This paper presents a factorization method for recovering scene geometry and camera motion from a sequence of images. The method is based on the rank theorem, which states that under orthographic projection, the measurement matrix of an image stream is of rank 3. This allows the matrix to be factored into two matrices representing object shape and camera motion. The method can handle partially filled measurement matrices, which occur when features appear and disappear due to occlusions or tracking failures. It does not introduce smoothing in either shape or motion and provides accurate results. The method is demonstrated with experiments on both laboratory and outdoor image streams, with and without occlusions. The factorization method is robust and can handle short intervals between frames, making feature tracking easier. The method is related to previous work on structure from motion, but it differs in that it uses world-centered coordinates rather than camera-centered ones, which simplifies the problem and avoids the need for retinotopic depth. The method is also robust to noise and can handle occlusions. The paper includes experiments on both controlled and outdoor environments, demonstrating the method's accuracy and robustness. The factorization method is based on singular value decomposition and is numerically stable. The method is able to recover shape and motion from a sequence of images without assuming a model of motion, such as constant translation or rotation. The method is able to handle occlusions and is robust to noise. The paper concludes that the rank theorem is both surprising and powerful, as it allows the recovery of shape and motion without assuming any specific motion or surface properties. The method is able to handle a wide range of image sequences and is robust to noise and occlusions. The research was sponsored by the U.S. Air Force.This paper presents a factorization method for recovering scene geometry and camera motion from a sequence of images. The method is based on the rank theorem, which states that under orthographic projection, the measurement matrix of an image stream is of rank 3. This allows the matrix to be factored into two matrices representing object shape and camera motion. The method can handle partially filled measurement matrices, which occur when features appear and disappear due to occlusions or tracking failures. It does not introduce smoothing in either shape or motion and provides accurate results. The method is demonstrated with experiments on both laboratory and outdoor image streams, with and without occlusions. The factorization method is robust and can handle short intervals between frames, making feature tracking easier. The method is related to previous work on structure from motion, but it differs in that it uses world-centered coordinates rather than camera-centered ones, which simplifies the problem and avoids the need for retinotopic depth. The method is also robust to noise and can handle occlusions. The paper includes experiments on both controlled and outdoor environments, demonstrating the method's accuracy and robustness. The factorization method is based on singular value decomposition and is numerically stable. The method is able to recover shape and motion from a sequence of images without assuming a model of motion, such as constant translation or rotation. The method is able to handle occlusions and is robust to noise. The paper concludes that the rank theorem is both surprising and powerful, as it allows the recovery of shape and motion without assuming any specific motion or surface properties. The method is able to handle a wide range of image sequences and is robust to noise and occlusions. The research was sponsored by the U.S. Air Force.