A Binary Characterization Method for Shape Convexity and Applications

TL;DR

This paper introduces a new binary function-based method for characterizing convex shapes, enabling improved image segmentation and convex hull computation with guaranteed convergence and efficiency.

Contribution

The paper presents a novel binary characterization approach for convex objects using quadratic inequalities, with algorithms for segmentation and convex hulls that outperform existing methods.

Findings

High accuracy in image segmentation tasks

Efficient convex hull computation with noise robustness

Guaranteed convergence of the proposed algorithm

Abstract

Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image processing. We present a new method for convex objects representations using binary functions, that is, the convexity of a region is equivalent to a simple quadratic inequality constraint on its indicator function. Models are proposed firstly by incorporating this result for image segmentation with convexity prior and convex hull computation of a given set with and without noises. Then, these models are summarized to a general optimization problem on binary function(s) with the quadratic inequality. Numerical algorithm is proposed based on linearization technique, where the linearized problem is solved by a proximal alternating direction method of multipliers with guaranteed convergent. Numerical experiments demonstrate the efficiency and effectiveness of the proposed methods for image segmentation and convex hull computation in accuracy and computing time.