Linear Osmosis Models for Visual Computing

Abstract

Osmosis is a transport phenomenon that is omnipresent in nature. It differs from diffusion by the fact that it allows nonconstant steady states. In our paper we lay the foundations of osmosis filtering for visual computing applications. We model filters with osmotic properties by means of linear drift-diffusion processes. They preserve the average grey value and the nonnegativity of the initial image. Most interestingly, however, we show how the nonconstant steady state of an osmosis evolution can be steered by its drift vector field. We interpret this behaviour as a data integration mechanism. In the integrable case, we characterise the steady state as a minimiser of a suitable energy functional. In the nonintegrable case, we can exploit osmosis as a framework to fuse incompatible data in a visually convincing way. Osmotic data fusion differs from gradient domain methods by its intrinsic invariance under multiplicative grey scale changes. The osmosis framework constitutes a novel class of methods that can be taylored to solve various problems in image processing, computer vision, and computer graphics. We demonstrate its versatility by proposing osmosis models for compact image respresentation, shadow removal, and seamless image cloning.