CAREER: Signal Processing for Surfaces

职业：表面信号处理

• 批准号: 0093390
• 负责人: Denis Zorin
• 金额: $ 31.59万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-02-15 至 2007-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0093390&HistoricalAwards=false
• 关键词: CAREER; Signal; Processing; Surfaces

Complex geometry becomes increasingly common in applicationsarising in diverse areas. Plastic surgeons use computermodels to plan and perform operations. Mechanical engineersvirtually assemble and test cars and planes. Animatorscreate complex characters and effects indistinguishable fromreality. Geometric modeling has found its way into artconservation: it is now feasible to create computer modelsof sculptures capturing the most subtle of details.Increasing complexity of geometric data calls for newefficient representations and algorithms. The goal of ourlong-term research plan is to study representations ofcomplex geometric data, surfaces in particular. We plan tolaunch a broad and fundamental program to explore threetypes of representations: piecewise-smooth surfaces,multiscale surfaces and combined volume-surfacerepresentations. Our approach to designing complex surfacerepresentations is based on the concept of subdivision, apowerful technique for modeling smooth surfaces. Subdivisionalgorithms, while being more flexible and general, retain anumber of useful properties of splines. Most importantly,the surfaces generated by these algorithms have a naturalhierarchical structure and are computed using efficientlocal rules; subdivision algorithms can be easily extendedto represent multiscale data. The general goal of ourresearch is to design representations supporting efficientalgorithms for construction, rendering, manipulation,processing, transmission and storage of surface data. Wewill explore in close coordination both theoreticalproperties of these representations (regularity, convergencerates, fairness, stability) and their practicalapplications. The specific goal of the proposed project isto generalize to surfaces the signal processing tools thatwere designed and are extensively used for images. Theresearch program is integrated with the education plan,which has three main goals: (1) prepare graduate studentsfor research in computer graphics and related areas, (2)incorporate the latest advances in research into curriculumat all levels, including undergraduate, and engage motivatedundergraduate students in research (3) transfer knowledgeabout latest research advances to professionals in theindustry.

复杂的几何形状在不同领域的应用中变得越来越普遍。整形外科医生使用计算机模型来计划和执行手术。机械工程师实际上组装和测试汽车和飞机。动画师创造出复杂的角色和效果，与现实难以区分。几何建模已经进入艺术保护领域：现在可以创建捕捉最微妙细节的雕塑计算机模型。几何数据的日益复杂要求新的高效表示和算法。我们长期研究计划的目标是研究复杂几何数据的表示，特别是曲面。我们计划推出一个广泛的和基本的程序，探索三种类型的表示：分段光滑表面，多尺度表面和组合体表面表示。我们的方法来设计复杂的surfacerepresentation是基于细分的概念，一个强大的技术建模光滑的表面。细分算法，虽然更灵活和通用，保留了一些有用的性质样条。最重要的是，这些算法生成的表面具有自然的层次结构，并使用高效的局部规则计算;细分算法可以很容易地扩展到表示多尺度数据。我们的研究的总体目标是设计表示支持高效的算法，用于构建，渲染，操作，处理，传输和存储表面数据。我们将密切合作，探讨这些表示（规则性，收敛率，公平性，稳定性）的理论属性及其实际应用。该项目的具体目标是将设计并广泛用于图像的信号处理工具推广到表面。该研究计划与教育计划相结合，该计划有三个主要目标：（1）为研究生在计算机图形学和相关领域的研究做好准备，（2）将研究的最新进展纳入各级课程，包括本科生，并鼓励本科生参与研究（3）将有关最新研究进展的知识转移给业内专业人士。