# Convex Shape Representation with Binary Labels for Image Segmentation: Models and Fast Algorithms

arXiv: https://arxiv.org/abs/2002.09600 · HTML: https://mlsanity.com/paper/2002.09600/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2020.

## Built on by (most cited first, 2 of 2)

- [JOINEDTrans: Prior Guided Multi-task Transformer for Joint Optic Disc/Cup Segmentation and Fovea Detection](https://mlsanity.com/paper/2305.11504/) (2023)
- [Inverse Evolution Layers: Physics-informed Regularizers for Deep Neural Networks](https://mlsanity.com/paper/2307.07344/) (2023)

## Abstract (arXiv)

We present a novel and effective binary representation for convex shapes. We show the equivalence between the shape convexity and some properties of the associated indicator function. The proposed method has two advantages. Firstly, the representation is based on a simple inequality constraint on the binary function rather than the definition of convex shapes, which allows us to obtain efficient algorithms for various applications with convexity prior. Secondly, this method is independent of the dimension of the concerned shape. In order to show the effectiveness of the proposed representation approach, we incorporate it with a probability based model for object segmentation with convexity prior. Efficient algorithms are given to solve the proposed models using Lagrange multiplier methods and linear approximations. Various experiments are given to show the superiority of the proposed methods.