Subspace Estimation with Uncertain and Correlated Data

TLDR: A new method for improving total least squares (TLS) based estimation with suitably chosen weights is presented and it will be shown how to compute them for general noise models.

Abstract: Parameter estimation problems in computer vision can be modelled as fitting uncertain data to complex geometric manifolds. Recent research provided several new and fast approaches for these problems which allow incorporation of complex noise models, mostly in form of covariance matrices. However, most algorithms can only account for correlations within the same measurement. But many computer vision problems, e.g. gradient-based optical flow estimation, show correlations between different measurements. In this paper, we will present a new method for improving total least squares (TLS) based estimation with suitably chosen weights and it will be shown how to compute them for general noise models. The new method is applicable to a wide class of problems which share the same mathematical core. For demonstration purposes, we included experiments for ellipse fitting from synthetic data.