# Enforcing connectivity of 3D linear structures using their 2D projections

arXiv: https://arxiv.org/abs/2207.06832 · HTML: https://mlsanity.com/paper/2207.06832/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 14 Jul 2022.

## Builds on (most cited first, 17 of 17)

- [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)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Med3D: Transfer Learning for 3D Medical Image Analysis](https://mlsanity.com/paper/1904.00625/) (2019)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [SpaceNet: A Remote Sensing Dataset and Challenge Series](https://mlsanity.com/paper/1807.01232/) (2018)
- [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)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [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)
- [Joint Segmentation and Path Classification of Curvilinear Structures](https://mlsanity.com/paper/1905.03892/) (2019)
- [Tracing in 2D to Reduce the Annotation Effort for 3D Deep Delineation](https://mlsanity.com/paper/1811.10508/) (2018)
- [DeepCenterline: a Multi-task Fully Convolutional Network for Centerline Extraction](https://mlsanity.com/paper/1903.10481/) (2019)

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

- [3D Vascular Segmentation Supervised by 2D Annotation of Maximum Intensity Projection](https://mlsanity.com/paper/2402.12128/) (2024)
- [CAPE: Connectivity-Aware Path Enforcement Loss for Curvilinear Structure Delineation](https://mlsanity.com/paper/2504.00753/) (2025)
- [Morphology Edge Attention Network and Optimal Geometric Matching Connection model for vascular segmentation](https://mlsanity.com/paper/2306.01808/) (2023)

## Abstract (arXiv)

Many biological and medical tasks require the delineation of 3D curvilinear structures such as blood vessels and neurites from image volumes. This is typically done using neural networks trained by minimizing voxel-wise loss functions that do not capture the topological properties of these structures. As a result, the connectivity of the recovered structures is often wrong, which lessens their usefulness. In this paper, we propose to improve the 3D connectivity of our results by minimizing a sum of topology-aware losses on their 2D projections. This suffices to increase the accuracy and to reduce the annotation effort required to provide the required annotated training data. Code is available at https://github.com/doruk-oner/ConnectivityOnProjections.