# clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation

arXiv: https://arxiv.org/abs/2003.07311 · HTML: https://mlsanity.com/paper/2003.07311/

## Key facts

- Cited by 294 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2020.

## Built on by (most cited first, 30 of 294)

- [Metrics reloaded: Recommendations for image analysis validation](https://mlsanity.com/paper/2206.01653/) (2022)
- [Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation](https://mlsanity.com/paper/2307.08388/) (2023)
- [Relationformer: A Unified Framework for Image-to-Graph Generation](https://mlsanity.com/paper/2203.10202/) (2022)
- [Common Limitations of Image Processing Metrics: A Picture Story](https://mlsanity.com/paper/2104.05642/) (2021)
- [Understanding metric-related pitfalls in image analysis validation](https://mlsanity.com/paper/2302.01790/) (2023)
- [ImageCAS: A Large-Scale Dataset and Benchmark for Coronary Artery Segmentation based on Computed Tomography Angiography Images](https://mlsanity.com/paper/2211.01607/) (2022)
- [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)
- [Skeleton Recall Loss for Connectivity Conserving and Resource Efficient Segmentation of Thin Tubular Structures](https://mlsanity.com/paper/2404.03010/) (2024)
- [Topology-Aware Uncertainty for Image Segmentation](https://mlsanity.com/paper/2306.05671/) (2023)
- [Directional Connectivity-based Segmentation of Medical Images](https://mlsanity.com/paper/2304.00145/) (2023)
- [Learning Topological Interactions for Multi-Class Medical Image Segmentation](https://mlsanity.com/paper/2207.09654/) (2022)
- [Efficient automatic segmentation for multi-level pulmonary arteries: The PARSE challenge](https://mlsanity.com/paper/2304.03708/) (2023)
- [Centerline Boundary Dice Loss for Vascular Segmentation](https://mlsanity.com/paper/2407.01517/) (2024)
- [Structure-Aware Image Segmentation with Homotopy Warping](https://mlsanity.com/paper/2112.07812/) (2021)
- [Learning Probabilistic Topological Representations Using Discrete Morse Theory](https://mlsanity.com/paper/2206.01742/) (2022)
- [blob loss: instance imbalance aware loss functions for semantic segmentation](https://mlsanity.com/paper/2205.08209/) (2022)
- [vesselFM: A Foundation Model for Universal 3D Blood Vessel Segmentation](https://mlsanity.com/paper/2411.17386/) (2024)
- [TA-Net: Topology-Aware Network for Gland Segmentation](https://mlsanity.com/paper/2110.14593/) (2021)
- [Synthetic optical coherence tomography angiographs for detailed retinal vessel segmentation without human annotations](https://mlsanity.com/paper/2306.10941/) (2023)
- [A skeletonization algorithm for gradient-based optimization](https://mlsanity.com/paper/2309.02527/) (2023)
- [Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation](https://mlsanity.com/paper/2411.03228/) (2024)
- [TopoCellGen: Generating Histopathology Cell Topology with a Diffusion Model](https://mlsanity.com/paper/2412.06011/) (2024)
- [RTNet: Relation Transformer Network for Diabetic Retinopathy Multi-lesion Segmentation](https://mlsanity.com/paper/2201.11037/) (2022)
- [Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstruction](https://mlsanity.com/paper/2203.01703/) (2022)
- [Human Treelike Tubular Structure Segmentation: A Comprehensive Review and Future Perspectives](https://mlsanity.com/paper/2207.11203/) (2022)
- [SAM-OCTA: A Fine-Tuning Strategy for Applying Foundation Model to OCTA Image Segmentation Tasks](https://mlsanity.com/paper/2309.11758/) (2023)
- [DeNVeR: Deformable Neural Vessel Representations for Unsupervised Video Vessel Segmentation](https://mlsanity.com/paper/2406.01591/) (2024)
- [Representing Topological Self-Similarity Using Fractal Feature Maps for Accurate Segmentation of Tubular Structures](https://mlsanity.com/paper/2407.14754/) (2024)
- [Do We Really Need Dice? The Hidden Region-Size Biases of Segmentation Losses](https://mlsanity.com/paper/2104.08717/) (2021)

## Abstract (arXiv)

Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their most important characteristic; particularly preserving connectedness: in the case of vascular networks, missing a connected vessel entirely alters the blood-flow dynamics. We introduce a novel similarity measure termed centerlineDice (short clDice), which is calculated on the intersection of the segmentation masks and their (morphological) skeleta. We theoretically prove that clDice guarantees topology preservation up to homotopy equivalence for binary 2D and 3D segmentation. Extending this, we propose a computationally efficient, differentiable loss function (soft-clDice) for training arbitrary neural segmentation networks. We benchmark the soft-clDice loss on five public datasets, including vessels, roads and neurons (2D and 3D). Training on soft-clDice leads to segmentation with more accurate connectivity information, higher graph similarity, and better volumetric scores.