# Topological Similarity Index and Loss Function for Blood Vessel Segmentation

arXiv: https://arxiv.org/abs/2107.14531 · HTML: https://mlsanity.com/paper/2107.14531/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 38 references that are in the map.
- First posted on arXiv 30 Jul 2021.

## Builds on (most cited first, 3 of 3)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Retinal vessel segmentation based on Fully Convolutional Neural Networks](https://mlsanity.com/paper/1812.07110/) (2018)
- [Boosting Connectivity in Retinal Vessel Segmentation via a Recursive Semantics-Guided Network](https://mlsanity.com/paper/2004.12776/) (2020)

## Built on by (most cited first, 8 of 8)

- [Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation](https://mlsanity.com/paper/2307.08388/) (2023)
- [The RETA Benchmark for Retinal Vascular Tree Analysis](https://mlsanity.com/paper/2111.11658/) (2021)
- [Representing Topological Self-Similarity Using Fractal Feature Maps for Accurate Segmentation of Tubular Structures](https://mlsanity.com/paper/2407.14754/) (2024)
- [DeformCL: Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image](https://mlsanity.com/paper/2506.05820/) (2025)
- [HarmonySeg: Tubular Structure Segmentation with Deep-Shallow Feature Fusion and Growth-Suppression Balanced Loss](https://mlsanity.com/paper/2504.07827/) (2025)
- [SIRE: scale-invariant, rotation-equivariant estimation of artery orientations using graph neural networks](https://mlsanity.com/paper/2311.05400/) (2023)
- [TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracy](https://mlsanity.com/paper/2503.03365/) (2025)
- [CASR-Net: An Image Processing-focused Deep Learning-based Coronary Artery Segmentation and Refinement Network for X-ray Coronary Angiogram](https://mlsanity.com/paper/2510.27315/) (2025)

## Abstract (arXiv)

Blood vessel segmentation is one of the most studied topics in computer vision, due to its relevance in daily clinical practice. Despite the evolution the field has been facing, especially after the dawn of deep learning, important challenges are still not solved. One of them concerns the consistency of the topological properties of the vascular trees, given that the best performing methodologies do not directly penalize mistakes such as broken segments and end up producing predictions with disconnected trees. This is particularly relevant in graph-like structures, such as blood vessel trees, given that it puts at risk the characterization steps that follow the segmentation task. In this paper, we propose a similarity index which captures the topological consistency of the predicted segmentations having as reference the ground truth. We also design a novel loss function based on the morphological closing operator and show how it allows to learn deep neural network models which produce more topologically coherent masks. Our experiments target well known retinal benchmarks and a coronary angiogram database.