# Cubical Ripser: Software for computing persistent homology of image and volume data

arXiv: https://arxiv.org/abs/2005.12692 · HTML: https://mlsanity.com/paper/2005.12692/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2020.

## Built on by (most cited first, 23 of 23)

- [A persistent homology-based topological loss for CNN-based multi-class segmentation of CMR](https://mlsanity.com/paper/2107.12689/) (2021)
- [Topology-Aware Focal Loss for 3D Image Segmentation](https://mlsanity.com/paper/2304.12223/) (2023)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmark](https://mlsanity.com/paper/2206.13932/) (2022)
- [TopoDiffusionNet: A Topology-aware Diffusion Model](https://mlsanity.com/paper/2410.16646/) (2024)
- [Efficient Betti Matching Enables Topology-Aware 3D Segmentation via Persistent Homology](https://mlsanity.com/paper/2407.04683/) (2024)
- [Self Pre-training with Topology- and Spatiality-aware Masked Autoencoders for 3D Medical Image Segmentation](https://mlsanity.com/paper/2406.10519/) (2024)
- [On Characterizing the Evolution of Embedding Space of Neural Networks using Algebraic Topology](https://mlsanity.com/paper/2311.04592/) (2023)
- [Topology Optimization in Medical Image Segmentation with Fast Euler Characteristic](https://mlsanity.com/paper/2507.23763/) (2025)
- [ParticleGrid: Enabling Deep Learning using 3D Representation of Materials](https://mlsanity.com/paper/2211.08506/) (2022)
- [TopoImages: Incorporating Local Topology Encoding into Deep Learning Models for Medical Image Classification](https://mlsanity.com/paper/2508.01574/) (2025)
- [Integrating Multi-scale and Multi-filtration Topological Features for Medical Image Classification](https://mlsanity.com/paper/2512.07190/) (2025)
- [Train-Free Segmentation in MRI with Cubical Persistent Homology](https://mlsanity.com/paper/2401.01160/) (2024)
- [CuMPerLay: Learning Cubical Multiparameter Persistence Vectorizations](https://mlsanity.com/paper/2510.12795/) (2025)
- [Fast Cubical Persistent Homology on 2D and 3D Images via Union-Find, Pruning, and Lookup Tables](https://mlsanity.com/paper/2606.04801/) (2026)
- [Tumor-Centered Patching for Enhanced Medical Image Segmentation](https://mlsanity.com/paper/2308.12168/) (2023)
- [A Topological Data Analysis Framework for Quantifying Necrosis in Glioblastomas](https://mlsanity.com/paper/2503.17331/) (2025)
- [Anatomica: Localized Control over Geometric and Topological Properties for Anatomical Diffusion Models](https://mlsanity.com/paper/2511.20587/) (2025)
- [Non-negative Matrix Factorisation with Topological Regularisation](https://mlsanity.com/paper/2606.17531/) (2026)
- [Topology-Informed Neural Networks for Flood Detection in Optical and Synthetic Aperture Radar Imagery](https://mlsanity.com/paper/2606.26204/) (2026)
- [TopoFuse: Topology-Aware Tri-Planar Fusion for 3D Cryo-Electron Tomography Segmentation](https://mlsanity.com/paper/2609.29717/) (2026)
- [Sparse cubical complexes for efficient topology-preservation in image data](https://mlsanity.com/paper/2609.37177/) (2026)
- [GPU-Accelerated Computation of Persistent Homology for Topological Analysis of Image Data](https://mlsanity.com/paper/2610.10959/) (2026)

## Abstract (arXiv)

We introduce Cubical Ripser for computing persistent homology of image and volume data (more precisely, weighted cubical complexes). To our best knowledge, Cubical Ripser is currently the fastest and the most memory-efficient program for computing persistent homology of weighted cubical complexes. We demonstrate our software with an example of image analysis in which persistent homology and convolutional neural networks are successfully combined. Our open-source implementation is available online.