A stable algorithm is proposed for image restoration based on the "mean curvature motion" equation. Existence and uniqueness of the "viscosity" solution of the equation are proved, a LX stable algorithm is given, experimental results are shown, and the subjacent vision model is compared with those introduced recently by several vision researchers. The algorithm presented appears to be the sharpest possible among the multiscale image smoothing methods preserving uniqueness and stability.
We introduce a notion of state-constraint viscosity solutions for one dimensional "junction"-type problems for Hamilton-Jacobi equations with non convex coercive Hamiltonians and study its wellposedness and stability properties. We show that viscosity approximations either select the stateconstraint solution or have a unique limit. We also introduce another type of approximation by fattening the domain. We also make connections with existing results for convex equations and discuss extensions to time dependent and/or multi-dimensional problems.
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