A Linear Algorithm for Motion from Three Weak Perspective Images Using Euler Angles

In this paper, we describe a new simple linear algorithm for motion and structure from three weak perspective projections using Euler angles. We first determine the epipolar equation between each pair of images, which determines the first and third Euler angles for the rotation between that pair of images, leaving only the second Euler angle undetermined. In the next step, combining the three rotations results in a very simple linear algorithm to determine the second Euler angles, up to a Necker reversal. Experimental results on synthetic and real images are presented. The degenerate cases are discussed. The program can be ftped from http://www.cv.cs.ritsumei.ac.jp/noriko/motion.html. Index Terms---Motion, structure, rotation matrix, Euler angles, epipolar equation, weak perspective projection. ------------------------ p ------------------------ 1 INTRODUCTION IT was shown by Ullman [7] that under orthographic projection, four correspondences in three distinct images are needed to ..