On the absolute orientation problem in computer vision

An important problem in computer vision is to determine the orientation of a rigid body in an image. This can be accomplished by matching points or line segments that naturally appear on the object. Several elegant and computationally fast algorithms based on the singular value decomposition and quaternions have been introduced to solve this problem. In this article, the authors first examine the important special case of identifying the attitude of 2D objects and introduce a particularly elegant solution based on the mathematical structure of the complex plane. Motivated by this simple solution to the 2D case, a new derivation of the 3D case based on the polar decomposition is presented. This derivation is in many ways more natural than previous derivations, particularly when the model and data contain no noise.