this framework. Our algorithm can align PCDs even when they are placed far apart, and is experimentally found to be more stable than pointtoplane ICP. We analyze the convergence behavior of our algorithm and of pointtopoint and pointtoplane ICP under our proposed framework, and derive bounds on their rate of convergence. We compare the stability and convergence properties of our algorithm with other registration algorithms on a variety of scanned data.
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.
Point Cloud Representation
, 2001
"... Reconstructing a surface out of a threedimensional set of points, which is obtained by sampling an object's boundary, is done by generating an arbitrary triangular mesh. Our approach is to obviate the computation of such a mesh connectivity and to represent the object's surface only by ..."
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Cited by 43 (3 self)
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Reconstructing a surface out of a threedimensional set of points, which is obtained by sampling an object's boundary, is done by generating an arbitrary triangular mesh. Our approach is to obviate the computation of such a mesh connectivity and to represent the object's surface only by the point cloud. We discuss how such a point cloud representation can be visualized and present processing steps like coarsifying and smoothing, which are important for dealing with the objects. Further we apply a multiresolution method to point cloud representations and use this technique as well as others for modelling purposes. 1
An Efficient Volumetric Method for Building Closed Triangular Meshes from 3D Image and Point Data
 IN GRAPHICS INTERFACE 97
, 1997
"... We present a volumetric method that can efficiently create triangular meshes from 3D geometric data. This data can be presented in the form of images, profiles or unordered points. The mesh model can be created at different resolutions and can also be closed to make a true volumetric model. ..."
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Cited by 39 (3 self)
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We present a volumetric method that can efficiently create triangular meshes from 3D geometric data. This data can be presented in the form of images, profiles or unordered points. The mesh model can be created at different resolutions and can also be closed to make a true volumetric model.
Multilevel Streaming for OutofCore Surface Reconstruction
, 2007
"... Reconstruction of surfaces from huge collections of scanned points often requires outofcore techniques, and most such techniques involve local computations that are not resilient to data errors. We show that a Poissonbased reconstruction scheme, which considers all points in a global analysis, ca ..."
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Cited by 33 (4 self)
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Reconstruction of surfaces from huge collections of scanned points often requires outofcore techniques, and most such techniques involve local computations that are not resilient to data errors. We show that a Poissonbased reconstruction scheme, which considers all points in a global analysis, can be performed efficiently in limited memory using a streaming framework. Specifically, we introduce a multilevel streaming representation, which enables efficient traversal of a sparse octree by concurrently advancing through multiple streams, one per octree level. Remarkably, for our reconstruction application, a sufficiently accurate solution to the global linear system is obtained using a single iteration of cascadic multigrid, which can be evaluated within a single multistream pass. We demonstrate scalable performance on several large datasets.
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.
DataDependent MLS for Faithful Surface Approximation
, 2007
"... In this paper we present a highfidelity surface approximation technique that aims at a faithful reconstruction of piecewisesmooth surfaces from a scattered point set. The presented method builds on the Moving LeastSquares (MLS) projection methodology, but introduces a fundamental modification: Wh ..."
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Cited by 26 (3 self)
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In this paper we present a highfidelity surface approximation technique that aims at a faithful reconstruction of piecewisesmooth surfaces from a scattered point set. The presented method builds on the Moving LeastSquares (MLS) projection methodology, but introduces a fundamental modification: While the classical MLS uses a fixed approximation space, i.e., polynomials of a certain degree, the new method is datadependent. For each projected point, it finds a proper local approximation space of piecewise polynomials (splines). The locally constructed spline encapsulates the local singularities which may exist in the data. The optional singularity for this local approximation space is modeled via a Singularity Indicator Field (SIF) which is computed over the input data points. We demonstrate the effectiveness of the method by reconstructing surfaces from real scanned 3D data, while being faithful to their most delicate features.