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

We study a model of multiscale analysis (or scalespace) 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 to associate with each multiscale analysis a partial differential equation (PDE) [3], [18]. We intend here to examine the case of movies, and to insist on the motion aspects. More precisely, it has been proved in [3] 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. In this paper, 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.