On errors-in-variables regression with arbitrary covariance and its application to optical flow estimation

TitleOn errors-in-variables regression with arbitrary covariance and its application to optical flow estimation
Publication TypeConference Paper
Year of Publication2008
AuthorsAndres, B, Kondermann, C, Kondermann, D, Hamprecht, FA, Garbe, CS
Conference NameIEEE Conference on Computer Vision and Pattern Recognition, CVPR 2008
PublisherIEEE
Abstract

Linear inverse problems in computer vision, including motion estimation, shape fitting and image reconstruction, give rise to parameter estimation problems with highly correlated errors in variables. Established total least squares methods estimate the most likely corrections Acirc and bcirc to a given data matrix [A, b] perturbed by additive Gaussian noise, such that there exists a solution y with [A + Acirc, b +bcirc]y = 0. In practice, regression imposes a more restrictive constraint namely the existence of a solution x with [A + Acirc]x = [b + bcirc]. In addition, more complicated correlations arise canonically from the use of linear filters. We, therefore, propose a maximum likelihood estimator for regression in the general case of arbitrary positive definite covariance matrices. We show that Acirc, bcirc and x can be found simultaneously by the unconstrained minimization of a multivariate polynomial which can, in principle, be carried out by means of a Grobner basis. Results for plane fitting and optical flow computation indicate the superiority of the proposed method.

DOI10.1109/CVPR.2008.4587571
Citation Keyandres2008