Abstract

Statistical analysis of medical data is a fast-growing field with broad applications. Rapid advances in imaging techniques have led to rich data for analyzing shapes across many subdisciplines. Examples include shapes of cancer cells, human biometrics, 3D genome, brain anatomical structures, and so on. Imposing statistical models and inferences on shapes seems daunting because the shape is an abstract notion and one requires mathematical representations to quantify shapes. In this talk, I will present some recent developments in elastic shape representations of complex structures such as curves, surfaces, trees, networks, and graphs. I will focus on statistical analyses: computing shape summaries, estimation under shape constraints, hypothesis testing, time-series models, and regression models involving shapes.