New closed-form solutions to image flow equations for EGO-motion applications considering variations of the focal distance

Ego-motion requires the determination of the position and trajectory of the moving vehicle just by analysing the sequence of images acquired along its movement. Here, we present an analytical procedure for the estimation of the three-dimensional kinematic parameters of the vehicle, and the depth map that describes the three-dimensional structure of the world that surrounds the acquisition camera (only monocular gray-level images are considered). Since we do not only consider the possibility of translational and rotational movement in the acquisition camera, but we also allow for variations in the focal distance of the lens (zoom), This proposal clearly extends the one proposed by Waxman et al. [IO]. Our proposed solution also provides the way to obtain an estimation of the variation of the focal distance that the camera has applied. The procedure is simple, and relies on the assumption of second order surface patches on the visualised objects.