Topology Estimation of Simulated 4D Image Data by Combining Downscaling and Convolutional Neural Networks

TL;DR

This paper presents a method combining downscaling and CNNs to estimate the topology of large 4D image data, overcoming computational challenges and outperforming persistent homology in accuracy.

Contribution

It introduces a novel approach that uses downscaling and CNNs to accurately estimate 4D data topology, even when traditional methods are computationally infeasible.

Findings

CNN achieves over 80% accuracy in Betti number estimation.

Downscaling enables topology estimation despite altered homology.

Vision-based cavity type training improves CNN performance.

Abstract

The topological analysis of four-dimensional (4D) image-type data is challenged by the immense size that these datasets can reach. This can render the direct application of methods, like persistent homology and convolutional neural networks (CNNs), impractical due to computational constraints. This study aims to estimate the topology type of 4D image-type data cubes that exhibit topological intricateness and size above our current processing capacity. The experiments using synthesised 4D data and a real-world 3D data set demonstrate that it is possible to circumvent computational complexity issues by applying downscaling methods to the data before training a CNN. This is achievable even when persistent homology software indicates that downscaling can significantly alter the homology of the training data. When provided with downscaled test data, the CNN can still estimate the Betti numbers of the original sample cubes with over 80\% accuracy, which outperforms the persistent homology approach, whose accuracy deteriorates under the same conditions. The accuracy of the CNNs can be further increased by moving from a mathematically-guided approach to a more vision-based approach where cavity types replace the Betti numbers as training targets.