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.
The aim of this note is to revisit the connections between some stochastic games, namely Tug-of-War games, and a class of nonlocal PDEs on graphs. We consider a general formulation of Tug-of-War games which is shown to be related to many classical PDEs in the continuous setting. We transcribe these equations on graphs using ad hoc differential operators and we show that it covers several nonlocal PDEs on graphs such as $$\infty $$
∞
-Laplacian, game p-Laplacian and the eikonal equation. This unifying mathematical framework allows us to easily design simple algorithms to solve several inverse problems in imaging and data science, with a particular focus on cultural heritage and medical imaging.
We suggest a new approach to solve a class of degenerate Hamilton-Jacobi equations without any assumptions on the emptiness of the Aubry set. It is based on the characterization of the maximal subsolution by means of the Fenchel-Rockafellar duality. This approach enables us to use augmented Lagrangian methods as alternatives to the commonly used methods for numerical approximation of the solution, based on finite difference approximation or on optimal control interpretation of the solution.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.