We present a new method for solving the problem of motion segmentation, identifying the objects within an image moving independently of the background. We utilize the fact that two views of a static 3D point set are linked by a 3 X 3 Fundamental Matrix (F). The Fundamental Matrix contains all the information on structure and motion from a given set of point correspondences and is derived by a least squares method under the assumption that the majority of the image is undergoing a rigid motion. Least squares is the most commonly used method of parameter estimation in computer vision algorithms. However the estimated parameters from a least squares fit can be corrupted beyond recognition in the presence of gross errors or outliers which plague any data from real imagery. Features with a motion independent of the background are those statistically inconsistent from the calculated value of (F). Well founded methods for detecting these outlying points are described.