A morphological, affine, and Galilean invariant scale-space for movies

We study a model of multiscale analysis (or scale-space) applied to movies. This model comes from a thorough formalization that has been done in the theory of scale-space of static image. This formulation has led one to associate with each multiscale analysis a partial differential equation (PDE). We examine the case of movies, and insist on the motion aspects. More precisely, it has been proved by Alvarez, Guichard, Lions and Morel (1993) that there exists a unique affine and morphological and Galilean invariant scale-space for movies, the AMG model. This model is described by a partial differential equation. We focus on terms appearing in that equation. We show that this model provides a reliable definition of an optical multiscale acceleration. At the practical level, scale is interpreted as a way of characterizing reliable trajectories. As we prove by experiments, the AMG model is a riddle for decimating spurious trajectories due to any kinds of nonadditive impurities and noise. Simple discrete formulae are given to implement the model.