Motion from \x" by Compensating \y" a Uniied Framework for Motion Estimation from Image Sequences by Compensating for the Image-motion of a Point, a Line or a Plane

This paper analyzes the geometry of the visual motion estimation problem in relation to transformations of the input (images) that stabilize particular output functions such as the motion of a point, a line and a plane in the image. By casting the problem within the popular \epipolar geometry", we provide a common framework for including constraints such as point, line of plane xation by just considering \slices" of the parameter manifold. The models we provide can be used for estimating motion from a batch using the preferred optimization techniques, or for deening dynamic lters that estimate motion from a causal sequence. We discuss methods for performing the necessary compensation by either controlling the support of the camera or by pre-processing the images. The compensation algorithms may be used also for recursively tting a plane in 3-D both from point-features or directly from brightness. Conversely, they may be used for estimating motion relative to the plane independent of its parameters.