# A Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science

arXiv: https://arxiv.org/abs/2207.10552 · HTML: https://mlsanity.com/paper/2207.10552/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 59 references that are in the map.
- First posted on arXiv 21 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [Green AI](https://mlsanity.com/paper/1907.10597/) (2019)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Deep learning in remote sensing: a review](https://mlsanity.com/paper/1710.03959/) (2017)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [A Survey on Green Deep Learning](https://mlsanity.com/paper/2111.05193/) (2021)
- [The Need for Ethical, Responsible, and Trustworthy Artificial Intelligence for Environmental Sciences](https://mlsanity.com/paper/2112.08453/) (2021)
- [Combining crowd-sourcing and deep learning to explore the meso-scale organization of shallow convection](https://mlsanity.com/paper/1906.01906/) (2019)
- [Using Persistent Homology to Quantify a Diurnal Cycle in Hurricane Felix](https://mlsanity.com/paper/1902.06202/) (2019)

## Built on by (most cited first, 7 of 7)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Improving Remote Sensing Classification using Topological Data Analysis and Convolutional Neural Networks](https://mlsanity.com/paper/2507.10381/) (2025)
- [Tools for Extracting Spatio-Temporal Patterns in Meteorological Image Sequences: From Feature Engineering to Attention-Based Neural Networks](https://mlsanity.com/paper/2210.12310/) (2022)
- [Learning on Persistence Diagrams as Radon Measures](https://mlsanity.com/paper/2212.08295/) (2022)
- [Notes on Applicability of Explainable AI Methods to Machine Learning Models Using Features Extracted by Persistent Homology](https://mlsanity.com/paper/2310.09780/) (2023)
- [Topology-enhanced machine learning for speech signal processing](https://mlsanity.com/paper/2311.15210/) (2023)
- [LightGBM robust optimization algorithm based on topological data analysis](https://mlsanity.com/paper/2406.13300/) (2024)

## Abstract (arXiv)

Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is particularly useful for the analysis of imagery, namely persistent homology. We briefly discuss the theoretical background but focus primarily on understanding the output of this tool and discussing what information it can glean. To this end, we frame our discussion around a guiding example of classifying satellite images from the Sugar, Fish, Flower, and Gravel Dataset produced for the study of mesocale organization of clouds by Rasp et. al. in 2020 (arXiv:1906:01906). We demonstrate how persistent homology and its vectorization, persistence landscapes, can be used in a workflow with a simple machine learning algorithm to obtain good results, and explore in detail how we can explain this behavior in terms of image-level features. One of the core strengths of persistent homology is how interpretable it can be, so throughout this paper we discuss not just the patterns we find, but why those results are to be expected given what we know about the theory of persistent homology. Our goal is that a reader of this paper will leave with a better understanding of TDA and persistent homology, be able to identify problems and datasets of their own for which persistent homology could be helpful, and gain an understanding of results they obtain from applying the included GitHub example code.