# Euler Characteristic Surfaces

arXiv: https://arxiv.org/abs/2102.08260 · HTML: https://mlsanity.com/paper/2102.08260/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2021.

## Built on by (most cited first, 8 of 8)

- [Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures](https://mlsanity.com/paper/2306.03801/) (2023)
- [Euler Characteristic Tools For Topological Data Analysis](https://mlsanity.com/paper/2303.14040/) (2023)
- [Euler Characteristic Curves and Profiles: a stable shape invariant for big data problems](https://mlsanity.com/paper/2212.01666/) (2022)
- [SCOPE: Structural Continuity Preservation for Medical Image Segmentation](https://mlsanity.com/paper/2304.14572/) (2023)
- [Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Data](https://mlsanity.com/paper/2502.16049/) (2025)
- [Interpretable Classification of Time Series Using Euler Characteristic Surfaces](https://mlsanity.com/paper/2603.15079/) (2026)
- [Machine learning and Topological data analysis identify unique features of human papillae in 3D scans](https://mlsanity.com/paper/2307.06255/) (2023)
- [Topological Characterization of Churn Flow and Unsupervised Correction to the Wu Flow-Regime Map in Small-Diameter Vertical Pipes](https://mlsanity.com/paper/2604.06167/) (2026)

## Abstract (arXiv)

We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of random fields. The goal of this paper is to present the extension of using the Euler characteristic in higher-dimensional parameter spaces. While topological data analysis of higher-dimensional parameter spaces using stronger invariants such as homology continues to be the subject of intense research, Euler characteristic is more manageable theoretically and computationally, and this analysis can be seen as an important intermediary step in multi-parameter topological data analysis. We show the usefulness of the techniques using artificially generated examples, and a real-world application of detecting diabetic retinopathy in retinal images.