Optimal extended optical flow and statistical constraints: A result of convergence

This work was motivated by the necessity of defining and computing a solution ρ of a transport equation (1) ∂ t ρ + v ⋅ ∇ x ρ = f ( t , x , ρ ) . subject to a non-convex pointwise constraint ρ ∈ C . For when the velocity v is a regular function and when f is a Lipschitz function, in [9] sufficient conditions are given for the solution to the transport equation (15) to satisfy such a constraint. In this paper an algorithm for computing a relaxed solution is investigated.