# PI-Net: A Deep Learning Approach to Extract Topological Persistence Images

arXiv: https://arxiv.org/abs/1906.01769 · HTML: https://mlsanity.com/paper/1906.01769/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2019.

## Built on by (most cited first, 12 of 12)

- [Artificial Text Detection via Examining the Topology of Attention Maps](https://mlsanity.com/paper/2109.04825/) (2021)
- [RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds](https://mlsanity.com/paper/2202.01725/) (2022)
- [Neural Approximation of Graph Topological Features](https://mlsanity.com/paper/2201.12032/) (2022)
- [Topological Attention for Time Series Forecasting](https://mlsanity.com/paper/2107.09031/) (2021)
- [Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds](https://mlsanity.com/paper/2307.09259/) (2023)
- [Synthetic Data Generation and Deep Learning for the Topological Analysis of 3D Data](https://mlsanity.com/paper/2309.16968/) (2023)
- [Dory: Overcoming Barriers to Computing Persistent Homology](https://mlsanity.com/paper/2103.05608/) (2021)
- [Leveraging Persistence Image to Enhance Robustness and Performance in Curvilinear Structure Segmentation](https://mlsanity.com/paper/2601.18045/) (2026)
- [Topological Persistence Guided Knowledge Distillation for Wearable Sensor Data](https://mlsanity.com/paper/2407.05315/) (2024)
- [Leveraging Topological Guidance for Improved Knowledge Distillation](https://mlsanity.com/paper/2407.05316/) (2024)
- [Challenges in 3D Data Synthesis for Training Neural Networks on Topological Features](https://mlsanity.com/paper/2511.04972/) (2025)
- [Steering Optimisation Trajectories in Diffusion Representation Learning](https://mlsanity.com/paper/2607.05319/) (2026)

## Abstract (arXiv)

Topological features such as persistence diagrams and their functional approximations like persistence images (PIs) have been showing substantial promise for machine learning and computer vision applications. This is greatly attributed to the robustness topological representations provide against different types of physical nuisance variables seen in real-world data, such as view-point, illumination, and more. However, key bottlenecks to their large scale adoption are computational expenditure and difficulty incorporating them in a differentiable architecture. We take an important step in this paper to mitigate these bottlenecks by proposing a novel one-step approach to generate PIs directly from the input data. We design two separate convolutional neural network architectures, one designed to take in multi-variate time series signals as input and another that accepts multi-channel images as input. We call these networks Signal PI-Net and Image PI-Net respectively. To the best of our knowledge, we are the first to propose the use of deep learning for computing topological features directly from data. We explore the use of the proposed PI-Net architectures on two applications: human activity recognition using tri-axial accelerometer sensor data and image classification. We demonstrate the ease of fusion of PIs in supervised deep learning architectures and speed up of several orders of magnitude for extracting PIs from data. Our code is available at https://github.com/anirudhsom/PI-Net.