Parametrizations of the Essential and the Fundamental Matrix based on Householder Transformations

In this paper we present a unified approach of decomposing the fundamental and the essential matrix using information about epipoles. In contrast to other methods our approach is based on Householder transformations and can deal with finite and infinite epipoles. Our decomposition is able to yield a minimal parametrization of the fundamental and the essential matrix and retains their characteristic properties. We give a geometrical interpretation and relate our approach to the singular value decomposition and to the epipolar line homography. Experiments show that our parametrization can be used as an alternative to existing ones in terms of speed and accuracy. Moreover, if epipoles are known a priori, our approach reduces the number of remaining parameters for determining the epipolar geometry of two images.