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 trajectory 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 modeling several effects not modeled under orthographic projection, while retaining linear algebraic properties. Our paraperspective factorization method can be applied to a much wider range of motion scenarios, including image sequences containing motion toward the camera and aerial image sequences of terrain taken from a low-altitude airplane. Index Terms---Motion analysis, shape recovery, factorization method, three-dimensional vision, image sequence analysis, singular value decomposition. ------------------------------ F ------------------------------ 1I NTRODUCTION ECOVERING the geometry of a scene and the motion of the camera from a stream of images is an important task in a variety of applications, including navigation, robotic manipulation, and aerial cartography. While this is possible in principle, traditional methods have failed to produce reliable results in many situations [2]. Tomasi and Kanade [13], [14] developed a robust and efficient method for accurately recovering the shape and motion of an object from a sequence of images, called the factorization method. It achieves its accuracy and robustness by ...

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