# Minimal Paths for Tubular Structure Segmentation with Coherence Penalty and Adaptive Anisotropy

arXiv: https://arxiv.org/abs/1809.07987 · HTML: https://mlsanity.com/paper/1809.07987/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2018.

## Built on by (most cited first, 9 of 9)

- [Sequential vessel segmentation via deep channel attention network](https://mlsanity.com/paper/2102.05229/) (2021)
- [Progressive Minimal Path Method with Embedded CNN](https://mlsanity.com/paper/2204.00944/) (2022)
- [Segmentation of Tubular Structures Using Iterative Training with Tailored Samples](https://mlsanity.com/paper/2309.08727/) (2023)
- [BioVessel-Net and RetinaMix: Unsupervised Retinal Vessel Segmentation from OCTA Images](https://mlsanity.com/paper/2509.23617/) (2025)
- [GAPNet: Granularity Attention Network with Anatomy-Prior-Constraint for Carotid Artery Segmentation](https://mlsanity.com/paper/2406.19485/) (2024)
- [Topology preserving Image segmentation using the iterative convolution-thresholding method](https://mlsanity.com/paper/2503.17792/) (2025)
- [Dynamic Exploration on Segment-Proposal Graphs for Tubular Centerline Tracking](https://mlsanity.com/paper/2506.18930/) (2025)
- [Topology-Aware Skeleton Detection via Lighthouse-Guided Structured Inference](https://mlsanity.com/paper/2604.20123/) (2026)
- [Geodesics with Unified Tangent-constrained Priors and Curvature Regularization](https://mlsanity.com/paper/2606.00139/) (2026)

## Abstract (arXiv)

The minimal path method has proven to be particularly useful and efficient in tubular structure segmentation applications. In this paper, we propose a new minimal path model associated with a dynamic Riemannian metric embedded with an appearance feature coherence penalty and an adaptive anisotropy enhancement term. The features that characterize the appearance and anisotropy properties of a tubular structure are extracted through the associated orientation score. The proposed dynamic Riemannian metric is updated in the course of the geodesic distance computation carried out by the efficient single-pass fast marching method. Compared to state-of-the-art minimal path models, the proposed minimal path model is able to extract the desired tubular structures from a complicated vessel tree structure. In addition, we propose an efficient prior path-based method to search for vessel radius value at each centerline position of the target. Finally, we perform the numerical experiments on both synthetic and real images. The quantitive validation is carried out on retinal vessel images. The results indicate that the proposed model indeed achieves a promising performance.