Monte Carlo geometry processing
Monte Carlo geometry processing
复制标题
蒙特卡洛几何处理
DOI：
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发表时间：
2020
影响因子：
6.2
通讯作者：
Keenan Crane
中科院分区：
文献类型：
--
作者：
Rohan Sawhney;Keenan Crane
本文探讨了如何利用无网格蒙特卡罗方法高效可靠地解决基于偏微分方程的几何处理中的核心问题。现代几何算法常常需要在几何复杂的域上求解类泊松方程。传统的方法通常是对域进行网格划分，这对于具有精细细节或缺陷（孔洞、自交等）的几何图形来说既具有挑战性又昂贵。相比之下，无网格蒙特卡罗方法完全避免了网格生成，而只是计算最近点查询。因此，它们不会离散空间、时间，甚至功能空间，并且即使在极具挑战性的模型上也能提供精确的解决方案（在预期中）。更广泛地说，它们与蒙特卡罗方法共享许多来自逼真渲染的好处：出色的缩放、琐碎的并行实现、依赖于视图的评估以及处理任何类型几何（包括隐式或过程描述）的能力。我们开发了一个完整的“黑盒”求解器，包括集成、方差减少和可视化，并探索如何将其用于各种几何处理任务。特别地，我们考虑了几种基本的常系数线性椭圆偏微分方程。总的来说，我们发现蒙特卡罗方法显着拓宽了几何处理的视野，因为它们很容易处理传统方法基本上无法解决的大小和复杂性问题。
This paper explores how core problems in PDE-based geometry processing can be efficiently and reliably solved via grid-free Monte Carlo methods. Modern geometric algorithms often need to solve Poisson-like equations on geometrically intricate domains. Conventional methods most often mesh the domain, which is both challenging and expensive for geometry with fine details or imperfections (holes, self-intersections, etc.). In contrast, grid-free Monte Carlo methods avoid mesh generation entirely, and instead just evaluate closest point queries. They hence do not discretize space, time, nor even function spaces, and provide the exact solution (in expectation) even on extremely challenging models. More broadly, they share many benefits with Monte Carlo methods from photorealistic rendering: excellent scaling, trivial parallel implementation, view-dependent evaluation, and the ability to work with any kind of geometry (including implicit or procedural descriptions). We develop a complete "black box" solver that encompasses integration, variance reduction, and visualization, and explore how it can be used for various geometry processing tasks. In particular, we consider several fundamental linear elliptic PDEs with constant coefficients on solid regions of Rn. Overall we find that Monte Carlo methods significantly broaden the horizons of geometry processing, since they easily handle problems of size and complexity that are essentially hopeless for conventional methods.
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DOI：
10.1145/3186564
发表时间：
2017-07
期刊：
ACM Transactions on Graphics (TOG)
影响因子：
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作者：
Oded Stein;E. Grinspun;M. Wardetzky;Alec Jacobson
通讯作者：
Oded Stein;E. Grinspun;M. Wardetzky;Alec Jacobson
基于边缘和面的矢量场的 3D hodge 分解
影响因子：
6.2
作者：
Zhao, Rundong;Desbrun, Mathieu;Wei, Guo-Wei;Tong, Yiying
通讯作者：
Tong, Yiying
影响因子：
6.2
作者：
Hu, Yixin;Zhou, Qingnan;Panozzo, Daniele
通讯作者：
Panozzo, Daniele
基于多尺度热核的体积形态特征。
DOI：
10.1007/978-3-319-24574-4_90
发表时间：
2015
期刊：
Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention
影响因子：
--
作者：
Wang,Gang;Wang,Yalin
通讯作者：
Wang,Yalin