Tracking Temporal Evolution of Topological Features in Image Data

TL;DR

This paper introduces a statistical framework using topological data analysis to detect and analyze the evolution of topological features in spatiotemporal image data, with applications to cell wound healing.

Contribution

It proposes a hypothesis testing approach to model and identify significant topological features over time in image sequences, incorporating temporal dynamics into topological analysis.

Findings

Method effectively captures topological feature evolution in wound healing images.

Outperforms existing approaches in simulation studies.

Successfully analyzes nonlinear, dynamic, spatiotemporal structures in cell repair images.

Abstract

Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). However, there is currently no widely accepted statistical framework for modeling spatiotemporal dependence in the evolution of topological features, such as holes, within a time series of images. We propose a hypothesis testing framework to identify statistically significant topological features of images in space and time, simultaneously. This addition of time may induce higher-dimensional topological features which can be used to establish temporal connections between the lower-dimensional features at each point in time. The temporal evolution of these lower-dimensional features is then represented on a zigzag persistence diagram, as a topological summary statistic focused on time dynamics. We demonstrate that the method effectively captures the emergence and progression of topological features in a study of a series of images of a wounded cell as it repairs. The proposed method outperforms a current approach in a simulation study that includes features of the wound healing process. Since, the wounded cell images exhibit nonlinear, dynamic, spatial, and temporal structures during single-cell repair, they provide a good application for this method.