Revisiting the redistancing problem using the Hopf-Lax formula

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.