Revisiting the redistancing problem using the Hopf-Lax formula

Abstract

This article presents a fast new numerical method for redistancing objective functions based on the Hopf-Lax formula [1]. The algorithm suggested here is a special case of the previous work in [2] and an extension that applies the Hopf-Lax formula for computing the signed distance to the front. We propose the split Bregman approach to solve the minimization problem as a solution of the eikonal equation obtained from Hopf-Lax formula. Our redistancing procedure is expected to be generalized and widely applied to many fields such as computational fluid dynamics, the minimal surface problem, and elsewhere. (C) 2016 Elsevier Inc. All rights reserved.