Anisotropic diffusion using power watersheds

Many computer vision applications such as image filtering, segmentation and stereo-vision can be formulated as optimization problems. Whereas in previous decades continuous-domain, iterative procedures were common, recently discrete, convex, globally optimal methods have received a lot of attention. However not all problems in computer vision are convex, for instance L₀ norm optimization such as seen in compressive sensing. Recently, a novel discrete framework encompassing many known segmentation methods was proposed: power watershed. We are interested to explore the possibilities of this minimizer to solve other problems than segmentation, in particular with respect to unusual norms optimization. In this article we reformulate the problem of anisotropic diffusion as an L₀ optimization problem, and we show that power watersheds are able to optimize this energy quickly and effectively. This study paves the way for using the power watershed as a useful general-purpose minimizer in many different computer vision contexts.