Generating Topologically and Geometrically Diverse Manifold Data in Dimensions Four and Below
It addresses the need for topologically rich synthetic data to train models in fields like medical imaging or physics, but it is incremental as it builds on existing methods and focuses on a roadmap rather than full implementation.
This paper tackles the problem of generating synthetic image-type data with diverse topological features in dimensions up to 4D, using algebraic topology and image processing to create data with topological labels for training neural networks.
Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological features in these data. These models also appear to tolerate the use of image preprocessing techniques where existing topological data analysis techniques such as persistent homology do not. This paper investigates how methods from algebraic topology, combined with image processing techniques such as morphology, can be used to generate topologically sophisticated and diverse-looking 2-, 3-, and 4D image-type data with topological labels in simulation. These approaches are illustrated in 2D and 3D with the aim of providing a roadmap towards achieving this in 4D.