# DeformCL: Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image

arXiv: https://arxiv.org/abs/2506.05820 · HTML: https://mlsanity.com/paper/2506.05820/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [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)
- [Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation](https://mlsanity.com/paper/2307.08388/) (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)
- [Voxel2Mesh: 3D Mesh Model Generation from Volumetric Data](https://mlsanity.com/paper/1912.03681/) (2019)
- [Deep Distance Transform for Tubular Structure Segmentation in CT Scans](https://mlsanity.com/paper/1912.03383/) (2019)
- [A Deep-Learning Approach For Direct Whole-Heart Mesh Reconstruction](https://mlsanity.com/paper/2102.07899/) (2021)
- [Deep Vessel Segmentation By Learning Graphical Connectivity](https://mlsanity.com/paper/1806.02279/) (2018)
- [Vox2Cortex: Fast Explicit Reconstruction of Cortical Surfaces from 3D MRI Scans with Geometric Deep Neural Networks](https://mlsanity.com/paper/2203.09446/) (2022)
- [3D Graph Anatomy Geometry-Integrated Network for Pancreatic Mass Segmentation, Diagnosis, and Quantitative Patient Management](https://mlsanity.com/paper/2012.04701/) (2020)
- [Topological Similarity Index and Loss Function for Blood Vessel Segmentation](https://mlsanity.com/paper/2107.14531/) (2021)
- [PointScatter: Point Set Representation for Tubular Structure Extraction](https://mlsanity.com/paper/2209.05774/) (2022)
- [Graph Convolution Based Cross-Network Multi-Scale Feature Fusion for Deep Vessel Segmentation](https://mlsanity.com/paper/2301.02393/) (2023)
- [Topology-Preserving Automatic Labeling of Coronary Arteries via Anatomy-aware Connection Classifier](https://mlsanity.com/paper/2307.11959/) (2023)
- [GraphMorph: Tubular Structure Extraction by Morphing Predicted Graphs](https://mlsanity.com/paper/2502.11731/) (2025)

## Built on by (most cited first, 5 of 5)

- [Towards High-Quality Image Segmentation: Improving Topology Accuracy by Penalizing Neighbor Pixels](https://mlsanity.com/paper/2603.18671/) (2026)
- [ImageCAS-X: a dataset and benchmark for coronary artery segmentation and centerline extraction in coronary CT angiography](https://mlsanity.com/paper/2608.30404/) (2026)
- [Uncertainty-Guided Conservative Propagation for Structured Inference in Vessel Segmentation](https://mlsanity.com/paper/2605.20543/) (2026)
- [Clinical Risk-Aware Multi-Level Grading for Coronary Artery Stenosis through Curved Feature Reconstruction](https://mlsanity.com/paper/2606.30082/) (2026)
- [End-to-End Autonomous Recursive Arborescence Deformable Flow and Non-Linear Hemodynamics for Patient-Specific Coronary Centerline Extraction](https://mlsanity.com/paper/2610.05900/) (2026)

## Abstract (arXiv)

In the field of 3D medical imaging, accurately extracting and representing the blood vessels with curvilinear structures holds paramount importance for clinical diagnosis. Previous methods have commonly relied on discrete representation like mask, often resulting in local fractures or scattered fragments due to the inherent limitations of the per-pixel classification paradigm. In this work, we introduce DeformCL, a new continuous representation based on Deformable Centerlines, where centerline points act as nodes connected by edges that capture spatial relationships. Compared with previous representations, DeformCL offers three key advantages: natural connectivity, noise robustness, and interaction facility. We present a comprehensive training pipeline structured in a cascaded manner to fully exploit these favorable properties of DeformCL. Extensive experiments on four 3D vessel segmentation datasets demonstrate the effectiveness and superiority of our method. Furthermore, the visualization of curved planar reformation images validates the clinical significance of the proposed framework. We release the code in https://github.com/barry664/DeformCL