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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 ..."
Abstract

Cited by 10 (1 self)
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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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Cited by 1 (0 self)
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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.
Approximating Geodesics on Point Set Surfaces
"... We present a technique for computing piecewise linear approximations of geodesics on point set surfaces by minimizing an energy function defined for piecewise linear path. The function considers path length, closeness to the surface for the nodes of the piecewise linear path and for the intermediate ..."
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We present a technique for computing piecewise linear approximations of geodesics on point set surfaces by minimizing an energy function defined for piecewise linear path. The function considers path length, closeness to the surface for the nodes of the piecewise linear path and for the intermediate line segments. Our method is robust with respect to noise and outliers. In order to avoid local minima, a good initial piecewise linear approximation of a geodesic is provided by Dijkstraâ€™s algorithm that is applied to a proximity graph constructed over the point set. As the proximity graph we use a sphereofinfluence weighted graph extended for surfel sets. The convergence of our method has been studied and compared to results of other methods by running experiments on surfaces whose geodesics can be computed analytically. Our method is presented and optimized for surfelbased representations but it has been implemented also for MLS surfaces. Moreover, it can also be applied to other surface representations, e.g., triangle meshes, radialbasis functions, etc. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Line and Curve Generation; I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations; I.3.5 [Computer Graphics]: