Singular Diffusion Equations: Minimally Stochastic Solution Schemes

Total variation (TV) and balanced forward-backward (BFB) diffusion are popular examples of singular diffusion processes: Finite extinction time, the experimentally observed tendency to create piecewise constant regions, and the absence of parameters makes them very interesting image processing tools. However, their appropriate numerical treatment is still a challenge. In this contribution a minimally stochastic approach to the underlying singular equations is presented. It relies on analytical solutions of two-pixel signals and stochastic rounding. This introduces regularisation via integer arithmetic and does not require any limits on the diffusivity. Experiments demonstrate the favourable performance of the proposed probabilistic method.