# Leveraging Persistence Image to Enhance Robustness and Performance in Curvilinear Structure Segmentation

arXiv: https://arxiv.org/abs/2601.18045 · HTML: https://mlsanity.com/paper/2601.18045/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 20 references that are in the map.
- First posted on arXiv 25 Jan 2026.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [Centerline Boundary Dice Loss for Vascular Segmentation](https://mlsanity.com/paper/2407.01517/) (2024)
- [Representing Topological Self-Similarity Using Fractal Feature Maps for Accurate Segmentation of Tubular Structures](https://mlsanity.com/paper/2407.14754/) (2024)
- [PI-Net: A Deep Learning Approach to Extract Topological Persistence Images](https://mlsanity.com/paper/1906.01769/) (2019)
- [GLCP: Global-to-Local Connectivity Preservation for Tubular Structure Segmentation](https://mlsanity.com/paper/2507.21328/) (2025)
- [Topology of Learning in Artificial Neural Networks](https://mlsanity.com/paper/1902.08160/) (2019)

## Built on by (most cited first, 1 of 1)

- [HadBalance: A Plug-and-Play Unified Global Geometric Prior Framework for Generalizable Biomedical Segmentation](https://mlsanity.com/paper/2606.15976/) (2026)

## Abstract (arXiv)

Segmenting curvilinear structures in medical images is essential for analyzing morphological patterns in clinical applications. Integrating topological properties, such as connectivity, improves segmentation accuracy and consistency. However, extracting and embedding such properties - especially from Persistence Diagrams (PD) - is challenging due to their non-differentiability and computational cost. Existing approaches mostly encode topology through handcrafted loss functions, which generalize poorly across tasks. In this paper, we propose PIs-Regressor, a simple yet effective module that learns persistence image (PI) - finite, differentiable representations of topological features - directly from data. Together with Topology SegNet, which fuses these features in both downsampling and upsampling stages, our framework integrates topology into the network architecture itself rather than auxiliary losses. Unlike existing methods that depend heavily on handcrafted loss functions, our approach directly incorporates topological information into the network structure, leading to more robust segmentation. Our design is flexible and can be seamlessly combined with other topology-based methods to further enhance segmentation performance. Experimental results show that integrating topological features enhances model robustness, effectively handling challenges like overexposure and blurring in medical imaging. Our approach on three curvilinear benchmarks demonstrate state-of-the-art performance in both pixel-level accuracy and topological fidelity.