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.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2022014
Keywords: Hamilton–Jacobi equation, Shape-from-Shading, primal-dual algorithm, numerical analysis
@article{M2AN_2022__56_2_485_0,
author = {Ennaji, Hamza and Igbida, Noureddine and Nguyen, Van Thanh},
title = {Continuous {Lambertian} shape from shading: {A} primal-dual algorithm},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {485--504},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {2},
doi = {10.1051/m2an/2022014},
mrnumber = {4385101},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2022014/}
}
TY - JOUR AU - Ennaji, Hamza AU - Igbida, Noureddine AU - Nguyen, Van Thanh TI - Continuous Lambertian shape from shading: A primal-dual algorithm JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2022 SP - 485 EP - 504 VL - 56 IS - 2 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2022014/ DO - 10.1051/m2an/2022014 LA - en ID - M2AN_2022__56_2_485_0 ER -
%0 Journal Article %A Ennaji, Hamza %A Igbida, Noureddine %A Nguyen, Van Thanh %T Continuous Lambertian shape from shading: A primal-dual algorithm %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2022 %P 485-504 %V 56 %N 2 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2022014/ %R 10.1051/m2an/2022014 %G en %F M2AN_2022__56_2_485_0
Ennaji, Hamza; Igbida, Noureddine; Nguyen, Van Thanh. Continuous Lambertian shape from shading: A primal-dual algorithm. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 2, pp. 485-504. doi: 10.1051/m2an/2022014
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