SGER: Scalable Shape Analysis in Non-Euclidean Spaces with Provable Guarantees

医学成像技术的进步使临床医生能够生成大量描述人体各个部位的形状数据。在这样做的过程中，目标是获得精确的统计概念，即“正常”形态是什么样子，以及不同类型的“异常”形态是什么样子，这样临床医生就可以根据这些分类对患者进行有针对性的治疗。开发用于形态学（即形状）统计分析的工具有可能从根本上改变医学成像过程，使我们能够大规模地了解人体器官的正常和异常变化，并提供人体的统计“地图”。在这项研究中，PI通过将非欧几里得形状空间的数学与近似和有效操纵这些空间的技术相结合，开发了用于形状统计分析的新工具。

ABSTRACTAdvances in medical imaging technology have allowed clinicians to generate vast amounts of shape data describing various parts of the human body. In doing so, the goal is to obtain precise statistical notions of what a "normal" morphology looks like, and what the different types of "abnormal" morphology look like, so that clinicians can target treatment to patients based on these classifications.Developing tools for the statistical analysis of morphology (i.e. shape) has the potential to transform medical imaging processes in a fundamental way, allowing us to understand at a large scale the normal and abnormal variations in human organs and provide a statistical "map" of the human body. In this research, the PI develops new tools for the statistical analysis of shape by combining the mathematics of non-Euclidean shape spaces with techniques for approximating and efficiently manipulating such spaces.