Statistical Analysis of Shapes and Images via Euler Characteristics

Music City Center 

In the 21st century, we have seen a growing availability of shape-valued and imaging data, prompting the development of new statistical methods to analyze them. Importantly, bridging the new methods and existing frameworks is advisable. In this talk, I will introduce several statistical inference methods for shapes and images based on Euler characteristics. These methods have applications in many fields, such as geometric morphometrics and radiomics. From a statistical perspective, these methods are naturally connected to functional data analysis and tensor regression. From a mathematical viewpoint, they are grounded in solid foundations, bridging various branches of mathematics: algebraic and tame topology, Euler calculus, functional analysis, and probability theory.

Topological data analysis

functional data analysis

geometric morphometrics