Estimation of the Epipole using Optical Flow at Antipodal Points

This paper develops an algorithm for estimating the epipole or direction of translation of a moving monocular observer. To this end, we use constraints arising from two points that are antipodal on the image sphere. The antipodal point condition is necessary for decoupling rotation from translation. One such pair of points constrains the epipole to lie on a plane, and using two pairs of points, we have two such planes. The intersection of these two planes gives an estimate of the epipole. This means we require image motion measurements at two pairs of antipodal points to obtain an estimate. Repeating this will yield a set of possible solutions and a variety of methods could be applied to obtain a robust and refined estimate from this set. One robust and simple method is chosen for illustrative purposes and results on real images are shown. With real sequences, results of below 2deg error in the estimate of the epipole can be obtained. Since antipodal points on an image sphere are required, this algorithm must use some kind of omnidirectional or large field-of-view (FOV) sensor.