# Universal Topology Refinement for Medical Image Segmentation with Polynomial Feature Synthesis

arXiv: https://arxiv.org/abs/2409.09796 · HTML: https://mlsanity.com/paper/2409.09796/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 15 Sep 2024.

## Builds on (most cited first, 18 of 18)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [nnU-Net: Self-adapting Framework for U-Net-Based Medical Image Segmentation](https://mlsanity.com/paper/1809.10486/) (2018)
- [Segment Anything Model for Medical Image Analysis: an Experimental Study](https://mlsanity.com/paper/2304.10517/) (2023)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [Boundary loss for highly unbalanced segmentation](https://mlsanity.com/paper/1812.07032/) (2018)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Medical image denoising using convolutional denoising autoencoders](https://mlsanity.com/paper/1608.04667/) (2016)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [The TopCoW Challenge -- Topology-Aware Circle of Willis Segmentation for CT and MR Angiography](https://mlsanity.com/paper/2312.17670/) (2023)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Post-DAE: Anatomically Plausible Segmentation via Post-Processing with Denoising Autoencoders](https://mlsanity.com/paper/2006.13791/) (2020)
- [Explicit topological priors for deep-learning based image segmentation using persistent homology](https://mlsanity.com/paper/1901.10244/) (2019)
- [Structure-Aware Image Segmentation with Homotopy Warping](https://mlsanity.com/paper/2112.07812/) (2021)
- [A persistent homology-based topological loss for CNN-based multi-class segmentation of CMR](https://mlsanity.com/paper/2107.12689/) (2021)
- [Learning Probabilistic Topological Representations Using Discrete Morse Theory](https://mlsanity.com/paper/2206.01742/) (2022)
- [Topologically Faithful Multi-class Segmentation in Medical Images](https://mlsanity.com/paper/2403.11001/) (2024)
- [Segmentation of the cortical plate in fetal brain MRI with a topological loss](https://mlsanity.com/paper/2010.12391/) (2020)

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

- [Topo-R1: Detecting Topological Anomalies via Vision-Language Models](https://mlsanity.com/paper/2603.13054/) (2026)
- [A Multi-Resolution Benchmark Framework for Spatial Reasoning Assessment in Neural Networks](https://mlsanity.com/paper/2508.12741/) (2025)
- [Topology-Driven Fusion of nnU-Net and MedNeXt for Accurate Brain Tumor Segmentation on Sub-Saharan Africa Dataset](https://mlsanity.com/paper/2604.15964/) (2026)

## Abstract (arXiv)

Although existing medical image segmentation methods provide impressive pixel-wise accuracy, they often neglect topological correctness, making their segmentations unusable for many downstream tasks. One option is to retrain such models whilst including a topology-driven loss component. However, this is computationally expensive and often impractical. A better solution would be to have a versatile plug-and-play topology refinement method that is compatible with any domain-specific segmentation pipeline. Directly training a post-processing model to mitigate topological errors often fails as such models tend to be biased towards the topological errors of a target segmentation network. The diversity of these errors is confined to the information provided by a labelled training set, which is especially problematic for small datasets. Our method solves this problem by training a model-agnostic topology refinement network with synthetic segmentations that cover a wide variety of topological errors. Inspired by the Stone-Weierstrass theorem, we synthesize topology-perturbation masks with randomly sampled coefficients of orthogonal polynomial bases, which ensures a complete and unbiased representation. Practically, we verified the efficiency and effectiveness of our methods as being compatible with multiple families of polynomial bases, and show evidence that our universal plug-and-play topology refinement network outperforms both existing topology-driven learning-based and post-processing methods. We also show that combining our method with learning-based models provides an effortless add-on, which can further improve the performance of existing approaches.