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

arXiv: https://arxiv.org/abs/2306.14442 · HTML: https://mlsanity.com/paper/2306.14442/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 76 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Generative and Discriminative Voxel Modeling with Convolutional Neural Networks](https://mlsanity.com/paper/1608.04236/) (2016)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Topological Approaches to Deep Learning](https://mlsanity.com/paper/1811.01122/) (2018)
- [Dominant Set Clustering and Pooling for Multi-View 3D Object Recognition](https://mlsanity.com/paper/1906.01592/) (2019)
- [Subsampling Methods for Persistent Homology](https://mlsanity.com/paper/1406.1901/) (2014)
- [From Geometry to Topology: Inverse Theorems for Distributed Persistence](https://mlsanity.com/paper/2101.12288/) (2021)
- [Approximating Persistent Homology for Large Datasets](https://mlsanity.com/paper/2204.09155/) (2022)
- [MicroLib: A library of 3D microstructures generated from 2D micrographs using SliceGAN](https://mlsanity.com/paper/2210.06541/) (2022)
- [Repulsive Surfaces](https://mlsanity.com/paper/2107.01664/) (2021)
- [Frontiers of sphere recognition in practice](https://mlsanity.com/paper/1405.3848/) (2014)

## Built on by (most cited first, 2 of 2)

- [Defining Neural Network Architecture through Polytope Structures of Dataset](https://mlsanity.com/paper/2402.02407/) (2024)
- [Generating Topologically and Geometrically Diverse Manifold Data in Dimensions Four and Below](https://mlsanity.com/paper/2410.07115/) (2024)

## Abstract (arXiv)

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.