Computer Vision and Image Understanding Extracting Group Transformations from Image Moments

Image distortion induced by the relative motion between an observer and the scene is an important cue for recovering the motion and the structure of the scene. It is known that the distortion in images can be described by transformation groups, such as Euclidean, a ne and projective groups. In this paper, we investigate how the moments of image curves are changed by group transformations, and we derive a relationship between the change in image moments and the invariant vector elds of the transformation groups. The results are used to formalise a method for extracting invariant vector elds of a ne transformations from changes in the moments of orientation of curve segments in images. The method is applied to realtime robot visual navigation task.