A Flexible Solution to the Osmosis Equation for Seamless Cloning and Shadow Removal

The osmosis model is a parabolic equation reconstructing a composite image from an input generally given by the drift fields extracted from one or several images. This global model is sometimes a valid alternative to Poisson editing. It is particularly adapted to tasks where the input images' contrast vary wildly, as is the case for the application to shadow removal. In this paper we prove that the osmosis global parabolic equation can be advantageously be replaced by a stationary local elliptic equation. We state its existence and uniqueness result and give it a consistent numerical scheme. We stress three advantages of our numerical model: it yields fast local solvers applied on the regions of interest only. It gives a new flexibility for the boundary conditions, that can be mixed and therefore distinguish in the restoration cast shadows from shaded zones. Finally it maintains intact the target image outside its modified regions, which is not possible with the global model.