(2)Department of Electrical and Computer Engineering
Rutgers University, Piscataway, NJ 08854-8058, USA
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.
