A study of Zernike moment computing
In this paper, we address a detailed analysis of the accuracy of Zernike moment computing in terms of its discretization error. It is found that there is an inherent limitation in the precision of computing the Zernike moment due to the geometric nature of a circular domain. This is explained by relating the accuracy issue to a celebrated problem in analytic number theory of evaluating the lattice points within a circle. We illustrate our theory by various numerical studies including the image reconstruction.
Unable to display preview. Download preview PDF.
- 1.H. Engels, Numerical Quadrature and Cubature. London: Academic Press Inc., 1980.Google Scholar
- 2.G.H. Hardy and E. Landau, “The lattice points of a circle”, Proc. Royal Soc. (A), 105 (1924), pp. 245–258.Google Scholar
- 3.M.K. Hu, “Visual problem recognition by moment invariant”, IRE Trans. Inform. Theory, vol. IT-8, pp. 179–187, Feb. 1962.Google Scholar
- 4.A. Khotanzad and Y.H. Hong, “Invariant image recognition by Zernike moments”, IEEE Trans. Pattern Anal. Mach. Intelligence PAMI-12, 1990, pp. 489–498.Google Scholar
- 5.H. Iwaniec and C.J. Mozzochi, “On the divisor and circle problems”, Journal of Number Theory, 29 (1988), pp. 60–93.Google Scholar
- 6.S. X. Liao, Image Analysis by Moments, Ph. D. dissertation, The University of Manitoba, 1993.Google Scholar
- 7.S. X. Liao and M. Pawlak, “On image analysis by moments”, IEEE Trans.Pattern Anal. Machine Intell., vol. PAMI-18, pp. 254–266, 1996.Google Scholar
- 8.M. Pawlak, “On the reconstruction aspects of moment descriptors”, IEEE Trans. Information Theory, vol. 38, No. 6, pp. 1698–1708, November, 1992.Google Scholar
- 9.M.R. Teague, “Image analysis via the general theory of moments”, J. Optical Soc. Am., vol. 70, pp. 920–930, August 1980.Google Scholar
- 10.C.H. Teh and R.T. Chin, “On image analysis by the methods of moments”, IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-10, pp. 496–512, July 1988.Google Scholar
- 11.F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode”, Physica, vol. 1, p. 689–701, 1934. *** DIRECT SUPPORT *** A0008188 00014Google Scholar