Additive Operator Splittings
An efficient numerical approach for the acceleration of algorithms is the use of so called splitting schemes. They allow for a decomposition of a single problem into multiple problems that offer certain advantages compared to the original one. In general, the resulting problems can be solved very efficiently with standard numerical methods. Some of them even offer advantages regarding a possible parallelisation.
Our research mainly focuses on additive operator splitting (AOS) schemes
(Lu et al. 1991), which have the advantage over multiplicative splittings
that the result does not depend on the order in which the operators are
applied. In  such an AOS
scheme has been introduced to the image processing and computer vision
community. Apart from nonlinear diffusion filtering,
variants for regularisation methods 
and optic flow computation  have been
developed. We have also used AOS schemes successfully in the context of
active contour models .