Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfaces

Wang, Xiaoning; Fang, Zheng; Xin, Shiqing; He, Ying

doi:10.1016/j.cagd.2017.03.010

Cited by 26 publications

(27 citation statements)

References 40 publications

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“…After adding the constraints (23) or (24), the new optimization problem is still convex and can be solved using ADMM similar to the original methods. Fig.…”

Section: No Topology Constraintmentioning

confidence: 99%

Parallel and Scalable Heat Methods for Geodesic Distance Computation

Tao

Zhang

Deng

et al. 2021

IEEE Trans. Pattern Anal. Mach. Intell.

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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 [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%. 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 128GB RAM, outperforming the original heat method and other state-of-the-art geodesic distance solvers.

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“…After adding the constraints (23) or (24), the new optimization problem is still convex and can be solved using ADMM similar to the original methods. Fig.…”

Section: No Topology Constraintmentioning

confidence: 99%

Parallel and Scalable Heat Methods for Geodesic Distance Computation

Tao

Zhang

Deng

et al. 2021

IEEE Trans. Pattern Anal. Mach. Intell.

Self Cite

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“…There are several algorithms computing this piecewise linear path. While earlier approaches where rather slow [MMP87, CH90], more sophisticated implementations could improve performance significantly [SSK*05, XW09, WFW*17]. Some of these algorithms can sacrifice accuracy for performance.…”

Section: Related Workmentioning

confidence: 99%

Efficient Computation of Smoothed Exponential Maps

Herholz

Alexa

2019

Computer Graphics Forum

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Many applications in geometry processing require the computation of local parameterizations on a surface mesh at interactive rates. A popular approach is to compute local exponential maps, i.e. parameterizations that preserve distance and angle to the origin of the map. We extend the computation of geodesic distance by heat diffusion to also determine angular information for the geodesic curves. This approach has two important benefits compared to fast approximate as well as exact forward tracing of the distance function: First, it allows generating smoother maps, avoiding discontinuities. Second, exploiting the factorization of the global Laplace–Beltrami operator of the mesh and using recent localized solution techniques, the computation is more efficient even compared to fast approximate solutions based on Dijkstra's algorithm.

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“…There exists approaches that do not solve the Eikonal equation, such as the Saddle Vertex Graph (SVG) [21], which encodes the geodesic information in a sparse undirected graph, and the method proposed by Wang [22] which outperformed the SVG by using a divide and conquer technique.…”

Section: Related Workmentioning

confidence: 99%

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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Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfaces

Cited by 26 publications

References 40 publications

Parallel and Scalable Heat Methods for Geodesic Distance Computation

Parallel and Scalable Heat Methods for Geodesic Distance Computation

Efficient Computation of Smoothed Exponential Maps

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

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