Uncovering Topological Structures in Unstructured Data

Abstract : This research project aims to examine topological structures of scanned point-cloud data. It has two stages. In the first stage, we analyzed scan data and extracted topologically critical points. We used these critical points to enhance the robustness of slicing scan data in additive manufacturing. In the second stage, we focused on how to analyze scan data of a population of objects. In this context, we discovered novel ways of computing covariance matrix of shape population and developed methods for optimizing correspondence across a shape population.