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An efficient method for the computation of Legendre moments.

Pew-Thian Yap1, Raveendran Paramesran

  • 1Department of Electrical Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia. ptyap@time.net.my

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Summary

This study introduces a novel method for calculating exact Legendre moments in digital images, reducing approximation errors. The new approach enhances image reconstruction accuracy compared to conventional techniques.

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Area of Science:

  • Image processing
  • Computer vision
  • Digital signal processing

Background:

  • Legendre moments are essential for image analysis but are prone to numerical errors in discrete spaces.
  • Existing methods often rely on approximations, leading to inaccuracies in moment values and reconstructed images.

Purpose of the Study:

  • To develop a method for computing exact Legendre moments by integrating Legendre polynomials over pixel intervals.
  • To reduce approximation errors inherent in discrete-space image analysis.
  • To improve the accuracy of image reconstruction using Legendre moments.

Main Methods:

  • Mathematical integration of Legendre polynomials over pixel intervals to derive exact moment values.
  • Comparison of the proposed method with conventional techniques for calculating Legendre moments.
  • Evaluation of image reconstruction quality using moments obtained from different methods.

Main Results:

  • The proposed method yields exact Legendre moment values that align with theoretical calculations.
  • Images reconstructed using these exact moments exhibit lower error than those from conventional methods.
  • The proposed method is computationally more efficient than deriving Legendre moments from geometric moments.

Conclusions:

  • The novel integration method accurately computes Legendre moments, overcoming discrete-space limitations.
  • This approach significantly improves image reconstruction fidelity and reduces computational overhead.
  • The findings offer a more precise and efficient way to utilize Legendre moments in image analysis.