Estimation of Nonlinear Errors-in-Variables Models for Computer Vision Applications

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 28; no. 10; pp. 1537 - 1552
• Main Authors: Matei, B.C., Meer, P.
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.10.2006; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 3D rigid motion; Additive noise; Algorithms; Application software; Applied sciences; Artificial Intelligence; camera calibration; Computer errors; Computer science; control theory; systems; Computer Simulation; Computer Society; Computer vision; Data Interpretation, Statistical; Estimating; Estimation error; Estimators; Exact sciences and technology; heteroscedastic regression; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Information Storage and Retrieval - methods; Mathematical analysis; Mathematical model; Mathematical models; Models, Statistical; Noise; Noise measurement; Noise reduction; Nonlinear Dynamics; Nonlinear least squares; Nonlinearity; Pattern Recognition, Automated - methods; Pattern recognition. Digital image processing. Computational geometry; Q measurement; Reproducibility of Results; Sensitivity and Specificity; Tasks; uncalibrated vision; Computer vision; Error estimation; camera calibration; uncalibrated vision; Calibration; 3D rigid motion; Intelligent agent; heteroscedastic regression; Heteroscedasticity; Least squares method; Non linear model; Renormalization; Nonlinear least squares; Pattern analysis; Moving body
• ISSN: 0162-8828; 1939-3539; 2160-9292
• DOI: 10.1109/TPAMI.2006.205

In an errors-in-variables (EIV) model, all the measurements are corrupted by noise. The class of EIV models with constraints separable into the product of two nonlinear functions, one solely in the variables and one solely in the parameters, is general enough to represent most computer vision problems. We show that the estimation of such nonlinear EIV models can be reduced to iteratively estimating a linear model having point dependent, i.e., heteroscedastic, noise process. Particular cases of the proposed heteroscedastic errors-in-variables (HEIV) estimator are related to other techniques described in the vision literature: the Sampson method, renormalization, and the fundamental numerical scheme. In a wide variety of tasks, the HEIV estimator exhibits the same, or superior, performance as these techniques and has a weaker dependence on the quality of the initial solution than the Levenberg-Marquardt method, the standard approach toward estimating nonlinear models