Stability and Inference of the Euler Characteristic Transform

Understand

The Euler characteristic transform (ECT) is a signature from topological data analysis (TDA) which summarises shapes embedded in Euclidean space.

• Compared with other TDA methods, the ECT is fast to compute and it is a sufficient statistic for a broad class of shapes.
• However, small perturbations of a shape can lead to large distortions in its ECT.
• In this paper, we propose a new metric on compact one-dimensional shapes and prove that the ECT is stable with respect to this metric.