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An Efficient Method for the Computation of Legendre Moments
December 2005 (vol. 27 no. 12)
pp. 1996-2002
ASCII Text
x 
 
Pew-Thian Yap, Raveendran Paramesran, "An Efficient Method for the Computation of Legendre Moments," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 12, pp. 1996-2002, December, 2005.
 
 
BibTex
x
 
@article{ 10.1109/TPAMI.2005.232,
author = {Pew-Thian Yap and Raveendran Paramesran},
title = {An Efficient Method for the Computation of Legendre Moments},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {27},
number = {12},
issn = {0162-8828},
year = {2005},
pages = {1996-2002},
doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.2005.232},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - An Efficient Method for the Computation of Legendre Moments
IS - 12
SN - 0162-8828
SP1996
EP2002
EPD - 1996-2002
A1 - Pew-Thian Yap,
A1 - Raveendran Paramesran,
PY - 2005
KW - Index Terms- Moments
KW - feature representation.
VL - 27
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 
Legendre moments are continuous moments, hence, when applied to discrete-space images, numerical approximation is involved and error occurs. This paper proposes a method to compute the exact values of the moments by mathematically integrating the Legendre polynomials over the corresponding intervals of the image pixels. Experimental results show that the values obtained match those calculated theoretically, and the image reconstructed from these moments have lower error than that of the conventional methods for the same order. Although the same set of exact Legendre moments can be obtained indirectly from the set of geometric moments, the computation time taken is much longer than the proposed method.

[1] M. Teague, “Image Analysis Via the General Theory of Moments,” J. Optical Soc. Am., vol. 70, pp. 920-930, Aug. 1980.
[2] C.-W. Chong, R. Paramesran, and R. Mukundan, “Translation and Scale Invariants of Legendre Moments,” Pattern Recognition, vol. 37, no. 1, pp. 119-129, 2004.
[3] M. Mandal, T. Aboulnasr, and S. Panchanathan, “Image Indexing Using Moments and Wavelets,” Proc. Int'l Conf. Consumer Electronics, Digest of Technical Papers, pp. 557-565, June 1996.
[4] J. Haddadnia, K. Faez, and P. Moallem, “Neural Network Based Face Recognition with Moment Invariants,” Proc. Int'l Conf. Image Processing, vol. 1, pp. 1018-1021, Oct. 2001.
[5] H. Qjidaa and L. Radouane, “Robust Line Fitting in a Noisy Image by the Method of Moments,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 11, pp. 1216-1223, Nov. 1999.
[6] R. Koekoek and R. Swarttouw, “The Askey-Scheme of Hypergeometric Orthogonal Polynomials and Its Q-Analogue,” Faculty of Technical Math. and Informatics Report 98-17, Delft, Netherlands: Technische Univ. Delft, pp. 46-47, 1998.
[7] A. Erdelyi, V. Magnus, F. Oberhettinger, and F. Tricomi, Higher Transcendental Functions. McGraw Hill, 1953.
[8] G. Szegö, Orthogonal Polynomials. New York: Am. Math. Soc., 1939.
[9] S. Liao, “Image Analysis by Moments,” PhD dissertation, Univ. of Manitoba, Winnipeg, Canada, 1993.
[10] S. Liao and M. Pawlak, “On Image Analysis by Moments,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 3, pp. 254-266, Mar. 1996.
[11] S.X. Liao and M. Pawlak, “On the Accuracy of Zernike Moments for Image Analysis,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 12, Dec. 1998.
[12] J.D. Zhou, H.Z. Shu, L.M. Luo, and W.X. Yu, “Two New Algorithms for Efficient Computation of Legendre Moments,” Pattern Recognition, vol. 35, no. 5, pp. 1143-1152, May 2002.
[13] H.Z. Shu, L.M. Luo, W.X. Yu, and J.D. Zhou, “Fast Computation of Legendre Moments of Polyhedra,” Pattern Recognition, vol. 34, no. 5, pp. 1119-1126, May 2001.
[14] H.Z. Shu, L.M. Luo, W.X. Yu, and Y. Fu, “A New Fast Method for Computing Legendre Moments,” Pattern Recognition, vol. 33, no. 2, pp. 341-348, Feb. 2000.
[15] R. Mukundan and K. Ramakrishnan, “Fast Computation of Legendre and Zernike Moments,” Pattern Recognition, vol. 28, no. 9, pp. 1433-1442, 1995.
[16] R. Mukundan and K.R. Ramakrishnan, Moment Functions in Image Analysis. Singapore: World Scientific Publishing, 1998.
[17] J. Shen and D. Shen, “Orthogonal Legendre Moments and Their Calculation,” Proc. 13th Int'l Conf. Pattern Recognition, pp. 241-245, 1996.
[18] C. Teh and R. Chin, “On Image Analysis by the Method of Moments,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 10, no. 4, pp. 496-513, 1988.
[19] E. Kreyszig, Advanced Engineering Mathematics, sixth ed. John Wiley and Sons, 1988.

Index Terms:
Index Terms- Moments, feature representation.
Citation:
Pew-Thian Yap, Raveendran Paramesran, "An Efficient Method for the Computation of Legendre Moments," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 12, pp. 1996-2002, Dec. 2005, doi:10.1109/TPAMI.2005.232
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