Geometric Modeling for Spatial Analysis of Bio-Medical Data

生物医学成像的进步，如显微镜、核磁共振、CT和PET扫描，正在产生越来越多的可用3D数据。虽然迄今为止，计算机建模主要集中在从这些数据中查看或恢复解剖结构的3D形状，但越来越多的应用领域涉及对数据本身的进一步分析。其中一个领域是对从不同个体或同一主体在不同时间收集的3D数据进行比较分析。这些比较通常是临床决策和科学假设的基础。支持对这类数据的多主题分析需要建立一个从一个人的卷到另一个人的卷的映射。这是一个具有挑战性的问题，不仅因为解剖结构的形状可能因人而异，而且还因为三维捕获过程中固有的噪声和分辨率问题。本研究的目标是开发一种新的建模范式，适用于不同受试者的三维数据的比较分析。该范式包括从单个主体的分割数据构建拓扑正确的表面，在其边界表面上建立所有个体之间的一致映射，以及从表面映射（2D）到封闭体之间的平滑映射（3D）的简单直接扩展。这些方法可以应用于流形和非流形表面表示，生成的体映射支持组织大型3D图像存储库，以实现高效的基于体的查询。随着边界的影响，这项研究将直接使医学研究人员受益，为他们提供必要的计算工具，以进行多学科，2D和3D数据比较。

Advances in bio-medical imaging, such as microscopy, MRI, CT, and PET scanning, are producing a growing body of available 3D data. While computer modeling to date has largely focused on viewing or recovering the 3D shapes of anatomical structures from this data, more and more application areas involve further analysis of the data itself. One such area is the comparative analysis of 3D data collected from different individuals or from the same subject at different times. These comparisons are often the basis for making clinical decisions as well as scientific hypothesis. Supporting multi-subject analysis on this type of data requires establishing a mapping from one individual's volume to another's. This is a challenging problem not only because the shape of anatomical structures may vary greatly from one individual to another, but also because of noise and resolution issues inherent in the 3D capture process.The goal of this research is to develop a new modeling paradigm suitable for comparative analysis of 3D data of different subjects. This paradigm consists of constructing a topologically correct surface from segmented data of individual subjects, establishing a consistent mapping among all individuals on their boundary surfaces, and a simple, direct extension from surface mapping (2D) to smooth mappings between enclosed volumes (3D). The methods can be applied to both manifold and non-manifold surface representations, and the resulting volume mapping supports organization of a large repository of 3D images for efficient volume-based queries. As the boarder impact, the research will directly benefits medical researchers by providing them with the necessary computational tools to perform multi-subject, 2D and 3D data comparisons.