# Efficient Computation of Image Persistence

arXiv: https://arxiv.org/abs/2201.04170 · HTML: https://mlsanity.com/paper/2201.04170/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2022.

## Built on by (most cited first, 3 of 3)

- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Fast Topological Signal Identification and Persistent Cohomological Cycle Matching](https://mlsanity.com/paper/2209.15446/) (2022)
- [Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds](https://mlsanity.com/paper/2402.15058/) (2024)

## Abstract (arXiv)

We present an algorithm for computing the barcode of the image of a morphisms in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. These algorithms make use of the clearing optimization and can be applied to inclusion-induced maps in persistent absolute homology and persistent relative cohomology for filtrations of pairs of simplicial complexes. They form the basis for our implementation for Vietoris-Rips complexes in the framework of the software Ripser.