This work focuses on mathematical shape representation methods for analyzing brain deep structural data from large human populations. Contemporary brain imaging technologies have provided a possibility to obtain morphological measures of brain structures at high resolution. Moreover, the complexity and variability of brain structures demands efficient and accurate powerful techniques derived from image analysis, computer vision, computer graphics and mathematics to analyze brain imaging data.

The essential task is to develop a mathematical and computational shape analysis system for analyzing brain structures from large human populations. The major goal of this dissertation is to develop a robust and accurate shape representation model to measure brain structural changes across large populations, time, age and gender or in different disease states.

A robust shape representation model is developed to measure and map deep brain structure (e.g. hippocampus) across large human populations, to detect morphological changes due to disease, and to illustrate dynamic processes in spatial and temporal spaces. The mathematical model for representing deep brain structure is developed to understand the relationships between deep brain structures and functions in research and clinical applications.