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.
The aim of this note is to give a Beckmann-type problem as well as the corresponding optimal mass transportation problem associated with a degenerate Hamilton-Jacobi equation
H
(
x
,
∇
u
)
=
0
,
H(x,\nabla u)=0,
coupled with non-zero Dirichlet condition
u
=
g
u=g
on
∂
Ω
\partial \Omega
. In this article, the Hamiltonian
H
H
is continuous in both arguments, coercive and convex in the second, but not enjoying any property of existence of a smooth strict sub-solution. We also provide numerical examples to validate the correctness of theoretical formulations.
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