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

This work was motivated by the necessity of defining and computing a solution ρρ of a transport equation equation(1)∂tρ+v⋅∇xρ=f(t,x,ρ).∂tρ+v⋅∇xρ=f(t,x,ρ). subject to a non-convex pointwise constraint ρ∈Cρ∈C. For when the velocity vv is a regular function and when ff 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.