Visual motion estimation from point features: unified view

All methods for recursive estimation of 3-D motion from sequences of perspective images of point-features may be cast within a common framework. The unifying concept is the decoupling of the states of the dynamic observer that estimates motion and structure parameters. Two techniques are possible: explicit decoupling, following the principles of the "reduced-order observer", and implicit, via stabilization (or "compensation"). While we know how to calculate explicit decoupling for a limited number of state variables combinations, for instance using the "essential constraint" of Longuet-Higgins (1981) or the "subspace constraint" of Heeger and Jepson (1992), implicit decoupling is always possible by stabilizing an appropriate smooth function of the motion parameters. We describe some of the most "natural" choices, which consist in compensating for the image-motion of a point, a line or a plane. All the models we derive are in the form of implicit dynamical systems with parameters on different manifolds. Estimating motion may be regarded as the identification of such models, which may be carried out using general methods available in the literature.