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

Bogdan C Matei1, Peter Meer

  • 1Vision Technologies Laboratory, Sarnoff Corporation, 201 Washington Road, Princeton, NJ 08540, USA. bmatei@sarnoff.com

IEEE Transactions on Pattern Analysis and Machine Intelligence
|September 22, 2006
PubMed
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This study introduces a new method for estimating nonlinear errors-in-variables (EIV) models, common in computer vision. The heteroscedastic errors-in-variables (HEIV) estimator offers robust performance and handles noisy measurements effectively.

Area of Science:

  • Computer Vision
  • Statistical Modeling
  • Optimization

Background:

  • Errors-in-variables (EIV) models are prevalent in computer vision, where measurements are inherently noisy.
  • Many computer vision problems can be framed as nonlinear EIV models with separable constraints.
  • Existing methods for estimating these models often struggle with noise and initial solution sensitivity.

Purpose of the Study:

  • To develop a robust and efficient estimation method for a general class of nonlinear EIV models.
  • To demonstrate that nonlinear EIV estimation can be simplified by reducing it to iteratively estimating a linear model with heteroscedastic noise.
  • To introduce the heteroscedastic errors-in-variables (HEIV) estimator.

Main Methods:

  • The proposed method iteratively estimates a linear model with point-dependent (heteroscedastic) noise.

Related Experiment Videos

  • The HEIV estimator is derived from this iterative linear estimation process.
  • The performance of HEIV is compared against established techniques like Sampson, renormalization, and Levenberg-Marquardt.

    • Main Results:

    • The HEIV estimator demonstrates comparable or superior performance to existing methods across various tasks.
    • HEIV shows a reduced dependence on the quality of the initial solution compared to the Levenberg-Marquardt method.
    • The method effectively handles noisy measurements in nonlinear EIV models.

    Conclusions:

    • The HEIV estimator provides a powerful new tool for addressing nonlinear EIV problems in computer vision.
    • This approach simplifies complex nonlinear estimation by transforming it into a series of linear estimations with specific noise characteristics.
    • HEIV offers a more robust and reliable alternative to current estimation techniques, particularly when dealing with noisy data and sensitive initial conditions.