A Variational Convex Hull Algorithm

Abstract

Finding the convex hull of a given object or a point set is a very important problem. In this paper, we propose a variational convex hull model and numerical algorithms to solve it. Our model is based on level set representation. Efficient numerical algorithms and implementations based on splitting ideas are given. To test our proposed model, we conduct many experiments for objects represented by binary images, and the results suggest that our model can identify the convex hull accurately. Even more, our model can be easily modified to handle the outliers, and this is also demonstrated by numerical examples.