A novel approach to the fast computation of Zernike moments

Sun Kyoo Hwang, Whoi-Yul Kim

Research output: Contribution to journalArticle

143 Citations (Scopus)

Abstract

This paper presents a novel approach to the fast computation of Zernike moments from a digital image. Most existing fast methods for computing Zernike moments have focused on the reduction of the computational complexity of the Zernike 1-D radial polynomials by introducing their recurrence relations. Instead, in our proposed method, we focus on the reduction of the complexity of the computation of the 2-D Zernike basis functions. As Zernike basis functions have specific symmetry or anti-symmetry about the x-axis, the y-axis, the origin, and the straight line y = x, we can generate the Zernike basis functions by only computing one of their octants. As a result, the proposed method makes the computation time eight times faster than existing methods. The proposed method is applicable to the computation of an individual Zernike moment as well as a set of Zernike moments. In addition, when computing a series of Zernike moments, the proposed method can be used with one of the existing fast methods for computing Zernike radial polynomials. This paper also presents an accurate form of Zernike moments for a discrete image function. In the experiments, results show the accuracy of the form for computing discrete Zernike moments and confirm that the proposed method for the fast computation of Zernike moments is much more efficient than existing fast methods in most cases.

Original languageEnglish
Pages (from-to)2065-2076
Number of pages12
JournalPattern Recognition
Volume39
Issue number11
DOIs
StatePublished - 2006 Nov 1

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Polynomials
Computational complexity
Experiments

Keywords

  • Discrete Zernike moments
  • Fast method
  • Symmetry/anti-symmetry
  • Zernike moments

Cite this

Hwang, Sun Kyoo ; Kim, Whoi-Yul. / A novel approach to the fast computation of Zernike moments. In: Pattern Recognition. 2006 ; Vol. 39, No. 11. pp. 2065-2076.
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A novel approach to the fast computation of Zernike moments. / Hwang, Sun Kyoo; Kim, Whoi-Yul.

In: Pattern Recognition, Vol. 39, No. 11, 01.11.2006, p. 2065-2076.

Research output: Contribution to journalArticle

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