The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Thomas Funkhouser - One of the best experts on this subject based on the ideXlab platform.
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A Reflective Symmetry Descriptor for 3D Models
Algorithmica, 2003Co-Authors: Michael Kazhdan, Bernard Chazelle, David P. Dobkin, Thomas Funkhouser, Szymon RusinkiewiczAbstract:Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. We show how to obtain a voxel grid from arbitrary 3D shapes and, using Fourier methods, we present an algorithm computes the symmetry descriptor in O(N4 log N) time for an N × N × N voxel grid and computes a Multiresolution Approximation in O(N3 log N) time. In our initial experiments, we have found that the symmetry descriptor is insensitive to noise and stable under point sampling. We have also found that it performs well in shape matching tasks, providing a measure of shape similarity that is orthogonal to existing methods.
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ECCV (2) - A Reflective Symmetry Descriptor
Computer Vision — ECCV 2002, 2002Co-Authors: Michael Kazhdan, Bernard Chazelle, David P. Dobkin, Adam Finkelstein, Thomas FunkhouserAbstract:Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper, we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D voxel model for all planes through the model's center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. Using Fourier methods, our algorithm computes the symmetry descriptor in O(N4 logN) time for an N × N × N voxel grid, and computes a Multiresolution Approximation in O(N3 logN) time. In our initial experiments, we have found the symmetry descriptor to be useful for registration, matching, and classification of shapes.
Michael Kazhdan - One of the best experts on this subject based on the ideXlab platform.
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A Reflective Symmetry Descriptor for 3D Models
Algorithmica, 2003Co-Authors: Michael Kazhdan, Bernard Chazelle, David P. Dobkin, Thomas Funkhouser, Szymon RusinkiewiczAbstract:Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. We show how to obtain a voxel grid from arbitrary 3D shapes and, using Fourier methods, we present an algorithm computes the symmetry descriptor in O(N4 log N) time for an N × N × N voxel grid and computes a Multiresolution Approximation in O(N3 log N) time. In our initial experiments, we have found that the symmetry descriptor is insensitive to noise and stable under point sampling. We have also found that it performs well in shape matching tasks, providing a measure of shape similarity that is orthogonal to existing methods.
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ECCV (2) - A Reflective Symmetry Descriptor
Computer Vision — ECCV 2002, 2002Co-Authors: Michael Kazhdan, Bernard Chazelle, David P. Dobkin, Adam Finkelstein, Thomas FunkhouserAbstract:Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper, we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D voxel model for all planes through the model's center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. Using Fourier methods, our algorithm computes the symmetry descriptor in O(N4 logN) time for an N × N × N voxel grid, and computes a Multiresolution Approximation in O(N3 logN) time. In our initial experiments, we have found the symmetry descriptor to be useful for registration, matching, and classification of shapes.
M. Unser - One of the best experts on this subject based on the ideXlab platform.
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Multiresolution Approximation using shifted splines
IEEE Transactions on Signal Processing, 1998Co-Authors: F. Muller, P. Brigger, K. Illgner, M. UnserAbstract:We consider the construction of least squares pyramids using shifted polynomial spline basis functions. We derive the pre and post-filters as a function of the degree n and the shift parameter /spl Delta/. We show that the underlying projection operator is entirely specified by two transfer functions acting on the even and odd signal samples, respectively. We introduce a measure of shift invariance and show that the most favorable configuration is obtained when the knots of the splines are centered with respect to the grid points (i.e., /spl Delta/=1/2 when n is odd and /spl Delta/=0 when n is even). The worst case corresponds to the standard Multiresolution setting where the spline spaces are nested.
Raghvendra V. Cowlagi - One of the best experts on this subject based on the ideXlab platform.
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Example of an intensity map and its vehicle-centric Multiresolution Approximation according to Eq (8).
2018Co-Authors: Benjamin S. Cooper, Raghvendra V. CowlagiAbstract:The vehicle’s location is indicated by the black dot near the center. (a) Original field map. (b) Vehicle-centric Multiresolution Approximation.
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CDC - Multiresolution path-planning with traversal costs based on time-varying spatial fields
53rd IEEE Conference on Decision and Control, 2014Co-Authors: Raghvendra V. CowlagiAbstract:We address the problem of finding an optimal path for a vehicle in a planar environment where traversal costs are based on a time-varying spatial field defined over the environment. We assume that the accuracy with which the values of the spatial field are known gradually decreases with increasing distance from the vehicle's current location. To extend previous results in the literature, we present a wavelet transform-based Multiresolution motion-planning approach that incorporates traversal costs based on a time-varying spatial field. To enable fast online computations, we use 2D wavelet transforms with time-varying coefficients, instead of computing wavelet transforms with three independent variables. We discuss methods to compute time-varying traversal costs and an optimal path with a Multiresolution Approximation of the spatial field, we illustrate the proposed approach with a simulation example.
Wang Hai - One of the best experts on this subject based on the ideXlab platform.
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reconstruction of high sample rate data based on wavelet Multiresolution Approximation
Information & Computation, 2000Co-Authors: Wang HaiAbstract:Reconstruction of high sample rate industry process data is important for multi rate control and identification problem. In this paper, a hierarchical error compensation algorithm is presented to treat data reconstruction issues based on wavelet Multiresolution analysis theory. The low sample rate data contaminat ed by noises is first filtered in the time frequency domain, then the proposed algorithm is used to reconstruct it to a new high sample rate signal. Reconstruction errors are given and analysis results are justified. This algorithm has the advantages of noise free, high reconstruction accuracy and explicit physical background. Simulation examples are given to illustrate the proposed algorithm.
