A density-based approach to feature detection in persistence diagrams for firn data

Abstract

Topological data analysis, and in particular persistence diagrams, are gaining popularity as tools for extracting topological information from noisy point cloud and digital data. Persistence diagrams track topological features in the form of \begin{document}$ k $\end{document} -dimensional holes in the data. Here, we construct a new, automated approach for identifying persistence diagram points that represent robust long-life features. These features may be used to provide a more accurate estimate of Betti numbers for the underlying space. This approach extends the established practice of using a lifespan cutoff on the features in order to take advantage of the observation that noisy features typically appear in clusters in the persistence diagram. We show that this approach offers more flexibility in partitioning features in the persistence diagram, resulting in greater accuracy in computed Betti numbers, especially in the case of high noise levels and varying image illumination. This work is motivated by 3-dimensional Micro-CT imaging of ice core samples, and is applicable for separating noise from robust signals in persistence diagrams from noisy data.