Statistical shape analysis using persistent homology

统计形状分析是对几何形状变化的定量研究。一种创新的方法以持久同调变换的形式应用代数拓扑中的概念。本项目旨在证明与持续同源变换相关的数学理论，发展新的统计理论和方法，并将该理论应用于包括鸟喙、人类头骨和干细胞边界轮廓分析在内的一系列应用。预期的目标是在拓扑数据分析中产生新的和重要的理论结果。预期的结果包括一个拓扑驱动的平台，用于形状分析，统计严谨，具有坚实的数学基础。

Statistical shape analysis is the quantitative study of variation in geometric shape. An innovative approach applies concepts from algebraic topology in the form of the persistent homology transform. This project aims to prove mathematical theory relating to the persistent homology transform, to develop new statistical theory and methodology, and to apply this theory to a range of applications including the analysis of bird beaks, human skulls and boundary contours of stem cells. An anticipated goal is the generation of new and significant theoretical results in topological data analysis. Expected outcomes include a topologically motivated platform for shape analysis that is statistically rigorous and has firm mathematical foundations.