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.
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