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Estimation of Nonlinear Errors-in-Variables Models for Computer Vision Applications
October 2006 (vol. 28 no. 10)
pp. 1537-1552
Bogdan C. Matei, IEEE Computer Society
Peter Meer, IEEE
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.

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Index Terms:
Nonlinear least squares, heteroscedastic regression, camera calibration, 3D rigid motion, uncalibrated vision.
Bogdan C. Matei, Peter Meer, "Estimation of Nonlinear Errors-in-Variables Models for Computer Vision Applications," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp. 1537-1552, Oct. 2006, doi:10.1109/TPAMI.2006.205
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