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

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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.