Reducing "structure from motion"

The literature on recursive estimation of structure and motion from monocular image sequences comprises a large number of different models and estimation techniques. We propose a framework that allows us to derive and compare all models by following the idea of dynamical system reduction. The "natural" dynamic model, derived by the rigidity constraint and the perspective projection, is first reduced by explicitly decoupling structure (depth) from motion. Then implicit decoupling techniques are explored, which consist of imposing that some function of the unknown parameters is held constant. By appropriately choosing such a function, not only can we account for all models seen so far in the literature, but we can also derive novel ones. Casting all the different models in a common framework allows us to compare their geometric properties on common experimental grounds.