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221
Optimized SubSampling of Point Sets for Surface Splatting
 Computer Graphics Forum
, 2004
"... Using surface splats as a rendering primitive has gained increasing attention recently due to its potential for highperformance and highquality rendering of complex geometric models. However, as with any other rendering primitive, the processing costs are still proportional to the number of prim ..."
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Cited by 26 (0 self)
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Using surface splats as a rendering primitive has gained increasing attention recently due to its potential for highperformance and highquality rendering of complex geometric models. However, as with any other rendering primitive, the processing costs are still proportional to the number of primitives that we use to represent a given object. This is why complexity reduction for pointsampled geometry is as important as it is, e.g., for triangle meshes. In this paper we present a new subsampling technique for dense point clouds which is specifically adjusted to the particular geometric properties of circular or elliptical surface splats. A global optimization scheme computes an approximately minimal set of splats that covers the entire surface while staying below a globally prescribed maximum error tolerance #. Since our algorithm converts pure point sample data into surface splats with normal vectors and spatial extent, it can also be considered as a surface reconstruction technique which generates a holefree piecewise linear C continuous approximation of the input data. Here we can exploit the higher flexibility of surface splats compared to triangle meshes. Compared to previous work in this area we are able to obtain significantly lower splat numbers for a given error tolerance.
Volumetric stereo with silhouette and feature constraints
 British Machine Vision Conference (BMVC
, 2006
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Efficient Reconstruction of Large Scattered Geometric Datasets Using the Partition of Unity and Radial Basis Functions
, 2004
"... We present a new scheme for the reconstruction of large geometric data. It is based on the wellknown radial basis function model combined with an adaptive spatial and functional subdivision associated with a family of functions forming a partition of unity. This combination offers robust and effi ..."
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Cited by 21 (1 self)
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We present a new scheme for the reconstruction of large geometric data. It is based on the wellknown radial basis function model combined with an adaptive spatial and functional subdivision associated with a family of functions forming a partition of unity. This combination offers robust and efficient solution to a great variety of 2D and 3D reconstruction problems, such as the reconstruction of implicit curves or surfaces with attributes starting from unorganized point sets, image or mesh repairing, shape morphing or shape deformation, etc. After having presented the theoretical background, the paper mainly focuses on implementation details and issues, as well as on applications and experimental results.
Support Vector Machines for 3D Shape Processing
, 2005
"... We propose statistical learning methods for approximating implicit surfaces and computing dense 3D deformation fields. Our approach is based on Support Vector (SV) Machines, which are state of the art in machine learning. It is straightforward to implement and computationally competitive; its parame ..."
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Cited by 21 (5 self)
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We propose statistical learning methods for approximating implicit surfaces and computing dense 3D deformation fields. Our approach is based on Support Vector (SV) Machines, which are state of the art in machine learning. It is straightforward to implement and computationally competitive; its parameters can be automatically set using standard machine learning methods. The surface approximation is based on a modified Support Vector regression. We present applications to 3D head reconstruction, including automatic removal of outliers and hole filling. In a second step, we build on our SV representation to compute dense 3D deformation fields between two objects. The fields are computed using a generalized SV Machine enforcing correspondence between the previously learned implicit SV object representations, as well as correspondences between feature points if such points are available. We apply the method to the morphing of 3D heads and other objects.
D.: Compression of pointbased 3d models by shapeadaptive wavelet coding of multiheight fields
 In Eurographics Symposium on PointBased Graphics (2004
"... In order to efciently archive and transmit large 3D models, lossy and lossless compression methods are needed. We propose a compression scheme for coordinate data of pointbased 3D models of surfaces. A pointbased model is processed for compression in a pipeline of three subsequent operations, part ..."
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Cited by 21 (6 self)
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In order to efciently archive and transmit large 3D models, lossy and lossless compression methods are needed. We propose a compression scheme for coordinate data of pointbased 3D models of surfaces. A pointbased model is processed for compression in a pipeline of three subsequent operations, partitioning, parameterization, and coding. First the point set is partitioned yielding a suitable number of point clusters. Each cluster corresponds to a surface patch, that can be parameterized as a height eld and resampled on a regular grid. The domains of the height elds have irregular shapes that are encoded losslessly. The height elds themselves are encoded using a shapeadaptive wavelet coder, producing a progressive bitstream for each patch. A ratedistortion optimization provides for an optimal bit allocation for the individual patch codes. With this algorithm design compact codes are produced that are scalable with respect to rate, quality, and resolution. In our encodings of complex 3D models competitive ratedistortion performances were achieved with excellent reconstruction quality at under 3 bits per point (bpp).
Bayesian Point Cloud Reconstruction
 EUROGRAPHICS 2006
, 2006
"... In this paper, we propose a novel surface reconstruction technique based on Bayesian statistics: The measurement process as well as prior assumptions on the measured objects are modeled as probability distributions and Bayes ’ rule is used to infer a reconstruction of maximum probability. The key id ..."
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Cited by 21 (5 self)
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In this paper, we propose a novel surface reconstruction technique based on Bayesian statistics: The measurement process as well as prior assumptions on the measured objects are modeled as probability distributions and Bayes ’ rule is used to infer a reconstruction of maximum probability. The key idea of this paper is to define both measurements and reconstructions as point clouds and describe all statistical assumptions in terms of this finite dimensional representation. This yields a discretization of the problem that can be solved using numerical optimization techniques. The resulting algorithm reconstructs both topology and geometry in form of a wellsampled point cloud with noise removed. In a final step, this representation is then converted into a triangle mesh. The proposed approach is conceptually simple and easy to extend. We apply the approach to reconstruct piecewisesmooth surfaces with sharp features and examine the performance of the algorithm on different synthetic and realworld data sets. Categories and Subject Descriptors (according to ACM CCS): I.5.1 [Models]: Statistical; I.3.5 [Computer Graphics]: Curve, surface, solid and object representations
Robust and efficient surface reconstruction from range data
 COMPUTER GRAPHICS FORUM
, 1981
"... We describe a robust but simple algorithm to reconstruct a surface from a set of merged range scans. Our key contribution is the formulation of the surface reconstruction problem as an energy minimisation problem that explicitly models the scanning process. The adaptivity of the Delaunay triangulati ..."
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Cited by 20 (1 self)
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We describe a robust but simple algorithm to reconstruct a surface from a set of merged range scans. Our key contribution is the formulation of the surface reconstruction problem as an energy minimisation problem that explicitly models the scanning process. The adaptivity of the Delaunay triangulation is exploited by restricting the energy to inside/outside labelings of Delaunay tetrahedra. Our energy measures both the output surface quality and how well the surface agrees with soft visibility constraints. Such energy is shown to perfectly fit into the minimum st cuts optimisation framework, allowing fast computation of a globally optimal tetrahedra labeling, while avoiding the “shrinking bias” that usually plagues graph cuts methods. The behaviour of our method confronted to noise, undersampling and outliers is evaluated on several data sets and compared with other methods through different experiments: its strong robustness would make our method practical not only for reconstruction from range data but also from typically more difficult dense point clouds, resulting for instance from stereo image matching. Our effective modeling of the surface acquisition inverse problem, along with the unique combination of Delaunay triangulation and minimum st cuts, makes the computational requirements of the algorithm scale well with respect to the size of the input point cloud.
Robust smooth feature extraction from point clouds
 IEEE INTERNATIONAL CONFERENCE ON SHAPE MODELING AND APPLICATIONS
, 2007
"... Defining sharp features in a given 3D model facilitates a better understanding of the surface and aids visualizations, reverse engineering, filtering, simplification, nonphoto realism, reconstruction and other geometric processing applications. We present a robust method that identifies sharp featu ..."
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Cited by 19 (2 self)
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Defining sharp features in a given 3D model facilitates a better understanding of the surface and aids visualizations, reverse engineering, filtering, simplification, nonphoto realism, reconstruction and other geometric processing applications. We present a robust method that identifies sharp features in a point cloud by returning a set of smooth curves aligned along the edges. Our feature extraction is a multistep refinement method that leverages the concept of Robust Moving Least Squares to locally fit surfaces to potential features. Using Newton’s method, we project points to the intersections of multiple surfaces then grow polylines through the projected cloud. After resolving gaps, connecting corners, and relaxing the results, the algorithm returns a set of complete and smooth curves that define the features. We demonstrate the benefits of our method with two applications: surface meshing and pointbased geometry compression.
Meshless ThinShell Simulation based on Global Conformal Parameterization
 IEEE Transactions on Visualization and Computer Graphics
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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.