Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

In this presentation, we will explore the osmosis equation and their wide applications, initially focused on images and subsequently extended to surfaces. Osmosis is a transport phenomenon that is present in nature. It differs from diffusion by the fact that it allows non-constant steady states. We begin by introducing the osmosis equation as applied to images by presenting several applications such that shadow removal, compact data representation and seamless image cloning. Based on these results, we explore the potential of extending these osmosis-based applications to surface modeling. Therefore, we define the osmosis equation in the context of surfaces, we discretize the equation both in time and space allowing us to derive numerical results. One such application is shadow removal, where our osmosis approach reveals its ability to extract intricate details and provide realistic results.