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. We cast the problem in the framework of "epipolar geometry", and propose a filter based upon implicit dynamical model for recursively estimating motion under the fixation constraint. This allows us to compare the quality of the estimates directly against the ones 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, and a recursive estimator of the relative pose between the viewer and the scene.