2023/09/29 by Dylan Peek, Peek, Dylan, Matt P. Skerritt +3 · 2 citations
Computer Science · Earth and Planetary Sciences · Mathematics · #Algorithm #Artificial intelligence #Artificial neural network #Computer Vision and Pattern Recognition (cs.CV) #Computer science #Data mining #Deep learning #FOS: Computer and information sciences #Geological Modeling and Analysis #Mathematics #Pattern recognition (psychology) #Perceptron #Persistent homology #Point cloud #Segmentation #Synthetic data #Topological and Geometric Data Analysis #Topological data analysis #Topology (electrical circuits)
paper · pdf · doi:10.48550/arxiv.2309.16968
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.