Motion from Fixation

We study the problem of estimating rigid motion from a sequence of monocular perspective images obtained by navigating around an object while fixating a particular feature-point. The motivation comes from the mechanics of the human eye, which either pursues smoothly some fixation point in the scene, or `saccades? between different fixation points. In particular, we are interested in understanding whether fixation helps the process of estimating motion in the sense that it makes it more robust, better conditioned or simpler to solve.We cast the problem in the framework of `Epipolar geometry?, and propose a filter based upon an implicit dynamical model for recursively estimating motion under the fixation constraint. This allows us to compare directly the quality of the estimates of motion obtained by imposing the fixation constraint against the estimates obtained assuming a general rigid motion simply by changing the geometry of the parameter space, while maintaining the same structure of the recursive estimator. We also present a closed-form static solution from two views, a recursive estimator of the relative attitude between the viewer and the scene and assess how the estimates degrade in the presence of disturbances in the tracking procedure. All recursive filters are suitable for real-time implementation.