Parallel and Scalable Heat Methods for Geodesic Distance Computation

Tao, Jiong; Zhang, Jie; Deng, Bailin; Fang, Zheng; Peng, Yue; He, Ying

doi:10.48550/arxiv.1812.06060

Cited by 1 publication

(2 citation statements)

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“…However, the accuracy of the distance map computation is sensitive to the choice of a parameter. A parallel and scalable version of the Heat method was proposed by Tao et al [24]. Finally, Litman and Bronstein [25] proposed a method that also works on the spectral domain, called the Spectrometer.…”

Section: Related Workmentioning

confidence: 99%

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A minimalistic approach for fast computation of geodesic distances on triangular meshes

Calla

Perez

Montenegro

2019

Computers & Graphics

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The computation of geodesic distances is an important research topic in Geometry Processing and 3D Shape Analysis as it is a basic component of many methods used in these areas. In this work, we present a minimalistic parallel algorithm based on front propagation to compute approximate geodesic distances on meshes. Our method is practical and simple to implement, and does not require any heavy pre-processing. The convergence of our algorithm depends on the number of discrete level sets around the source points from which distance information propagates. To appropriately implement our method on GPUs taking into account memory coalescence problems, we take advantage of a graph representation based on a breadth-first search traversal that works harmoniously with our parallel front propagation approach. We report experiments that show how our method scales with the size of the problem. We compare the mean error and processing time obtained by our method with such measures computed using other methods. Our method produces results in competitive times with almost the same accuracy, especially for large meshes. We also demonstrate its use for solving two classical geometry processing problems: the regular sampling problem and the Voronoi tessellation on meshes.

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Section: Related Workmentioning

confidence: 99%

“…In the case of CPU, the Cholmod library is more stable and we got a good result for the armadillo mesh. Recently, Tao et al [24] proposed a scalable version of the Heat Method, which has been tested only on CPU for large meshes. This method uses Gauss-Seidel iterations instead of solving the linear system using Cholesky decomposition.…”

Section: Performancementioning

confidence: 99%