Seminar series
Date
Fri, 14 Feb 2025
15:00
15:00
Location
L4
Speaker
Nina Otter
Organisation
Inria Saclay
Note: we would recommend to join the meeting using the Teams client for best user experience.
The persistent homology transform (PHT) was introduced in the field of Topological Data Analysis about 10 years ago, and has since been proven to be a very powerful descriptor of Euclidean shapes. The PHT consists of scanning a shape from all possible directions and then computing the persistent homology of sublevel set filtrations of the respective height functions; this results in a sufficient and continuous descriptor of Euclidean shapes.
In this talk I will introduce a generalisation of the PHT in which we consider arbitrary parameter spaces and sublevel-set filtrations with respect to any function. In particular, we study transforms, defined on the Grassmannian AG(m,n) of affine subspaces of n-dimensional Euclidean space, which allow to scan a shape by probing it with all possible affine m-dimensional subspaces P, for fixed dimension m, and by then computing persistent homology of sublevel-set filtrations of the function encoding the distance from the flat P. We call such transforms "distance-from-flat PHTs". I will discuss how these transforms generalise known examples, how they are sufficient descriptors of shapes and finally present their computational advantages over the classical persistent homology transform introduced by Turner-Mukherjee-Boyer.