×

zbMATH — the first resource for mathematics

Translation and scale invariants of Tchebichef moments. (English) Zbl 1120.68094
Summary: Discrete orthogonal moments such as Tchebyshev moments have been successfully used in the field of image analysis. However, the invariance property of these moments has not been studied mainly due to the complexity of the problem. Conventionally, the translation and scale invariant functions of Tchebyshev moments can be obtained either by normalizing the image or by expressing them as a linear combination of the corresponding invariants of geometric moments. In this paper, we present a new approach that is directly based on Tchebyshev polynomials to derive the translation and scale invariants of Tchebyshev moments. Both derived invariants are unchanged under image translation and scale transformation. The performance of the proposed descriptors is evaluated using a set of binary characters. Examples of using the Tchebyshev moments invariants as pattern features for pattern classification are also provided.

MSC:
68T10 Pattern recognition, speech recognition
68U10 Computing methodologies for image processing
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hu, M.K., Visual pattern recognition by moment invariants, IRE trans. inform. theory, IT-8, 179-187, (1962) · Zbl 0102.13304
[2] Liu, J.; Zhang, T.X., Fast algorithm for generation of moment invariants, Pattern recognition, 37, 1745-1756, (2004) · Zbl 1070.68587
[3] Zhu, Y.; De Silva, L.C.; Ko, C.C., Using moment invariants and HMM in facial expression, Pattern recognition lett., 23, 83-91, (2002) · Zbl 0996.68167
[4] Lin, C.Y.; Wu, M.; Bloom, J.A.; Cox, I.J.; Miller, M.L.; Lui, Y.M., Rotation, scale, and translation resilient watermaking for images, IEEE trans. image process., 10, 767-782, (2001) · Zbl 1037.68778
[5] Gope, C.; Kehtarnavaz, N.; Hillman, G.; Wursig, B., An affine invariant curve matching method for photo-identification of marine mammals, Pattern recognition, 38, 125-132, (2005)
[6] Sheynin, S.; Tuzikov, A., Moment computation for objects with spline curve boundary, IEEE trans. pattern anal. Mach. intel., 25, 1317-1322, (2003)
[7] Luo, L.M.; Hamitouche, C.; Dilleseger, J.L.; Coatrieux, J.L., A moment-based three-dimensional edge operator, IEEE. trans. biomed. eng., 40, 693-703, (1993)
[8] Kan, C.; Srinath, M.D., Combined features of cubic B-spline wavelet moments and Zernike moments for invariant character recognition, (), 511-515
[9] -H Teh, C.; Chin, R.T., On image analysis by the method of moments, IEEE trans. pattern anal. Mach. intel., 10, 496-513, (1988) · Zbl 0709.94543
[10] Mukundan, R.; Ramakrishnan, K.R., Moment functions in image analysis—theory and applications, (1998), World Scientific Singapore · Zbl 0998.94506
[11] Teague, M.R., Image analysis via the general theory of moments, J. opt. soc. amer., 70, 920-930, (1980)
[12] Mukundan, R.; Ramakrishnan, K.R., Fast computation of Legendre and Zernike moments, Pattern recognition, 28, 1433-1442, (1995)
[13] Shu, H.Z.; Luo, L.M.; Bao, X.D.; Yu, W.X., An efficient method for computation of Legendre moments, Graph. models, 62, 237-262, (2000)
[14] Nassery, P.; Faez, K., Signature pattern recognition using pseudo-Zernike moments and a fuzzy logic classifier, (), 197-200
[15] Liao, S.X.; Pawlak, M., On image analysis by moments, IEEE trans. pattern anal. Mach. intel., 18, 254-266, (1996)
[16] Palaniappan, R.; Raveendran, P.; Omatu, S., New invariant moments for non-uniformly scaled images, Pattern anal. appl., 3, 78-87, (2000)
[17] Miao, Z.J., Zernike moment-based image shape analysis and its application, Pattern recognition lett., 20, 169-177, (2000)
[18] Flusser, J., On the independence of rotation moment invariants, Pattern recognition, 33, 1405-1410, (2000)
[19] Khotanzad, A., Invariant image recognition by Zernike moments, IEEE trans. pattern anal. Mach. intel., 12, 489-497, (1990)
[20] Palaniappan, R.; Raveendran, P.; Omatu, S., New invariant moments for non-uniformly scaled images, Pattern anal. appl., 3, 78-87, (2000)
[21] Chong, C.-W.; Raveendran, P.; Mukundan, R., Translation invariants of Zernike moments, Pattern recognition, 36, 1765-1773, (2003) · Zbl 1055.68135
[22] Chong, C.-W.; Raveendran, P.; Mukundan, R., Translation and scale invariants of Legendre moments, Pattern recognition, 37, 119-129, (2004) · Zbl 1067.68593
[23] Chong, C.-W.; Raveendran, P.; Mukundan, R., The scale invariants of pseudo-Zernike moments, Pattern anal. appl., 6, 176-184, (2003)
[24] Mukundan, R.; Ong, S.H.; Lee, P.A., Image analysis by tchebichef moments, IEEE trans. image process., 10, 1357-1364, (2001) · Zbl 1037.68782
[25] Yap, P.T.; Paramesran, R.; Ong, S.H., Image analysis by krawtchouk moments, IEEE trans. image process., 12, 1367-1377, (2003)
[26] Mukundan, R., A new class of rotational invariants using discrete orthogonal moments, (), 80-84
[27] Mukundan, R., Some computational aspects of discrete orthonormal moments, IEEE trans. image process., 13, 1055-1059, (2004)
[28] Comtet, L., Advanced combinatorics: the art of finite and infinite expansions, (1974), D. Reidel Publishing Company Dordrecht, Holland
[29] \(\langle\)http://www.mapsofworld.com/world-major-island.htm⟩.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.