Estimating motion/geometry parameters using optical flow information is an important research issue in computer vision. A two-stage approach is often taken: first, computing a flow-field, and then estimating the motion/geometry parameters based on this field. The major shortcomings here are the high computational requirements and the low estimation accuracy, due to the artificial imposition of 'smoothness constraints' for flow computability. A one-stage approach is presented in this paper. The basic idea is that with a rigid imaged surface, image flow arises solely because of the sensor's self motion in both rotation and translation relative to the imaged world. By assuming simple sensor and world models, we can then establish constraint relationships between the motion/geometry parameters and the image intensity measurements, and then estimate, in a single stage, the optimal parameters that account for the observed image flow, in a least-squares modern estimation framework. This new approach simultaneously reduces computational requirements and improves overall estimation accuracy. Using computer generated imagery and actual video imagery, we demonstrate system performance across a range of system design and operational parameters.