# Chromatic Alpha Complexes

arXiv: https://arxiv.org/abs/2212.03128 · HTML: https://mlsanity.com/paper/2212.03128/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2022.

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

- [Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds](https://mlsanity.com/paper/2402.15058/) (2024)
- [Magnitude-Based Features for Multispecies Spatial Data](https://mlsanity.com/paper/2606.11775/) (2026)

## Abstract (arXiv)

Motivated by applications in the medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay and alpha complexes, and code that does these computations is provided.