Parallel and Scalable Heat Methods for Geodesic Distance Computation

In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes. Our key observation is that the recovery of geodesic distance with the heat method <xref ref-type="bibr" rid="ref1">[1] can be reformulated as optimization of it...

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Vydané v:IEEE transactions on pattern analysis and machine intelligence Ročník 43; číslo 2; s. 579 - 594
Hlavní autori: Tao, Jiong, Zhang, Juyong, Deng, Bailin, Fang, Zheng, Peng, Yue, He, Ying
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: United States IEEE 01.02.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Apexes
Approximation algorithms
Computation
Computational modeling
heat diffusion
Heat method
Heat recovery
Linear systems
Memory management
Optimization
parallel algorithm
Parallel processing
poisson equation
Random access memory
scalability
Solvers
ISSN:0162-8828, 1939-3539, 2160-9292, 1939-3539
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Shrnutí:In this paper, we propose a parallel and scalable approach for geodesic distance computation on triangle meshes. Our key observation is that the recovery of geodesic distance with the heat method <xref ref-type="bibr" rid="ref1">[1] can be reformulated as optimization of its gradients subject to integrability, which can be solved using an efficient first-order method that requires no linear system solving and converges quickly. Afterward, the geodesic distance is efficiently recovered by parallel integration of the optimized gradients in breadth-first order. Moreover, we employ a similar breadth-first strategy to derive a parallel Gauss-Seidel solver for the diffusion step in the heat method. To further lower the memory consumption from gradient optimization on faces, we also propose a formulation that optimizes the projected gradients on edges, which reduces the memory footprint by about 50 percent. Our approach is trivially parallelizable, with a low memory footprint that grows linearly with respect to the model size. This makes it particularly suitable for handling large models. Experimental results show that it can efficiently compute geodesic distance on meshes with more than 200 million vertices on a desktop PC with 128 GB RAM, outperforming the original heat method and other state-of-the-art geodesic distance solvers.
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ISSN:0162-8828
1939-3539
2160-9292
1939-3539
DOI:10.1109/TPAMI.2019.2933209