Stable, fast computation of high-order Zernike moments using a recursive method

Pattern Recognition

Volumn 56, Issue , 2016, Pages 16-25

  Deng, An Wen ^a   Wei, Chia Hung ^a,b   Gwo, Chih Ying ^a  

^a CHING YUN UNIVERSITY   (Taiwan)

^b TAIPEI MEDICAL UNIVERSITY   (Taiwan)

Author keywords

Farey sequence; Prata s method; q Recursive method; Zernike moments; Zernike radial polynomials

Indexed keywords

IMAGE PROCESSING; MEAN SQUARE ERROR; PATTERN RECOGNITION; POLYNOMIALS;

FAREY SEQUENCE; PRATA'S METHOD; RECURSIVE METHODS; ZERNIKE; ZERNIKE MOMENTS;

FEATURE EXTRACTION;

EID: 85011064028     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2016.02.014     Document Type: Article

References (28)

1. [1] Kim, W.Y., Kim, Y.S., A region-based shape descriptor using Zernike moments. Signal Process.: Image Commun. 16 (2000), 95–102.
2. [2] Novotni, M., Klein, R., Shape retrieval using 3D Zernike descriptors. Comput.-Aided Des. 36 (2004), 1047–1062.
3. [3] Bouziane, A., Chahir, Y., Molina, M., Jouen, F., Unified framework for human behaviour recognition: An approach using 3D Zernike moments. Neurocomputing 100 (2013), 107–116.
4. [4] Nagarajan, B., Devendran, V., Vehicle classification under cluttered background and mild occlusion using Zernike features. Procedia Eng. 30 (2012), 201–209.
5. [5] Zeng, Y., Lan, J., Han, C., Huang, K., Li, J., Shi, X., Aircraft recognition based on improved iterative threshold selection and skeleton Zernike moment. Opt. – Int. J. Light. Electron Opt. 125 (2014), 3733–3737.
6. [6] Elshoura, S.M., Megherbi, D.B., Analysis of noise sensitivity of Tchebichef and Zernike moments with application to image watermarking. J. Vis. Commun. Image Represent. 24 (2013), 567–578.
7. [7] Wang, X.Y., Ma, T.X., Niu, P.P., A pseudo-Zernike moment based audio watermarking scheme robust against desynchronization attacks. Comput. Electr. Eng. 37 (2011), 425–443.
8. [8] Yuan, X.C., Pun, C.M., Chen, C.L.P., Geometric invariant watermarking by local Zernike moments of binary image patches. Signal Process. 93 (2013), 2087–2095.
9. [9] Chen, B.J., Shu, H.Z., Zhang, H., Chen, G., Toumoulin, C., Dillenseger, J.L., Luo, L.M., Quaternion Zernike moments and their invariants for color image analysis and object recognition. Signal Process. 92 (2012), 308–318.
10. [10] Singh, C., Pooja, Improving image retrieval using combined features of Hough transform and Zernike moments. Opt. Lasers Eng. 49 (2011), 1384–1396.
11. [11] Radhika, K.R., Venkatesha, M.K., Sekhar, G.N., An approach for on-line signature authentication using Zernike moments. Pattern Recognit. Lett. 32 (2011), 749–760.
12. [12] Wee, C.Y., Paramesran, R., On the computational aspects of Zernike moments. Image Vis. Comput. 25 (2007), 967–980.
13. [13] Papakostas, G.A., Boutalis, Y.S., Karras, D.A., Mertzios, B.G., A new class of Zernike moments for computer vision applications. Inf. Sci. 177 (2007), 2802–2819.
14. [14] Wei, C.H., Li, Y., Chau, W.Y., Li, C.T., Trademark image retrieval using synthetic features for describing global shape and interior structure. Pattern Recognit. 42 (2009), 386–394.
15. [15] J. Haddadnia, M. Ahmadi, K. Faez, An efficient method for recognition of human faces using higher orders pseudo Zernike moment invariant, in: Proceedings of the Fifth IEEE International Conference on Automatic Face and Gesture Recognition IEEE, Washington, DC, USA, 2002, pp. 330–335.
16. [16] Gayathri, R., Ramamoorthy, P., Automatic palmprint identification based on high order Zernike moment. Am. J. Appl. Sci. 9 (2012), 759–765.
17. [17] Papakostas, G.A., Boutalis, Y.S., Papaodysseus, C.N., Fragoulis, D.K., Numerical error analysis in Zernike moments computation. Image Vis. Comput. 24 (2006), 960–969.
18. [18] Singh, C., Walia, E., Fast and numerically stable methods for the computation of Zernike moments. Pattern Recognit. 43 (2010), 2497–2506.
19. [19] Chong, C.W., Raveendran, P., Mukundan, R., A comparative analysis of algorithms for fast computation of Zernike moments. Pattern Recognit. 36 (2003), 731–742.
20. [20] Belkasim, S.O., Ahmadi, M., Shridhar, M., An efficient algirthm for fast computation of Zernike moments. IEEE 39th Midwest Symp., 1996, 1401–1404.
21. [21] Prata, A., Rusch, W.V.T., Algorithm for computation of Zernike polynomials expansion coefficients. Appl. Opt. 28 (1989), 749–754.
22. [22] Kintner, E.C., On the mathematical properties of the Zernike polynomials. Opt. Acta 23 (1976), 679–680.
23. [23] Qin, H., Qin, L., Xue, L., Yu, C., A parallel recurrence method for the fast computation of Zernike moments. Appl. Math. Comput. 219 (2012), 1549–1561.
24. [24] Shakibaei, B.H., Paramesran, R., Recursive formula to compute Zernike radial polynomials. Opt. Lett. 38 (2013), 2487–2489.
25. [25] Janssen, A.J.E.M., Dirksen, P., Computing Zernike polynomials of arbitrary degree using the discrete Fourier transform. J. Eur. Opt. Soc. – Rapid Publ. 2 (2007), 1–3.
26. [26] Li, S., Boyd, J.P., Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the symmetry group; Interpolation within a squircle, Part I. J. Comput. Phys. 258 (2014), 931–947.
27. [27] Apostol, T.M., Modular Functions and Dirichlet Series in Number Theory. 2nd ed., 1997, Springer, New York.
28. [28] Ogilvy, C.S., Anderson, J.T., Excursions in Number Theory. 1988, Dover Publications, Inc., New York.