# Convexity Shape Prior for Level Set based Image Segmentation Method

arXiv: https://arxiv.org/abs/1805.08676 · HTML: https://mlsanity.com/paper/1805.08676/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2018.

## Built on by (most cited first, 10 of 10)

- [A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings](https://mlsanity.com/paper/2210.03299/) (2022)
- [Double-well Net for Image Segmentation](https://mlsanity.com/paper/2401.00456/) (2023)
- [Geodesic Models with Convexity Shape Prior](https://mlsanity.com/paper/2111.00794/) (2021)
- [A Binary Characterization Method for Shape Convexity and Applications](https://mlsanity.com/paper/2203.11395/) (2022)
- [Contour Flow Constraint: Preserving Global Shape Similarity for Deep Learning based Image Segmentation](https://mlsanity.com/paper/2504.09384/) (2025)
- [Shape Prior Segmentation Guided by Harmonic Beltrami Signature](https://mlsanity.com/paper/2407.04360/) (2024)
- [A Registration-Based Star-Shape Segmentation Model and Fast Algorithms](https://mlsanity.com/paper/2508.07721/) (2025)
- [Contour Field based Elliptical Shape Prior for the Segment Anything Model](https://mlsanity.com/paper/2504.12556/) (2025)
- [D-Convexity: A Unified Differentiable Convex Shape Prior via Quasi-Concavity for Data-driven Image Segmentation](https://mlsanity.com/paper/2605.19210/) (2026)
- [From level set evolution to threshold optimization: A grayscale level set framework for image segmentation](https://mlsanity.com/paper/2607.22255/) (2026)

## Abstract (arXiv)

We propose a geometric convexity shape prior preservation method for variational level set based image segmentation methods. Our method is built upon the fact that the level set of a convex signed distanced function must be convex. This property enables us to transfer a complicated geometrical convexity prior into a simple inequality constraint on the function. An active set based Gauss-Seidel iteration is used to handle this constrained minimization problem to get an efficient algorithm. We apply our method to region and edge based level set segmentation models including Chan-Vese (CV) model with guarantee that the segmented region will be convex. Experimental results show the effectiveness and quality of the proposed model and algorithm.