Revisiting the redistancing problem using the Hopf-Lax formula

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• 作者：Byungjoon Lee^a ; ^{asone30@snu.ac.kr} ; Jé ; rô ; me Darbon^c ; ^{jerome_darbon@brown.edu} ; Stanley Osher^b ; ^{sjo@math.ucla.edu} ; Myungjoo Kang^a ; ^{mkang@snu.ac.kr}
• 关键词：Reinitialization ; Level set method ; Hopf&ndash ; Lax formula ; Hamilton&ndash ; Jacobi equations ; Split Bregman Method
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：330
• 期：Complete
• 页码：268-281
• 全文大小：12141 K
• 卷排序：330

文摘

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.