Optimal estimation of homogeneous vectors

Abstract

Estimation of inhomogeneous vectors is well-studied in estimation theory. For instance, given covariance matrices of input data allow to compute optimal estimates and characterize their certainty. But a similar statement does not hold for homogeneous vectors and unfortunately, the majority of estimation problems arising in computer vision refers to such homogeneous vectors... The aim of this paper is twofold: First, we will describe several iterative estimation schemes for homogeneous estimation problems in a unified framework, thus presenting the missing link between those apparently different approaches. And secondly, we will present a novel approach called IETLS (for iterative equilibrated total least squares) which is insensitive to data preprocessing and shows better stability in presence of higher noise levels where other schemes often fail to converge. © Springer-Verlag Berlin Heidelberg 2005.