# CAPE: Connectivity-Aware Path Enforcement Loss for Curvilinear Structure Delineation

arXiv: https://arxiv.org/abs/2504.00753 · HTML: https://mlsanity.com/paper/2504.00753/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 1 Apr 2025.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Deep Retinal Image Understanding](https://mlsanity.com/paper/1609.01103/) (2016)
- [Promoting Connectivity of Network-Like Structures by Enforcing Region Separation](https://mlsanity.com/paper/2009.07011/) (2020)
- [Coronary Artery Centerline Extraction in Cardiac CT Angiography Using a CNN-Based Orientation Classifier](https://mlsanity.com/paper/1810.03143/) (2018)
- [ N4 -Fields: Neural Network Nearest Neighbor Fields for Image Transforms](https://mlsanity.com/paper/1406.6558/) (2014)
- [A persistent homology-based topological loss function for multi-class CNN segmentation of cardiac MRI](https://mlsanity.com/paper/2008.09585/) (2020)
- [Persistent Homology with Improved Locality Information for more Effective Delineation](https://mlsanity.com/paper/2110.06295/) (2021)
- [DeepCenterline: a Multi-task Fully Convolutional Network for Centerline Extraction](https://mlsanity.com/paper/1903.10481/) (2019)
- [Enforcing connectivity of 3D linear structures using their 2D projections](https://mlsanity.com/paper/2207.06832/) (2022)

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

- [From Reconstruction to Decision: A Post-Encoder Plug-in Adapter for Curvilinear Segmentation](https://mlsanity.com/paper/2606.23486/) (2026)
- [Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentation](https://mlsanity.com/paper/2607.07123/) (2026)

## Abstract (arXiv)

Promoting the connectivity of curvilinear structures, such as neuronal processes in biomedical scans and blood vessels in CT images, remains a key challenge in semantic segmentation. Traditional pixel-wise loss functions, including cross-entropy and Dice losses, often fail to capture high-level topological connectivity, resulting in topological mistakes in graphs obtained from prediction maps. In this paper, we propose CAPE (Connectivity-Aware Path Enforcement), a novel loss function designed to enforce connectivity in graphs obtained from segmentation maps by optimizing a graph connectivity metric. CAPE uses the graph representation of the ground truth to select node pairs and determine their corresponding paths within the predicted segmentation through a shortest-path algorithm. Using this, we penalize both disconnections and false positive connections, effectively promoting the model to preserve topological correctness. Experiments on 2D and 3D datasets, including neuron and blood vessel tracing demonstrate that CAPE significantly improves topology-aware metrics and outperforms state-of-the-art methods.