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Isometryinvariant matching of point set surfaces
 In Proc. of the Eurographics workshop on 3D object retrieval
, 2008
"... Shape deformations preserving the intrinsic properties of a surface are called isometries. An isometry deforms a surface without tearing or stretching it, and preserves geodesic distances. We present a technique for matching point set surfaces, which is invariant with respect to isometries. A set of ..."
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Shape deformations preserving the intrinsic properties of a surface are called isometries. An isometry deforms a surface without tearing or stretching it, and preserves geodesic distances. We present a technique for matching point set surfaces, which is invariant with respect to isometries. A set of reference points, evenly distributed on the point set surface, is sampled by farthest point sampling. The geodesic distance between reference points is normalized and stored in a geodesic distance matrix. Each row of the matrix yields a histogram of its elements. The set of histograms of the rows of a distance matrix is taken as a descriptor of the shape of the surface. The dissimilarity between two point set surfaces is computed by matching the corresponding sets of histograms with bipartite graph matching. This is an effective method for classifying and recognizing objects deformed with isometric transformations, e.g., nonrigid and articulated objects in different postures.
3D COMPLEX CURVED SURFACE RECONSTRUCTION OF DISCRETE POINT CLOUD BASED ON SURFELS
"... A Surfels 3D reconstruction method based on improved KDTree is put forward, firstly collecting the discrete point cloud data through RGBD camera, replacing the circular or oval surfel model with hexagonal model for modeling and determining the surfel radius in light of neighborhood distribution of ..."
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A Surfels 3D reconstruction method based on improved KDTree is put forward, firstly collecting the discrete point cloud data through RGBD camera, replacing the circular or oval surfel model with hexagonal model for modeling and determining the surfel radius in light of neighborhood distribution of sample points; Moreover, doing inside and outside relations test between one point model and another discrete point model, building KDTree for each model, setting the axis with the longest projection length as the separating axis, improving segmentation rules, accelerating the detection of inside and outside and intersecting relations. Experiments show this algorithm has great reconstruction effects on the 3D reconstruction both of heterogeneous sample points and discrete point cloud with different resolution with steady and efficient calculation.
PROCESSING OF TEXTURED SURFACES REPRESENTED AS SURFEL SETS: REPRESENTATION, COMPRESSION AND GEODESIC PATHS
"... A method for representation and lossy compression of textured surfaces is presented. The input surfaces are represented by surfels (surface elements), i.e., by a set of colored, oriented, and sized disks. The position and texture of each surfel are mapped onto a sphere. The mapping is optimized for ..."
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A method for representation and lossy compression of textured surfaces is presented. The input surfaces are represented by surfels (surface elements), i.e., by a set of colored, oriented, and sized disks. The position and texture of each surfel are mapped onto a sphere. The mapping is optimized for preservation of geodesic distances. The components of the resulting spherical vectorvalued function are decorrelated by the KarhunenLoève transform and represented by spherical wavelets. Successful representation and reconstruction is demonstrated. Methods for geodesic distance computation on surfaces represented by surfels are presented. 1.
Geometric Integrability and Consistency of 3D Point Clouds
"... Numerous applications processing 3D point data will gain from the ability to estimate reliably normals and differential geometric properties. Normal estimates are notoriously noisy, the errors propagate and may lead to flawed, inaccurate, and inconsistent curvature estimates. FrankotChellappa intro ..."
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Numerous applications processing 3D point data will gain from the ability to estimate reliably normals and differential geometric properties. Normal estimates are notoriously noisy, the errors propagate and may lead to flawed, inaccurate, and inconsistent curvature estimates. FrankotChellappa introduced the use of integrability constraints in normal estimation. Their approach deals with graphs z = f(x, y). We present a newly discovered General Orientability Constraint (GOC) for 3D point clouds sampled from general surfaces, not just graphs. It provides a tool to quantify the confidence in the estimation of normals, topology, and geometry from a point cloud. Furthermore, similarly to the FrankotChellappa constraint, the GOC can be used directly to extract the topology and the geometry of the manifolds underlying 3D point clouds. As an illustration we describe an automatic CloudtoGeometry pipeline which exploits the GOC. 1.
PROCESSING OF TEXTURED SURFACES REPRESENTED AS SURFEL SETS: REPRESENTATION, COMPRESSION AND GEODESIC PATHS
"... A method for representation and lossy compression of textured surfaces is presented. The input surfaces are represented by surfels (surface elements), i.e., by a set of colored, oriented, and sized disks. The position and texture of each surfel are mapped onto a sphere. The mapping is optimized for ..."
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A method for representation and lossy compression of textured surfaces is presented. The input surfaces are represented by surfels (surface elements), i.e., by a set of colored, oriented, and sized disks. The position and texture of each surfel are mapped onto a sphere. The mapping is optimized for preservation of geodesic distances. The components of the resulting spherical vectorvalued function are decorrelated by the KarhunenLoève transform and represented by spherical wavelets. Successful representation and reconstruction is demonstrated. Methods for geodesic distance computation on surfaces represented by surfels are presented. 1.
Surface Reconstruction from Scattered Point via RBF Interpolation on GPU
"... Abstract—In this paper we describe a parallel implicit method based on radial basis functions (RBF) for surface reconstruction. Practical applicability of RBF methods is hindered by their high computational demand, that requires the solution of linear systems of size equal to the number of data poin ..."
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Abstract—In this paper we describe a parallel implicit method based on radial basis functions (RBF) for surface reconstruction. Practical applicability of RBF methods is hindered by their high computational demand, that requires the solution of linear systems of size equal to the number of data points. The implementation of our method relies on parallel scientific libraries and is designed for exploiting Graphic Processor Units (GPUs) acceleration. The performance of the proposed method in terms of accuracy of the reconstruction and computing time shows that RBF interpolation can be very effective for large scale surface reconstruction problems. I.