Statistical shape analysis using persistent homology

使用持久同源性的统计形状分析

• 批准号: DE200100056
• 负责人: A/Prof Katharine Turner
• 金额: $ 28.3万
• 依托单位: The Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2020
• 资助国家: 澳大利亚
• 起止时间: 2020-09-01 至 2024-10-13
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE200100056
• 关键词: Statistical; shape; analysis; using; persistent

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.

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了代数拓扑中的概念。该项目旨在证明与持久同源变换有关的数学理论，发展新的统计理论和方法，并将这一理论应用于一系列应用，包括分析鸟类喙、人类头骨和干细胞的边界轮廓。一个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。预期结果包括一个用于形状分析的拓扑激励平台，该平台在统计上是严格的，并具有坚实的数学基础。