Optimal Estimation of Homogeneous Vectors

13 years 10 months ago

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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...

Matthias Mühlich, Rudolf Mester

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