Deeper understanding of the homography decomposition for vision-based control

Abstract

The displacement of a calibrated camera between two images of a planar object
\ncan be estimated by decomposing a homography matrix. The aim of this document is to
\npropose a new method for solving the homography decomposition problem. This new method
\nprovides analytical expressions for the solutions of the problem, instead of the traditional
\nnumerical procedures. As a result, expressions of the translation vector, rotation matrix and
\nobject-plane normal are explicitly expressed as a function of the entries of the homography
\nmatrix. The main advantage of this method is that it will provide a deeper understanding
\non the homography decomposition problem. For instance, it allows to obtain the relations
\namong the possible solutions of the problem. Thus, new vision-based robot control laws can
\nbe designed. For example the control schemes proposed in this report combine the two final
\nsolutions of the problem (only one of them being the true one) assuming that there is no a
\npriori knowledge for discerning among them.