Optimal Estimation of Homogeneous Vectors

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 (exceptions are usually caused by model restrictions, e.g. affine motion model). This justifies to examine homogeneous estimation schemes on a more theoretical level. 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 (i.e. it does not need data normalization) and shows better stabil...

• Type: Conference
• Year: 2005
• Where: SCIA
• Authors: Matthias Mühlich, Rudolf Mester
• Keywords: Estimation, Estimation Schemes, Homogeneous Estimation, SCIA 2005