A Non-convex PDE Scale Space

For image filtering applications, it has been observed recently that both diffusion filtering and associated regularization models provide similar filtering properties. The comparison has been performed for regularization functionals with convex penalization functional. In this paper we discuss the relation between non-convex regularization functionals and associated time dependent diffusion filtering techniques (in particular the Mean Curvature Flow equation). Here, the general idea is to approximate an evolution process by a sequence of minimizers of iteratively convexified energy (regularization) functionals.