How marginal likelihood inference unifies entropy, correlation and SNR-based stopping in nonlinear diffusion scale-spaces

Abstract

Iterative smoothing algorithms are frequently applied in image restoration tasks. The result depends crucially on the optimal stopping (scale selection) criteria. An attempt is made towards the unification of the two frequently applied model selection ideas: (i) the earliest time when the 'entropy of the signal' reaches its steady state, suggested by J. Sporring and J. Weickert (1999), and (ii) the time of the minimal 'correlation' between the diffusion outcome and the noise estimate, investigated by P. Mrázek and M. Navara (2003). It is shown that both ideas are particular cases of the marginal likelihood inference. Better entropy measures are discovered and their connection to the generalized signal-to-noise ratio is emphasized. © Springer-Verlag Berlin Heidelberg 2007.