Statistical Modelling of Epipolar Misalignment

We investigate whether epipolar misalignment can be automatically detected and corrected without explicit knowledge of point correspondences. In this regard, the work is closely related to the problem of structure-and-motion from two frames. However, the motion estimation described here is independent of any estimation of the structure of the scene and consequently is expected to be signiicantly more robust than structure-and-motion algorithms in which the number of unknowns is proportional to the number of pixels in the image. Instead, it may be thought of as forming the basis of a motion-without-structure algorithm, i.e. the solution requires neither knowledge nor estimation of structure or associated properties such as correspondences or ow elds, in order to estimate motion. Of course, structure may be determined by subsequent processing. In particular, we present a method for recovering camera motion for the special cases of (1) known rotation and (2) known translation. The method does not require optical ow elds, feature point correspondences or intensity derivatives. Instead, it relies on a simple statistical characteristic of neighbouring image intensity levels. Speciically, that the variance in intensity between two arbitrary points in an image increases (approximately) monotonically with distance between the two points. Then, it is shown that a simple measure taken across the image can yield a very robust measure of the likelihood of an estimated motion. The likelihood measure allows motion estimation to be cast as an eecient search over the space of possible rotations or translations. The relation between image statistics (textures, etc.) and the accuracy of the estimated motion is discussed and experimental results on real images are presented.