A Paraperspective Factorization Method for Shape and Motion Recovery

Abstract

The factorization method, first developed by Tomasi and Kanade, recovers both the shape of an object and its motion from a sequence of images, using many images and tracking many feature points to obtain highly redundant feature position information. The method robustly processes the feature trajec-tory information using singular value decomposition (SVD), taking advantage of the linear algebraic properties of orthographic projection. However, an orthographic formulation limits the range of motions the method can accommodate. Paraperspective projection, first introduced by Ohta, is a projection model that closely approximates perspective projection by modelling several effects not modelled under orthographic projection, while retaining linear algebraic properties. Our paraperspective factorization method can be applied to a much wider range of motion scenarios, such as image sequences containing significant translational motion toward the camera or across the image. The method also can accommo-date missing or uncertain tracking data, which occurs when feature points are occluded or leave the field of view. We present the results of several experiments which illustrate the method?s performance in a wide range of situations, including an aerial image sequence of terrain taken from a low-altitude air-plane.