# Geodesic Models with Convexity Shape Prior

arXiv: https://arxiv.org/abs/2111.00794 · HTML: https://mlsanity.com/paper/2111.00794/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 51 references that are in the map.
- First posted on arXiv 1 Nov 2021.

## Builds on (most cited first, 5 of 5)

- [Global Minimum for a Finsler Elastica Minimal Path Approach](https://mlsanity.com/paper/1612.00343/) (2016)
- [Convexity Shape Prior for Level Set based Image Segmentation Method](https://mlsanity.com/paper/1805.08676/) (2018)
- [Convexity Shape Constraints for Image Segmentation](https://mlsanity.com/paper/1509.02122/) (2015)
- [A Region-based Randers Geodesic Approach for Image Segmentation](https://mlsanity.com/paper/1912.10122/) (2019)
- [Geodesic Paths for Image Segmentation with Implicit Region-based Homogeneity Enhancement](https://mlsanity.com/paper/2008.06909/) (2020)

## Built on by (most cited first, 4 of 4)

- [Grouping Boundary Proposals for Fast Interactive Image Segmentation](https://mlsanity.com/paper/2309.04169/) (2023)
- [A Registration-Based Star-Shape Segmentation Model and Fast Algorithms](https://mlsanity.com/paper/2508.07721/) (2025)
- [Geodesics with Unified Tangent-constrained Priors and Curvature Regularization](https://mlsanity.com/paper/2606.00139/) (2026)
- [Mask Proposal Voting Based on Geodesic Framework for Robust Image Segmentation](https://mlsanity.com/paper/2606.14912/) (2026)

## Abstract (arXiv)

The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with geometric regularization terms, such as Euclidean curve length or curvature-penalized length, for computing geodesic curves. In this paper, we take into account a more complicated problem: finding curvature-penalized geodesic paths with a convexity shape prior. We establish new geodesic models relying on the strategy of orientation-lifting, by which a planar curve can be mapped to an high-dimensional orientation-dependent space. The convexity shape prior serves as a constraint for the construction of local geodesic metrics encoding a particular curvature constraint. Then the geodesic distances and the corresponding closed geodesic paths in the orientation-lifted space can be efficiently computed through state-of-the-art Hamiltonian fast marching method. In addition, we apply the proposed geodesic models to the active contours, leading to efficient interactive image segmentation algorithms that preserve the advantages of convexity shape prior and curvature penalization.