Numerical Methods for p-Harmonic Flows and Applications to Image Processing

We propose in this paper an alternative approach for computing p-harmonic maps and flows: instead of solving a constrained minimization problem on SN−1, we solve an unconstrained minimization problem on the entire space of functions. This is possible, using the projection on the sphere of any arbitrary function. Then we show how this formulation can be used in practice, for problems with both isotropic and anisotropic diffusion, with applications to image processing, using a new finite difference scheme.