Coarse-to-fine low-rank structure-from-motion

We address the problem of deformable shape and motion recovery from point correspondences in multiple perspective images. We use the low-rank shape model, i.e. the 3D shape is represented as a linear combination of unknown shape bases. We propose a new way of looking at the low-rank shape model. Instead of considering it as a whole, we assume a coarse-to-fine ordering of the deformation modes, which can be seen as a model prior. This has several advantages. First, the high level of ambiguity of the original low-rank shape model is drastically reduced since the shape bases can not anymore be arbitrarily re-combined. Second, this allows us to propose a coarse-to-fine reconstruction algorithm which starts by computing the mean shape and iteratively adds deformation modes. It directly gives the sought after metric model, thereby avoiding the difficult upgrading step required by most of the other methods. Third, this makes it possible to automatically select the number of deformation modes as the reconstruction algorithm proceeds. We propose to incorporate two other priors, accounting for temporal and spatial smoothness, which are shown to improve the quality of the recovered model parameters. The proposed model and reconstruction algorithm are successfully demonstrated on several videos and are shown to outperform the previously proposed algorithms.