# Topology-Preserving Downsampling of Binary Images

arXiv: https://arxiv.org/abs/2407.17786 · HTML: https://mlsanity.com/paper/2407.17786/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 25 Jul 2024.

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

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Beyond the Pixel-Wise Loss for Topology-Aware Delineation](https://mlsanity.com/paper/1712.02190/) (2017)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Structure-Aware Image Segmentation with Homotopy Warping](https://mlsanity.com/paper/2112.07812/) (2021)
- [The Distance Transform and its Computation](https://mlsanity.com/paper/2106.03503/) (2021)
- [Computational Network Design from Functional Specifications](https://mlsanity.com/paper/1510.09203/) (2015)

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

- [Skelite: Compact Neural Networks for Efficient Iterative Skeletonization](https://mlsanity.com/paper/2503.07369/) (2025)
- [Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentation](https://mlsanity.com/paper/2607.07123/) (2026)

## Abstract (arXiv)

We present a novel discrete optimization-based approach to generate downsampled versions of binary images that are guaranteed to have the same topology as the original, measured by the zeroth and first Betti numbers of the black regions, while having good similarity to the original image as measured by IoU and Dice scores. To our best knowledge, all existing binary image downsampling methods do not have such topology-preserving guarantees. We also implemented a baseline morphological operation (dilation)-based approach that always generates topologically correct results. However, we found the similarity scores to be much worse. We demonstrate several applications of our approach. First, generating smaller versions of medical image segmentation masks for easier human inspection. Second, improving the efficiency of binary image operations, including persistent homology computation and shortest path computation, by substituting the original images with smaller ones. In particular, the latter is a novel application that is made feasible only by the full topology-preservation guarantee of our method.