Stability of topological descriptors for neuronal morphology

TL;DR

This paper demonstrates that topological morphology descriptors of neurons, represented as persistence diagrams and images, are stable under small morphological perturbations, ensuring reliable classification and analysis.

Contribution

The study proves the stability of topological morphology descriptors and their persistence images against perturbations, enhancing their reliability for neuronal shape analysis.

Findings

Persistence diagrams are stable under 1-Wasserstein distance for neuron trees.

Persistence images derived from these diagrams are also stable and reliable.

Results support the use of topological descriptors in neuronal morphology classification.

Abstract

The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descriptors are vectorized using persistence images, which can help classify and characterize the morphology of broad groups of neurons. We study the stability of topological morphology descriptors under small changes to neuronal morphology. We show that the persistence diagram arising from the topological morphology descriptor of a neuron is stable for the 1-Wasserstein distance against a range of perturbations to the tree. These results guarantee that persistence images of topological morphology descriptors are stable against the same set of perturbations and reliable.