| Issue |
ESAIM: M2AN
Volume 56, Number 2, March-April 2022
|
|
|---|---|---|
| Page(s) | 485 - 504 | |
| DOI | https://doi.org/10.1051/m2an/2022014 | |
| Published online | 24 February 2022 | |
Continuous Lambertian shape from shading: A primal-dual algorithm
1
Institut de recherche XLIM-DMI, UMR-CNRS 6172, Faculté des Sciences et Techniques, Université de Limoges, Limoges, France
2
Department of Mathematics and Statistics, Quy Nhon University, Binh Dinh, Vietnam
* Corresponding author: noureddine.igbida@unilim.fr.
Received:
19
October
2020
Accepted:
28
January
2022
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 well-known 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.
Mathematics Subject Classification: 49L25 / 62H35 / 65K10 / 49Q22 / 78A05
Key words: Hamilton–Jacobi equation / Shape-from-Shading / primal-dual algorithm / numerical analysis
© The authors. Published by EDP Sciences, SMAI 2022
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