Multiscale analysis of movies for depth recovery

We reformulate the “shape from motion” problem in terms of movie processing: how to focus the redundant depth information of a noisy image sequence into a perfect depth-coherent movie? We give an answer in the simple case of a straight movement of the camera parallel to the focal plane. From an axiomatic approach, we deduce a unique multiscale analysis of movies compatible with the depth recovery, and study its properties both in the image and the scene space. In particular, we show that this movie filtering preserves the geometrical constraints satisfied by ideal movies of rigid 3D scenes. We also study a numerical scheme in agreement with the theoretical axioms: and produce some experiments on synthetic noisy movies