Topology Estimation of Simulated 4D Image Data by Combining Downscaling
  and Convolutional Neural Networks
Khalil Mathieu Hannouch Stephan Chalup
Four-dimensional image-type data can quickly become prohibitively large, and
it may not be feasible to directly apply methods, such as persistent homology
or convolutional neural networks, to determine the topological characteristics
of these data because they can encounter complexity issues. This study aims to
determine the Betti numbers of large four-dimensional image-type data. The
experiments use synthetic data, and demonstrate that it is possible to
circumvent these issues by applying downscaling methods to the data prior to
training a convolutional neural network, even when persistent homology software
indicates that downscaling can significantly alter the homology of the training
data. When provided with downscaled test data, the neural network can estimate
the Betti numbers of the original samples with reasonable accuracy.