A Depth-Compatible Multiscale Analysis of Movies

Using an axiomatic formulation, we devise a diiusion equation on movies that preserves the 3D structure of objects, an interesting property for depth recovery tasks. Since this equation presents a strong singularity and is not handled by the classical theory of viscosity solutions, we study the existence and unicity of weak solutions, and point out some properties, including a variational interpretation. Last, we propose a very simple numerical scheme based on inf-sup operators and show some experiments on a real movie.