STOR colloquium: Dirk Lorenz, Braunschweig Technical University

Dirk Lorenz

Braunschweig Technical University

Probabilistic Image Models and Extensions of the
Perona-Malik Filter

The Perona-Malik model has been very successful at restoring images from noisy input.  In this paper, we show how the Perona-Malik model can be reinterpreted and extended using the language of Gaussian scale mixtures.  Specifically, we show how the expectation-maximization EM algorithm applied to Gaussian scale mixtures leads to the lagged-diffusivity algorithm for computing stationary points of the Perona-Malik diffusion equations.  Moreover, we show how mean field approximations to these Gaussian scale mixtures lead to a modification of the lagged-diffusivity algorithm that better captures the uncertainties in the restoration.  Since this modification can be hard to compute in practice we propose relaxations to the mean field objective to make the algorithm computationally feasible.  Our numerical experiments show that this modified lagged-diffusivity algorithm often performs better at restoring textured areas and fuzzy edges than the unmodified algorithm. As a second application of the Gaussian scale mixture framework, we show how an efficient sampling procedure can be obtained for the probabilistic model, making the computation of the conditional mean and other expectations algorithmically feasible.  Again, the resulting algorithm has a strong resemblance to the lagged-diffusivity algorithm.

Refreshments will be served at 3:00pm in the 3^rd floor lounge of Hanes Hall