Variational image processing translates image processing tasks into optimisation problems.
The practical success of this approach depends on the type of optimisation problem and on the properties of the ensuing algorithm. A recent breakthrough was to realise that old first-order optimisation algorithms based on operator splitting are particularly suited for modern data analysis problems. Operator splitting techniques decouple complex optimisation problems into many smaller and simpler sub-problems.
In this talk I will revise the variational segmentation problem and a common family of algorithms to solve such optimisation problems. I will show that operator splitting leads to a divide-and-conquer strategy that allows to derive simple and massively parallel updates suitable for GPU implementations. The technique decouples the likelihood from the prior term and allows to use a data-driven model estimating the likelihood from data, using for example deep learning. Using a different decoupling strategy together with general consensus optimisation leads to fully distributed algorithms especially suitable for large-scale segmentation problems. Motivating applications are 3d yeast-cell reconstruction and segmentation of histology data.