{"title":"Continuous Lambertian shape from shading: a primal-dual algorithm","authors":"Hamza Ennaji, N. Igbida, Van Thanh Nguyen","doi":"10.1051/m2an/2022014","DOIUrl":null,"url":null,"abstract":"The continuous Lambertian shape from shading is studied using a PDE approach\n\nin terms of Hamilton–Jacobi equations. The latter will then be characterized by a maximization\n\nproblem. In this paper we show the convergence of discretization and propose to use the wellknown\n\nChambolle–Pock primal-dual algorithm to solve numerically the shape from shading\n\nproblem. The saddle-point structure of the problem makes the Chambolle–Pock algorithm\n\nsuitable to approximate solutions of the discretized problems.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/m2an/2022014","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
The continuous Lambertian shape from shading is studied using a PDE approach
in terms of Hamilton–Jacobi equations. The latter will then be characterized by a maximization
problem. In this paper we show the convergence of discretization and propose to use the wellknown
Chambolle–Pock primal-dual algorithm to solve numerically the shape from shading
problem. The saddle-point structure of the problem makes the Chambolle–Pock algorithm
suitable to approximate solutions of the discretized problems.
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