Topological analysis of scalar fields with outliers

Understand

Given a real-valued function $f$ defined over a manifold $M$ embedded in $\mathbb{R}^d$, we are interested in recovering structural information about $f$ from the sole information of its values on a finite sample $P$.

• Existing methods provide approximation to the persistence diagram of $f$ when geometric noise and functional noise are bounded.
• However, they fail in the presence of aberrant values, also called outliers, both in theory and practice.
• We propose a new algorithm that deals with outliers.