A Rational Algebraic Formulation of the Problem of Relative Orientation

Abstract The problem of relative orientation involves the determination of the elements of at least one orthogonal matrix. Hitherto a difficulty has arisen in that, in this context, orthogonal matrices have not been expressed in terms of three independent parameters without the use of circular functions. In this paper a more tractable form of the orthogonal matrix is used to set up a rational algebraic equation expressing the relative orientation condition. This equation turns out to be of the third order in the five unknowns. A set of such equations may be solved by a rapidly converging process of iteration.