The Experts below are selected from a list of 126 Experts worldwide ranked by ideXlab platform

Max Wardetzky - One of the best experts on this subject based on the ideXlab platform.

  • geodesics in heat a new approach to Computing Distance based on heat flow
    ACM Transactions on Graphics, 2013
    Co-Authors: Keenan Crane, Clarisse Weischedel, Max Wardetzky
    Abstract:

    We introduce the heat method for Computing the geodesic Distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting systems can be prefactored once and subsequently solved in near-linear time. In practice, Distance is updated an order of magnitude faster than with state-of-the-art methods, while maintaining a comparable level of accuracy. The method requires only standard differential operators and can hence be applied on a wide variety of domains (grids, triangle meshes, point clouds, etc.). We provide numerical evidence that the method converges to the exact Distance in the limit of refinement; we also explore smoothed approximations of Distance suitable for applications where greater regularity is required.

  • Geodesics in heat: A new approach to Computing Distance based on heat flow
    ACM Transactions on Graphics, 2013
    Co-Authors: Keenan Crane, Clarisse Weischedel, Max Wardetzky
    Abstract:

    We introduce the heat method for Computing the shortest geodesic Distance to an arbitrary subset of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting algorithm represents a significant breakthrough in the practical computation of Distance on a wide variety of geometric domains, since these problems can be prefactored once and subsequently solved in linear time. In practice, Distance can be updated via the heat method an order of magnitude faster than with state-of-the-art methods while maintaining a comparable level of accuracy. We demonstrate that the method converges to the exact geodesic Distance in the limit of refinement; we also explore smoothed approximations of Distance suitable for applications where differentiability is required.

Sagar A Pandit - One of the best experts on this subject based on the ideXlab platform.

  • Computing Distance histograms efficiently in scientific databases
    International Conference on Data Engineering, 2009
    Co-Authors: Shaoping Chen, Sagar A Pandit
    Abstract:

    Particle simulation has become an important re- search tool in many scientific and engineering fields. Data gen- erated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial Distance histogram (SDH) query, is the building block of many high-level analytics, and requires quadratic time to compute using a straightforward algorithm. In this paper, we propose a novel algorithm to compute SDH based on a data structure called density map, which can be easily implemented by augmenting a Quad-tree index. We also show the results of rigorous mathematical analysis of the time complexity of the proposed algorithm: our algorithm runs on Θ(N 3 2 ) for two-dimensional data and Θ(N 5 3 ) for three-dimensional data, respectively. We also propose an approximate SDH processing algorithm whose running time is unrelated to the input size N. Experimental results confirm our analysis and show that the approximate SDH algorithm achieves very high accuracy.

  • Computing Distance Histograms Ef?ciently in Scientific Databases
    2009 IEEE 25th International Conference on Data Engineering, 2009
    Co-Authors: Shaoping Chen, Sagar A Pandit
    Abstract:

    Particle simulation has become an important research tool in many scientific and engineering fields. Data generated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial Distance histogram (SDH) query, is the building block of many high-level analytics, and requires quadratic time to compute using a straightforward algorithm. In this paper, we propose a novel algorithm to compute SDH based on a data structure called density map, which can be easily implemented by augmenting a Quad-tree index. We also show the results of rigorous mathematical analysis of the time complexity of the proposed algorithm: our algorithm runs on O(N^{3/ 2}) for two-dimensional data and O(N^{5/3}) for three-dimensional data, respectively. We also propose an approximate SDH processing algorithm whose running time is unrelated to the input size N. Experimental results confirm our analysis and show that the approximate SDH algorithm achieves very high accuracy.

Keenan Crane - One of the best experts on this subject based on the ideXlab platform.

  • geodesics in heat a new approach to Computing Distance based on heat flow
    ACM Transactions on Graphics, 2013
    Co-Authors: Keenan Crane, Clarisse Weischedel, Max Wardetzky
    Abstract:

    We introduce the heat method for Computing the geodesic Distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting systems can be prefactored once and subsequently solved in near-linear time. In practice, Distance is updated an order of magnitude faster than with state-of-the-art methods, while maintaining a comparable level of accuracy. The method requires only standard differential operators and can hence be applied on a wide variety of domains (grids, triangle meshes, point clouds, etc.). We provide numerical evidence that the method converges to the exact Distance in the limit of refinement; we also explore smoothed approximations of Distance suitable for applications where greater regularity is required.

  • Geodesics in heat: A new approach to Computing Distance based on heat flow
    ACM Transactions on Graphics, 2013
    Co-Authors: Keenan Crane, Clarisse Weischedel, Max Wardetzky
    Abstract:

    We introduce the heat method for Computing the shortest geodesic Distance to an arbitrary subset of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting algorithm represents a significant breakthrough in the practical computation of Distance on a wide variety of geometric domains, since these problems can be prefactored once and subsequently solved in linear time. In practice, Distance can be updated via the heat method an order of magnitude faster than with state-of-the-art methods while maintaining a comparable level of accuracy. We demonstrate that the method converges to the exact geodesic Distance in the limit of refinement; we also explore smoothed approximations of Distance suitable for applications where differentiability is required.

Clarisse Weischedel - One of the best experts on this subject based on the ideXlab platform.

  • geodesics in heat a new approach to Computing Distance based on heat flow
    ACM Transactions on Graphics, 2013
    Co-Authors: Keenan Crane, Clarisse Weischedel, Max Wardetzky
    Abstract:

    We introduce the heat method for Computing the geodesic Distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting systems can be prefactored once and subsequently solved in near-linear time. In practice, Distance is updated an order of magnitude faster than with state-of-the-art methods, while maintaining a comparable level of accuracy. The method requires only standard differential operators and can hence be applied on a wide variety of domains (grids, triangle meshes, point clouds, etc.). We provide numerical evidence that the method converges to the exact Distance in the limit of refinement; we also explore smoothed approximations of Distance suitable for applications where greater regularity is required.

  • Geodesics in heat: A new approach to Computing Distance based on heat flow
    ACM Transactions on Graphics, 2013
    Co-Authors: Keenan Crane, Clarisse Weischedel, Max Wardetzky
    Abstract:

    We introduce the heat method for Computing the shortest geodesic Distance to an arbitrary subset of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting algorithm represents a significant breakthrough in the practical computation of Distance on a wide variety of geometric domains, since these problems can be prefactored once and subsequently solved in linear time. In practice, Distance can be updated via the heat method an order of magnitude faster than with state-of-the-art methods while maintaining a comparable level of accuracy. We demonstrate that the method converges to the exact geodesic Distance in the limit of refinement; we also explore smoothed approximations of Distance suitable for applications where differentiability is required.

Shaoping Chen - One of the best experts on this subject based on the ideXlab platform.

  • Computing Distance histograms efficiently in scientific databases
    International Conference on Data Engineering, 2009
    Co-Authors: Shaoping Chen, Sagar A Pandit
    Abstract:

    Particle simulation has become an important re- search tool in many scientific and engineering fields. Data gen- erated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial Distance histogram (SDH) query, is the building block of many high-level analytics, and requires quadratic time to compute using a straightforward algorithm. In this paper, we propose a novel algorithm to compute SDH based on a data structure called density map, which can be easily implemented by augmenting a Quad-tree index. We also show the results of rigorous mathematical analysis of the time complexity of the proposed algorithm: our algorithm runs on Θ(N 3 2 ) for two-dimensional data and Θ(N 5 3 ) for three-dimensional data, respectively. We also propose an approximate SDH processing algorithm whose running time is unrelated to the input size N. Experimental results confirm our analysis and show that the approximate SDH algorithm achieves very high accuracy.

  • Computing Distance Histograms Ef?ciently in Scientific Databases
    2009 IEEE 25th International Conference on Data Engineering, 2009
    Co-Authors: Shaoping Chen, Sagar A Pandit
    Abstract:

    Particle simulation has become an important research tool in many scientific and engineering fields. Data generated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial Distance histogram (SDH) query, is the building block of many high-level analytics, and requires quadratic time to compute using a straightforward algorithm. In this paper, we propose a novel algorithm to compute SDH based on a data structure called density map, which can be easily implemented by augmenting a Quad-tree index. We also show the results of rigorous mathematical analysis of the time complexity of the proposed algorithm: our algorithm runs on O(N^{3/ 2}) for two-dimensional data and O(N^{5/3}) for three-dimensional data, respectively. We also propose an approximate SDH processing algorithm whose running time is unrelated to the input size N. Experimental results confirm our analysis and show that the approximate SDH algorithm achieves very high accuracy.