# Promoting Connectivity of Network-Like Structures by Enforcing Region Separation

arXiv: https://arxiv.org/abs/2009.07011 · HTML: https://mlsanity.com/paper/2009.07011/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2020.

## Built on by (most cited first, 19 of 19)

- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [DeepMesh: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2106.11795/) (2021)
- [Enabling Uncertainty Estimation in Iterative Neural Networks](https://mlsanity.com/paper/2403.16732/) (2024)
- [Persistent Homology with Improved Locality Information for more Effective Delineation](https://mlsanity.com/paper/2110.06295/) (2021)
- [CP-loss: Connectivity-preserving Loss for Road Curb Detection in Autonomous Driving with Aerial Images](https://mlsanity.com/paper/2107.11920/) (2021)
- [Enhancing Boundary Segmentation for Topological Accuracy with Skeleton-based Methods](https://mlsanity.com/paper/2404.18539/) (2024)
- [PointScatter: Point Set Representation for Tubular Structure Extraction](https://mlsanity.com/paper/2209.05774/) (2022)
- [Enforcing connectivity of 3D linear structures using their 2D projections](https://mlsanity.com/paper/2207.06832/) (2022)
- [CAPE: Connectivity-Aware Path Enforcement Loss for Curvilinear Structure Delineation](https://mlsanity.com/paper/2504.00753/) (2025)
- [Topology-Guaranteed Image Segmentation: Enforcing Connectivity, Genus, and Width Constraints](https://mlsanity.com/paper/2601.11409/) (2026)
- [Adjusting the Ground Truth Annotations for Connectivity-Based Learning to Delineate](https://mlsanity.com/paper/2112.02781/) (2021)
- [TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracy](https://mlsanity.com/paper/2503.03365/) (2025)
- [Towards High-Quality Image Segmentation: Improving Topology Accuracy by Penalizing Neighbor Pixels](https://mlsanity.com/paper/2603.18671/) (2026)
- [BuyTheDips: PathLoss for improved topology-preserving deep learning-based image segmentation](https://mlsanity.com/paper/2207.11446/) (2022)
- [Holistically-Nested Structure-Aware Graph Neural Network for Road Extraction](https://mlsanity.com/paper/2407.02639/) (2024)
- [Vision-Based Power Line Cables and Pylons Detection for Low Flying Aircraft](https://mlsanity.com/paper/2407.14352/) (2024)
- [Enhancing the automatic segmentation and analysis of 3D liver vasculature models](https://mlsanity.com/paper/2411.15778/) (2024)
- [SDF-TopoNet: A Two-Stage Framework for Tubular Structure Segmentation via SDF Pre-training and Topology-Aware Fine-Tuning](https://mlsanity.com/paper/2503.14523/) (2025)
- [Continuous-tone Simple Points: An ℓ0-Norm of Cyclic Gradient for Topology-Preserving Data-Driven Image Segmentation](https://mlsanity.com/paper/2604.28159/) (2026)

## Abstract (arXiv)

We propose a novel, connectivity-oriented loss function for training deep convolutional networks to reconstruct network-like structures, like roads and irrigation canals, from aerial images. The main idea behind our loss is to express the connectivity of roads, or canals, in terms of disconnections that they create between background regions of the image. In simple terms, a gap in the predicted road causes two background regions, that lie on the opposite sides of a ground truth road, to touch in prediction. Our loss function is designed to prevent such unwanted connections between background regions, and therefore close the gaps in predicted roads. It also prevents predicting false positive roads and canals by penalizing unwarranted disconnections of background regions. In order to capture even short, dead-ending road segments, we evaluate the loss in small image crops. We show, in experiments on two standard road benchmarks and a new data set of irrigation canals, that convnets trained with our loss function recover road connectivity so well, that it suffices to skeletonize their output to produce state of the art maps. A distinct advantage of our approach is that the loss can be plugged in to any existing training setup without further modifications.