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

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 ^A and ^b to a given data matrix [A, b] perturbed by additive Gaussian noise, such that there exists a solution y with [A + ^A, b + ^b]y = 0. In practice, regression imposes a more restrictive constraint namely the existence of a solution x with [A + ^A]x = [b + ^b]. 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 ^A,^b 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 Gr?obner basis. Results for plane fitting and opti...

• Type: Conference
• Year: 2008
• Where: CVPR
• Authors: Björn Andres, Claudia Kondermann, Daniel Kondermann, Ullrich Köthe, Fred A. Hamprecht, Christoph S. Garbe
• Keywords: Additive Gaussian Noise, Computer Vision, CVPR 2008, Definite Covariance Matrices, Linear Inverse Problems, Maximum Likelihood Estimator, Optical Flow Computation