A new variational approach based on level-set function for convex hull problem with outliers

Seeking the convex hull of an object (or point set) is a very fundamental problem arising from various tasks. In this work, we propose variational approach based on level-set representation for hulls 2-dimensional objects. This method can adapt to exact and inexact problems. addition, compute multiple simultaneously. model, characterized by zero sublevel-set function. For case, require be contain whole given object, where convexity non-negativity Laplacian Then, obtained minimizing area sublevel-set. instead requiring all points are included, penalize distance Especially, model handle set with outliers well, while most existing methods fail. An efficient numerical scheme using alternating direction multipliers developed. Numerical examples demonstrate advantages proposed methods.