1 - Algorithmes optimaux pour la génération de pyramides d'images passe-bas et laplaciennes

Multiple resolution representations are often used in computer vision, as they provide a natural way for describing an image by a hierarchy of structures . However, because of the resampling process, the images they provide are corrupted by an aliasing noise which makes difficult the detection of structures, specially when the detection process implies the computation of derivatives. Choosing the filtering kernel is thus essential . Paradoxically, the importance of proper signal-to-noise analysis have been widely neglected by the vision community . In this paper, we study two commonly used algorithme from the point of view of the aliasing noise they create. Then we propose an optimum filtering kernel which minimizes the aliasing noise, does not create new structures, has interesting properties of rotational symmetry and reduced computation cost . We also propose a fast algorithm for the computation of low-pass and laplacian octave-spaced pyramids .