  This research uses deep learning to estimate the topology of manifolds
represented by sparse, unordered point cloud scenes in 3D. A new labelled
dataset was synthesised to train neural networks and evaluate their ability to
estimate the genus of these manifolds. This data used random homeomorphic
deformations to provoke the learning of visual topological features. We
demonstrate that deep learning models could extract these features and discuss
some advantages over existing topological data analysis tools that are based on
persistent homology. Semantic segmentation was used to provide additional
geometric information in conjunction with topological labels. Common point
cloud multi-layer perceptron and transformer networks were both used to compare
the viability of these methods. The experimental results of this pilot study
support the hypothesis that, with the aid of sophisticated synthetic data
generation, neural networks can perform segmentation-based topological data
analysis. While our study focused on simulated data, the accuracy achieved
suggests a potential for future applications using real data.
