Unbiased Errors-In-Variables Estimation Using Generalized Eigensystem Analysis

Recent research provided several new and fast approaches for the class of parameter estimation problems that are common in computer vision. Incorporation of complex noise model (mostly in form of covariance matrices) into errors-in-variables or total least squares models led to a considerable improvement of existing algorithms. However, most algorithms can only account for covariance of 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 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 have chosen ellipse fitting as a experimental example.