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Related Experiment Videos

Maximum-likelihood estimation of circle parameters via convolution.

Emanuel E Zelniker1, I Vaughan L Clarkson

  • 1School of Information Technology and Electrical Engineering, University of Queensland Queensland, 4072, Australia.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|April 4, 2006
PubMed
Summary

This study interprets circle fitting estimators as image convolutions. A novel convolution-based maximum-likelihood estimator (MLE) provides accurate circle parameter estimates in digital images, achieving subpixel accuracy.

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Area of Science:

  • Computer Vision
  • Image Processing
  • Computational Geometry

Background:

  • Accurate circle fitting to noisy data is a significant challenge in image analysis.
  • Existing methods like Maximum-Likelihood Estimator (MLE) and Delogne-Kåsa Estimator (DKE) have limitations in digital image applications.

Purpose of the Study:

  • To interpret MLE and DKE for circle parameter estimation as image convolutions.
  • To develop a convolution-based MLE approach for robust circle fitting in digital images.
  • To investigate the relationship between phase-coded kernels (PCK) and MLE for improved accuracy.

Main Methods:

  • Interpreting circle fitting estimators (MLE, DKE) via image convolution.
  • Developing a convolution-based MLE for estimating circle parameters in digital images.

Related Experiment Videos

  • Analyzing the convolution of ideal images with phase-coded kernels (PCK).

    • Main Results:

    • The convolution-based MLE approach yields effective preliminary estimates for circle parameters in digital images.
    • The phase-coded kernel (PCK) is shown to be an approximate MLE (AMLE).
    • The AMLE method demonstrates comparable or superior performance to MLE, DKE, and Cramér-Rao Lower Bound in various image types.

    Conclusions:

    • The convolution-based MLE offers a novel and effective method for circle parameter estimation in digital images.
    • The AMLE, derived from PCK convolution, provides a practical and accurate alternative for subpixel circle fitting.
    • This work bridges theoretical estimation principles with practical image processing techniques for enhanced accuracy.