Abstract
The rise of the digital imaging is remarkable, and the methods and techniques of image processing and analysis of the digital one must also accompany this technological evolution. In a line of research on the moments theory associated with digital imaging, values are extracted from digital images for the needs of classifications or even of reconstruction, as unique descriptors of an image, our work fits. In this paper, we propose a new method, fast and efficient, for calculating orthogonal moments on the discrete 3D image. We opted for the orthogonal polynomials of Meixner and for a new representation of the 3D image by cuboids having same gray levels called image cuboid representation. Based on this representation, we calculate the moments on each cuboid before summing all cuboids in order to obtain the global moments of a 3D image. Through a set of simulations, we prove that our method allows to reduce the time required for the calculation of moment on a 3D image of any size and any order, but not only, this method makes it possible to improve the quality of 3D image reconstruction from low-order moment.
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References
Zhu, H.: Image representation using separable two-dimensional continuous and discrete orthogonal moments. Pattern Recognit. 45, 1540–1558 (2012)
Rahmalan, H., Abu, N.A., Wong, S.L.: Using Tchebichef moment for fast and efficient image compression. Pattern Recognit. Image Anal. 20, 505–512 (2010)
Tsougenis, E.D., Papakostas, G.A., Koulouriotis, D.E.: Image watermarking via separable moments. Multimed. Tools Appl. 74, 3985–4012 (2015)
Hmimid, A., Sayyouri, M., Qjidaa, H.: Fast computation of separable two-dimensional discrete invariant moments for image classification. Pattern Recognit. 48, 509–521 (2015)
Mandal, M.K., Aboulnasr, T., Panchanathan, S.: Image indexing using moments and wavelets. IEEE Trans. Consum. Electron. 42(3), 557–565 (1996)
Sayyouri, M., Hmimid, A., Qjidaa, H.: Improving the performance of image classification by Hahn moment invariants. JOSA A 30(11), 2381–2394 (2013)
Flusser, J., Suk, T.: Pattern recognition by affine moment invariants. Pattern Recognit. 26, 167–174 (1993)
Liu, X.L., Han, G.N., Wu, J.S., Shao, Z.H., Coatrieux, G., Shu, H.Z.: Fractional Krawtchouk transform with an application to image watermarking. IEEE Trans. Signal Process. 65(7), 1894–1908 (2017)
Chen, B.J., Coatrieux, G., Wu, J.S., Dong, Z.F., Coatrieux, J.L., Shu, H.Z.: Fast computation of sliding discrete Tchebichef moments and its application in duplicated regions detection. IEEE Trans. Signal Process. 63(20), 5424–5436 (2015)
Wu, J.S., Qiu, S.J., Kong, Y.Y., Chen, Y., Senhadji, L., Shu, H.Z.: MomentsNet: a simple learning-free method for binary image recognition. In: 2017 IEEE International Conference on Image Processing, IEEE ICIP, pp. 2667–2671 (2017)
Hu, M.-K.: Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory 8(2), 179–187 (1962)
Hickman, M.S.: Geometric moments and their invariants. J. Math. Imaging Vis. 44(3), 223–235 (2012)
Teague, M.R.: Image analysis via the general theory of moments. J. Opt. Soc. Am. 70(8), 920–930 (1980)
Zhang, H., Shu, H., Han, G.-N., Coatrieux, G., Luo, L., Coatrieux, J.L.: Blurred image recognition by Legendre moment invariants. IEEE Trans. Image Process. 19(3), 596–611 (2010)
Wee, C.-Y., Paramesran, R.: Derivation of blur-invariant features using orthogonal Legendre moments. IET Comput. Vis. 1(2), 66–77 (2007)
Zhu, H., Liu, M., Ji, H., Li, Y.: Combined invariants to blur and rotation using Zernike moment descriptors. Pattern Anal. Appl. 3(13), 309–319 (2010)
Farokhi, S., Sheikh, U.U., Flusser, J., Yang, B.: Near infrared face recognition using Zernike moments and Hermite kernels. Inf. Sci. 316, 234–245 (2015)
Hosny, K.M.: Fast computation of accurate Gaussian–Hermite moments for image processing applications. Digit. Signal Process. 22(3), 476–485 (2012)
Hosny, K.M.: Image representation using accurate orthogonal Gegenbauer moments. Pattern Recognit. Lett. 32(6), 795–804 (2011)
Upneja, R., Singh, C.: Fast computation of Jacobi–Fourier moments for invariant image recognition. Pattern Recognit. 48(5), 1836–1843 (2015)
Wang, G., Wang, S.: Recursive computation of Tchebichef moment and its inverse transform. Pattern Recognit. 39(1), 47–56 (2006)
Chang, K.-H., Paramesran, R., Honarvar, B., Lim, C.-L.: Efficient hardware accelerators for the computation of Tchebichef moments. IEEE Trans. Circuits Syst. Video Technol. 22(3), 414–425 (2012)
Honarvar, B., Flusser, J.: Fast computation of Krawtchouk moments. Inf. Sci. 288, 73–86 (2014)
Zhang, L., Xiao, W.-W., Ji, Z.: Local affine transform invariant image watermarking by Krawtchouk moment invariants. IET Inf. Secur. 1(3), 97–105 (2007)
Yap, P.-T., Paramesran, R., Ong, S.-H.: Image analysis using Hahn moments. IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 2057–2062 (2007)
Wu, H., Yan, S.: Bivariate Hahn moments for image reconstruction. Int. J. Appl. Math. Comput. Sci. 24(2), 417–428 (2014)
Hmimid, A., Sayyouri, M., Qjidaa, H.: Image classification using a new set of separable two-dimensional discrete orthogonal invariant moments. J. Electron. Imaging 23(1), 013026 (2014)
Sayyouri, M., Hmimid, A., Qjidaa, H.: A fast computation of novel set of Meixner invariant moments for image analysis. Circuits Syst. Signal Process. 34(3), 875–900 (2015)
Papakostas, G.A., Karakasis, E.G., Koulouriotis, D.E.: Efficient and accurate computation of geometric moments on gray-scale images. Pattern Recognit. 41(6), 1895–1904 (2008)
Shu, H., Zhang, H., Chen, B., Haigron, P., Luo, L.: Fast computation of Tchebichef moments for binary and grayscale images. IEEE Trans. Image Process. 19(12), 3171–3180 (2010)
Honarvar, B., Paramesran, R., Lim, C.-L.: The fast recursive computation of Tchebichef moment and its inverse transform based on Z-transform. Digit. Signal Process. 23(5), 1738–1746 (2013)
Hwang, S.-K., Kim, W.-Y.: A novel approach to the fast computation of Zernike moments. Pattern Recognit. 39(11), 2065–2076 (2006)
Spiliotis, I.M., Mertzios, B.G.: Real-time computation of two-dimensional moments on binary images using image block representation. IEEE Trans. Image Process. 7(11), 1609–1615 (1998)
Fu, B., Zhou, J.-Z., Li, Y.-H., Peng, B., Liu, L.-Y., Wen, J.-Q.: Novel recursive and symmetric algorithm of computing two kinds of orthogonal radial moments. Image Sci. J. 56(6), 333–341 (2008)
Nikiforov, A.F., Suslov, S.K., Uvarov, B.: Classical orthogonal polynomials of a discrete variable. Springer, New York (1991)
Hmimid, A., Sayyouri, M., Qjidaa, H.: Image classification using novel set of Charlier moment invariants. WSEAS Trans. Signal Process. 10(1), 156–167 (2014)
Papakostas, G.A., Koulouriotis, D.E., Karakasis, E.G.: A unified methodology for the efficient computation of discrete orthogonal image moments. Inf. Sci. 179, 3619–3633 (2009)
http://www.cim.mcgill.ca/~shape/benchMark/airplane.html (2017). Accessed 31 July 2017
Wu, H., Coatrieux, J.L., Shu, H.: New algorithm for constructing and computing scale invariants of 3D Tchebichef moments. Math. Probl. Eng. 2013, 813606 (2013)
Karmouni, H., Hmimid, A., Jahid, T., Sayyouri, M., Qjidaa, H., Rezzouk, A.: Fast and stable computation of the Charlier moments and their inverses using digital filters and image block representation. Circuits Syst. Signal Process. 37, 4015–4033 (2018)
Jahid, T., Hmimid, A., Karmouni, H., Sayyouri, M., Qjidaa, H., Rezzouk, A.: Image analysis by Meixner moments and a digital filter. Multimed. Tools Appl. 77, 19811–19831 (2017)
Jain, A.K.: Fundamentals of Digital Image Processing. Information & Series. Prentice-Hall, Englewood Cliffs (1989)
Batioua, I., Benouini, R., Zenkouar, K., Zahi, A.: 3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials. Pattern Recognit. 71, 264–277 (2017)
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
Wang, Z., Bovik, A.C.: Mean squared error: love it or leave it? A new look at signal fidelity measures. IEEE Signal Process. Mag. 26(1), 98–117 (2009)
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Jahid, T., Karmouni, H., Sayyouri, M. et al. Fast Algorithm of 3D Discrete Image Orthogonal Moments Computation Based on 3D Cuboid. J Math Imaging Vis 61, 534–554 (2019). https://doi.org/10.1007/s10851-018-0860-7
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DOI: https://doi.org/10.1007/s10851-018-0860-7