Estimation of nonlinear errors-in-variables models for computer vision applications

Bogdan C. Matei, Peter Meer

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1537-1552
Number of pages16
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number10
StatePublished - 2006

All Science Journal Classification (ASJC) codes

  • Software
  • Artificial Intelligence
  • Applied Mathematics
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics


  • 3D rigid motion
  • Camera calibration
  • Heteroscedastic regression
  • Nonlinear least squares
  • Uncalibrated vision


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