1. A method of operating a video device, comprising: acquiring video data from a two-dimensional sensor of a succession of image frames; pre-stabilizing individual image frames in sequence by individually cropping image frames of the acquired video data in accordance with motion vectors between images of two preceding image frames; making a first calculation using a motion estimation algorithm based upon the acquired video data of a first set of quantities estimating motion of components of a current acquired image frame with respect to components of a another acquired image frame, said first calculation being made at least in part by passing the acquired video data though an electronic circuit that executes the given motion estimation algorithm; calculating an estimate of an overall motion of the current image frame with respect to said another image frame from the first set of quantities estimating motion of components of the current frame with respect to components of said another frame; modifying the acquired video data of the current image frame by the estimate of the overall motion of the current image frame with respect to said another image frame in a manner to provide data of a stabilized image frame; compressing the data of the stabilized image frame, including passing the data of the stabilized image frame through said electronic circuit to make a second calculation of a second set of quantities estimating motion of components of the current stabilized image frames with respect to another stabilized image frame by executing said given motion estimation algorithm; and storing the compressed data of the stabilized image frame.