CRII: CHS: A Plug-and-Play Deformable Model Based on Extended Domain Decomposition

CRII：CHS：基于扩展域分解的即插即用变形模型

• 批准号: 1464306
• 负责人: Yin Yang
• 金额: $ 17.48万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-03-01 至 2018-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1464306&HistoricalAwards=false
• 关键词: CRII; CHS; Plug; Play; Deformable

Advances in data acquisition tools have led to a dramatic increase in the geometric complexity of 3D data. Efficiently modeling, simulating, and analyzing these scanned large-scale real-world models become a serious challenge, because the numerical integration of high dimensional partial differential equations (over millions of degrees of freedom) is prohibitive for time-critical applications such as surgical simulation, bio-medical imaging, virtual/augmented reality, and physically-based animation. The problem becomes significantly more acute in situations where the rest-shape geometries of the 3D models are frequently altered and there is a need for collision detection/response coupled with high fidelity visualization of heterogeneous material properties and efficient transmission over the network to facilitate collaborative interaction. In this project the PI will address this challenge by developing a research program to create a modularized computational framework for efficient deformable simulation by partitioning the deformable body into small-size domains and re-connecting them back using weakened linkages. Domain-level computations are independent and reusable; thus, the expensive deformable simulation is reframed as a plug-and-play computational assemblage just like playing with LEGO blocks, and orders of magnitude speedup can be obtained. The plug-and-play deformable model that will be the primary project outcome will advance state-of-the-art techniques in physical simulation, animation and visualization, and will also profoundly benefit a broad range of interdisciplinary fields that directly impact people in their daily lives, from the modeling and registration of deformable human organs for surgical simulation, to the analysis of roadway pavement stress, to silent speech recognition.The PI's approach pivots on the transformative concept of divide-and-conquer deformable model. Unlike most state-of-the-art techniques that simulate a deformable object in its entirely by means of a "one-stop" solver, the PI will develop innovative algorithms that break a simulation into independent computational modules, with the final result being obtained by incrementally assembling the local computations. The PI will seek theoretical solutions to two general questions: "how to smartly divide" and "how to effectively conquer" in the context of deformable simulation. In particular, he will investigates a theoretically grounded domain decomposition and coupling mechanism so that domain-level computation is independent, reusable, modularized and also a good fit with existing parallel computing architectures such as multi-core CPUs or GPUs. The PI will develop a new theory for the real-time spectral deformation processing that divides the simulation not only spatially but also spectrally, based on a power iteration and inertia analysis. He will also explore possible solutions to the problem of optimal domain partitioning, in which the simulation is parameterized geometrically and the most effective partition is obtained by solving a geometry optimization problem similar to the Voronoi diagram. As the test-bed for the aforementioned theoretical and algorithmic advances, the PI will develop a haptic-enabled collaborative digital fabrication system, which will ultimately allow multiple users, from distant sites to smoothly interact to design and craft physically simulated virtual objects, which can then be 3D printed if desired.

数据采集工具的进步导致3D数据的几何复杂性急剧增加。高效地对这些扫描的大规模真实世界模型进行建模、仿真和分析成为一个严峻的挑战，因为高维偏微分方程组(超过数百万个自由度)的数值积分对于诸如手术仿真、生物医学成像、虚拟/增强现实和基于物理的动画等时间关键型应用是不可能的。在3D模型的静止形状几何形状被频繁改变并且需要碰撞检测/响应与异质材料属性的高保真可视化和网络上的高效传输相结合以促进协作交互的情况下，该问题变得明显地更加尖锐。在这个项目中，PI将通过开发一个研究计划来解决这一挑战，该计划通过将可变形物体划分为小尺寸的区域并使用减弱的链接重新连接它们来创建用于高效可变形模拟的模块化计算框架。域级计算是独立的和可重用的，因此，昂贵的可变形模拟被重组为即插即用的计算组件，就像玩乐高积木一样，可以获得数量级的加速比。即插即用的可变形模型将成为项目的主要成果，它将推动物理模拟、动画和可视化方面的最先进技术，并将深刻地受益于广泛的跨学科领域，这些领域直接影响人们的日常生活，从用于手术模拟的可变形人体器官的建模和注册，到路面应力分析，再到无声语音识别。PI的方法以分而治之的可变形模型的转变概念为基础。与大多数最先进的技术不同，PI完全通过“一站式”解算器在其内部模拟可变形对象，PI将开发创新的算法，将模拟分解为独立的计算模块，最终结果通过增量组合本地计算获得。PI将在可变形模拟的背景下寻求两个一般问题的理论解决方案：如何巧妙地划分和如何有效地征服。特别是，他将研究一种理论上扎根的域分解和耦合机制，以便域级计算是独立的、可重用的、模块化的，并与现有的并行计算架构(如多核CPU或GPU)很好地匹配。PI将为实时光谱变形处理开发一种新的理论，该理论基于功率迭代和惯性分析，不仅在空间上而且在光谱上划分模拟。他还将探索最优域划分问题的可能解决方案，其中模拟在几何上是参数化的，最有效的划分是通过解决类似于Voronoi图的几何优化问题来获得的。作为前述理论和算法进步的试验台，PI将开发一种支持触觉的协作数字制造系统，最终将允许来自遥远地点的多个用户顺利交互，设计和制作物理模拟的虚拟对象，然后可以根据需要进行3D打印。