Surface Construction and Comparison using Manifolds

使用流形的表面构造和比较

• 批准号: 0429856
• 负责人: Cindy Grimm
• 金额: --
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-11-01 至 2008-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0429856&HistoricalAwards=false
• 关键词: Surface; Construction; Comparison; using; Manifolds

This research focuses on the comparison of surfaces which are similar, but not identical. For example, almost all leg bones are similar in shape (a cylinder with knobs on the ends) but may differ greatly in length, diameter, size and shape of the knobs, etc. The goal of this research is to provide robust methods for comparing, categorizing, and analyzing surfaces of this type. Researchers in the bio-medical, physical anthropology, and forensics fields, to name a few, currently rely on human experts to perform these measurements. The types of measurements they can make are also limited to simple ones, such as length and circumference. These measurements are used to answer questions such as: What race/sex is this bone from? How tall was the person? Is the surface is abnormal? Was there an injury at some time? Why does the joint not function normally? Analytical measurements will not only remove the (sometimes subjective) human component, but will also broaden the scope of surface comparison beyond simple length measurements. The first part of this research is a constructive approach for creating manifolds of arbitrary topology. These manifolds provide a natural mechanism for analyzing specific subsets of the surface via the creation of local maps that cover any desired portion of the surface. Manifolds also provide a parameterization mechanism for identifying corresponding points on surfaces. The research addresses theoretical issues related to manifolds such as improved local map placement, more controllable blend strategies, manifolds with boundary, and using manifolds to parameterize existing meshes or point clouds. The second part of his research, detailed surface comparison, is a relatively novel task, and includes a well-posed statement of the problem in addition to the development of algorithmic solutions. For example: What is a feature? How do we quantitatively measure feature differences in a meaningful way? How do we measure the quality of the correspondence between two surfaces?

这项研究的重点是比较相似但不相同的表面。例如，几乎所有腿骨的形状相似（两端有旋钮的圆柱体），但在长度、直径、旋钮的大小和形状等方面可能有很大差异。这项研究的目的是提供稳健的方法来比较、分类和分析这种类型的表面。仅举几例，生物医学、体质人类学和法医学领域的研究人员目前依靠人类专家来执行这些测量。他们可以进行的测量类型也仅限于简单的测量，例如长度和周长。这些测量结果用于回答以下问题：这块骨头来自哪个种族/性别？那人有多高？表面是否异常？有没有受过伤？为什么关节不能正常运作？分析测量不仅会消除（有时是主观的）人为因素，而且还将扩大表面比较的范围，超越简单的长度测量。这项研究的第一部分是创建任意拓扑流形的建设性方法。这些流形提供了一种自然机制，用于通过创建覆盖表面任何所需部分的局部地图来分析表面的特定子集。流形还提供了用于识别表面上对应点的参数化机制。该研究解决了与流形相关的理论问题，例如改进的局部地图放置、更可控的混合策略、具有边界的流形以及使用流形参数化现有网格或点云。他的研究的第二部分，详细的表面比较，是一项相对新颖的任务，除了算法解决方案的开发之外，还包括对问题的适当陈述。例如：什么是功能？我们如何以有意义的方式定量测量特征差异？我们如何测量两个表面之间对应的质量？