Robust estimation of egomotion from normal flow

Abstract

This paper investigates the robustness of an algorithm due to Horn and Weldon (1988) for recovery of egomotion from optic-flow. Assuming only normal components of flow vectors are availableand that 3D angular velocity is known, tight constraints can be constructed on the direction of translational motion or, equivalently, on the focus of expansion. In practice however this is unacceptably restrictive. Some allowance must be made for uncertainty in angular velocity. We show that the algorithm can indeed be extended to cope with such uncertainty with graceful degradation in accuracy of estimated position of the focus of expansion. The shape of the error distribution depends on whether the focus of expansion is inside or outside the field of view. If it is inside, the error distribution is isotropic. As it moves outside the distribution becomes increasingly anisotropic. Results from an implementation of the algorithm confirm the validity of the error bounds.