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Issue No.07 - July (2010 vol.32)
pp: 1259-1270
Pew-Thian Yap , Nanyang Technological University, Singapore
Xudong Jiang , Nanyang Technological University, Singapore
Alex Chichung Kot , Nanyang Technological University, Singapore
This paper introduces a set of 2D transforms, based on a set of orthogonal projection bases, to generate a set of features which are invariant to rotation. We call these transforms Polar Harmonic Transforms (PHTs). Unlike the well-known Zernike and pseudo-Zernike moments, the kernel computation of PHTs is extremely simple and has no numerical stability issue whatsoever. This implies that PHTs encompass the orthogonality and invariance advantages of Zernike and pseudo-Zernike moments, but are free from their inherent limitations. This also means that PHTs are well suited for application where maximal discriminant information is needed. Furthermore, PHTs make available a large set of features for further feature selection in the process of seeking for the best discriminative or representative features for a particular application.
Polar harmonic transforms, harmonic kernels, rotation invariance, Zernike moments, pseudo-Zernike moments, orthogonal moments.
Pew-Thian Yap, Xudong Jiang, Alex Chichung Kot, "Two-Dimensional Polar Harmonic Transforms for Invariant Image Representation", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.32, no. 7, pp. 1259-1270, July 2010, doi:10.1109/TPAMI.2009.119
[1] M. Teague, "Image Analysis via the General Theory of Moments," J. Optical Soc. Am., vol. 70, no. 8, pp. 920-930, Aug. 1980.
[2] 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, July 1988.
[3] D. Iskander, M. Collins, and B. Davis, "Optimal Modeling of Corneal Surfaces with Zernike Polynomials," IEEE Trans. Biomedical Eng., vol. 48, no. 1, pp. 87-95, Jan. 2001.
[4] H.S. Kim and H.-K. Lee, "Invariant Image Watermark Using Zernike Moments," IEEE Trans. Circuits and Systems for Video Technology, vol. 13, no. 8, pp. 766-775, Aug. 2003.
[5] N.H. Foon, Y.-H. Pang, A.T.B. Jin, and D.N.C. Ling, "An Efficient Method for Human Face Recognition Using Wavelet Transform and Zernike Moments" Proc. Int'l Conf. Computer Graphics, Imaging, and Visualization, pp. 65-69, July 2004.
[6] C. Kan and M.D. Srinath, "Invariant Character Recognition with Zernike and Orthogonal Fourier-Mellin Moments," Pattern Recognition, vol. 35, no. 1, pp. 143-154, Jan. 2002.
[7] L. Wang and G. Healey, "Using Zernike Moments for the Illumination and Geometry Invariant Classification of Multispectral Texture," IEEE Trans. Image Processing, vol. 7, no. 2, pp. 196-203, Feb. 1998.
[8] S. Ghosal and R. Mehrotra, "Detection of Composite Edges," IEEE Trans. Image Processing, vol. 3, no. 1, pp. 14-25, Jan. 1994.
[9] Y. Abu-Mostafa and D. Psaltis, "Recognitive Aspects of Moment Invariants," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 698-706, Nov. 1984.
[10] Y. Abu-Mostafa and D. Psaltis, "Image Normalization by Complex Moments," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 7, no. 1, pp. 46-55, Jan. 1985.
[11] H. Shu, L. Luo, and J.-L. Coatrieux, "Moment-Based Approaches in Imaging. Part 1: Basic Features," IEEE Eng. in Medicine and Biology Magazine, vol. 26, no. 5, pp. 70-74, Sept./Oct. 2007.
[12] J.-L. Coatrieux, "Moment-Based Approaches in Imaging. Part 2: Invariance," IEEE Eng. in Medicine and Biology Magazine, vol. 27, no. 1, pp. 81-83, Jan./Feb. 2008.
[13] J.-L. Coatrieux, "Moment-Based Approaches in Imaging. Part 3: Computational Considerations," IEEE Eng. in Medicine and Biology Magazine, vol. 27, no. 3, pp. 89-91, Aug. 2008.
[14] R. Mukundan and K. Ramakrishnan, Moment Functions in Image Analysis—Theory and Applications. World Scientific, 1998.
[15] H. Ren, A. Liu, J. Zou, D. Bai, and Z. Ping, "Character Reconstruction with Radial-Harmonic-Fourier Moments," Proc. Fourth Int'l Conf. Fuzzy Systems and Knowledge Discovery, vol. 3, pp. 307-310, Aug. 2007.
[16] A. Bhatia and E. Wolf, "On the Circle Polynomials of Zernike and Related Orthogonal Sets," Proc. Cambridge Philosophical Soc., vol. 50, pp. 40-48, 1954.
[17] Y. Sheng and L. Shen, "Orthogonal Fourier-Mellin Moments for Invariant Pattern Recognition," J. Optical Soc. Am. A, vol. 11, no. 6, pp. 1748-1757, June 1994.
[18] Y. Sheng and J. Duvernoy, "Circular Fourier-Radial Mellin Descriptors for Pattern Recognition," J. Optical Soc. Am. A, vol. 3, no. 6, pp. 885-888, June 1986.
[19] C.-W. Chong and R.P.R. Mukundan, "A Comparative Analysis of Algorithms for Fast Computation of Zernike Moments," Pattern Recognition, vol. 36, no. 3, pp. 731-742, 2003.
[20] M. Al Rawi, "Fast Zernike Moments," J. Real-Time Image Processing, vol. 3, nos. 1/2, pp. 89-96, Mar. 2008.
[21] J. Flusser and T. Suk, "Construction of Complete and Independent Systems of Rotation Moment Invariants," Computer Analysis of Images and Patterns, pp. 41-48, Springer, 2003.
[22] D. Jackson, Fourier Series and Orthogonal Polynomials, ch. VII and XI. Math. Assoc. Am., 1941.
[23] M. Novotni and R. Klein, "3D Zernike Descriptors for Content Based Shape Retrieval," Proc. Eighth ACM Symp. Solid Modeling and Applications, June 2003.
[24] N. Canterakis, "3D Zernike Moments and Zernike Affine Invariants for 3D Image Analysis and Recognition," Proc. 11th Scandinavian Conf. Image Analysis, pp. 85-93, 1999.
[25] T. Funkhouser, P. Min, M. Kazhdan, J. Chen, A. Halderman, D. Dobkin, and D. Jacobs, "A Search Engine for 3D Models," ACM Trans. Graphics, vol. 22, no. 1, pp. 83-105, 2003.
[26] C.H. Lo and H.S. Don, "3-D Moment Forms: Their Construction and Application to Object Identification and Positioning," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 10, pp. 1053-1064, Oct. 1989.
[27] S. Liao and M. Pawlak, "On the Accuracy of Zernike Moments for Image Analysis," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 12, pp. 1358-1364, Dec. 1998.
[28] Y. Freund and R.E. Schapire, "1997, A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting," Proc. European Conf. Computational Learning Theory, pp. 23-37, 1995.
[29] R.E. Schapire, P.B.Y. Freund, and W.S. Lee, "Boosting the Margin: A New Explanation for the Effectiveness of Voting Methods," Proc. 14th Int'l Conf. Machine Learning, pp. 322-330, 1997.
[30] P.-T. Yap, X.D. Jiang, and A. Kot, "Boosted Complex Moments for Discriminant Rotation Invariant Object Recognition," Proc. Int'l Conf. Pattern Recognition, pp. 1-4, 2008.
[31] J.Z. Wang, J. Li, and G. Wiederhold, "SIMPLIcity: Semantics-Sensitive Integrated Matching for Picture Libraries," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 9, pp. 947-963, Sept. 2001.
[32] Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, "Gradient-Based Learning Applied to Document Recognition," Proc. IEEE, vol. 86, no. 11, pp. 2278-2324, Nov. 1998.
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