Abstract
Nowadays, with the increased use of digital images, almost all of which are in color format. Conventional methods process color images by converting them into gray scale, which is definitely not effective in representing and which may lose some significant color information. Recently, a novel method of the Color Angular Radial Transform (CART) is presented. This transform combines the information by considering the shape information inherent in the color. However, ART is adapted on the MPEG-7 standard is only limited to binary images and gray-scale images has many properties: invariant to rotation, Translation and scaling, ability to describe complex objects, so it cannot handle color images directly. To solve this problem we proposed in this article to generalize ART from complex domain to hypercomplex domain using quaternion algebras to achieve the Quaternion Angular Radial Transform (QART) to describe finally two dimensional color images and to insure these properties robustness to all possible rotations and translation and scaling. The performance of QART is then evaluated with large database of color image as an example. We first provide a general formula of ART from which we derive a set of quaternion-valued QART properties transformations by eliminating the influence of transformation parameters. The experimental results show that the QART performs better than the commonly used Quaternion form Zernike Moment (QZM) in terms of image representation capability and numerical stability.
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References
S. O. Belkasim, M. Shridhar, and M. Ahmadi, “Pattern recognition with moment invariants: a comparative study and new results,” Pattern Recogn. 24, 1117–1138 (1991).
S. O. Khotanzad and Y. H. Hong, “Invariant image recognition by Zernike moments,” IEEE Trans. Pattern Anal. Mach. Intell. 12 (5), 489–497 (1990).
T. K. Tsui, X. P. Zhang, and D. Androutsos, “Color image watermarking using multidimensional Fourier transforms,” IEEE Trans. Inf. Forensics Security 3 (1), 16–28 (2008).
Y. Xu, L. C. Yu, H. T Xu, H. Zhang, and T. Nguyen, “Vector sparse representation of color image using quaternion matrix analysis,” IEEE Trans. Image Processing 24 (4), 1315–1329 (2015).
Z. Wang and A. C. Bovik, “Modern image quality assessment,” Synth. Lectures Image, Video, Multimedia Process. 2 (1), 1–156 (2006).
F. Ahmed, M. Siyal, and V. U. Abbas, “A secure and robust hash-based scheme for image authentication,” Signal Process. 90 (5), 1456–1470 (2010).
D. S. Alexiadis and G. D. Sergiadis, “Estimation of motions in color image sequences using hypercomplex Fourier transforms,” IEEE Trans. Image Process. 18 (1), 168–187 (2009).
F. N. Lang, J. L. Zhou, S. Cang, H. Yu, and Z. Shang, “A self-adaptive image normalization and quaternion PCA based color image watermarking algorithm,” Expert Syst. Appl. 39 (15), 12046–12060 (2012).
B. J. Chen, G. Coatrieux, G. Chen, X. M. Sun, J. L. Coatrieux, and H. Z. Shu, “Full 4D quaternion discrete Fourier transform based watermarking for color images,” Digit. Signal Process. 28 (1), 106–119 (2014).
Z. H. Shao, H. Z. Shu, J. S. Wu, B. J. Chen, and J. L. Coatrieux, “Quaternion Bessel-fourier moments and their invariant descriptors for object reconstruction and recognition,” Pattern Recogn. 47 (2), 603–611 (2014).
O. N. Subakan and B. C. Vemuri, “A quaternion framework for color image smoothing and segmentation,” Int. J. Comput. Vision 91 (3), 233–250 (2011).
W. R. Hamilton, Elements of Quaternions (Longmans Green, London, 1866).
T. A. Ell, and S.J. Sangwine, “Hypercomplex Fourier transforms of color images,” IEEE Trans. Image Process. 16 (1), 22–35 (2007).
S. J. Sangwine and T. A. Ell, “Hypercomplex Fourier transforms of colour images,” in Proc. IEEE Int. Conf. on Image Processing (ICIP 2001) (Thessaloniki, 2001), pp. 137–140.
N. Le Bihan and S.J. Sangwine, “Quaternion principal component analysis of colour images,” in Proc. IEEE Int. Conf. on Image Processing (ICIP) (Barcelona, 2003), pp. 809–812.
S. Sangwine and T. A. Ell, “The discrete Fourier transform of a colour image,” in Image Processing II: Mathematical Methods, Algorithms and Applications, Ed. by J. M. Blackledge and M. J. Turner (Horwood Publ., 2000), pp. 430–441.
T. A. Ell, “Hypercomplex spectral transforms,” Ph.D. Dissertation (Univ. Minnesota, Minneapolis, 1992).
C. E. Moxey, S. J. Sangwine, and T. A. Ell, “Colorgrayscale image registration using hypercomplex phase correlation,” in Proc. IEEE Int. Conf. on Image Processing (ICIP) (Rochester, 2002), pp. 385–388.
W. L. Chan, H. Choi, and R. G. Baraniuk, “Coherent multiscale image processing using dual-tree quaternion wavelets,” IEEE Trans. Image Process. 17 (7), 1069–1082 (2008).
W. L. Chan, H. Choi, and G. Baraniuk, “Directional hypercomplex wavelets for multidimensional signal analysis and processing,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP 2004) (Montreal, 2004), pp. 996–999.
T. Batard, M. Berthier, and C. Saint-Jean, “Clifford- Fourier transform for color image processing,” in Geometric Algebra Computing (Springer, London, 2010), pp. 135–162.
Y. N. Li, “Quaternion polar harmonic transforms for color images,” IEEE Signal Process. Lett. 20 (8), 803–806 (2013).
S. Li, M. C. Lee, and C. M. Pun, “Complex Zernike moment features for shape-based image retrieval,” IEEE Trans. Syst. Man Cyb. A 39 (1), 227–237 (2009).
A. Kolaman and O. Yadid-Pecht, “Quaternion structural similarity: a new quality index for color images,” IEEE Trans. Image Processing 21 (4), 1526–1536 (2012).
M. Bober, “MPEG-7 visual shape descriptors,” IEEE Trans. Circuits Syst. Video Technol. 11, 716–719 (2001).
S. J. Sangwine, “Fourier transforms of colour images using quaternion or hypercomplex, numbers,” Electron. Lett. 32 (21), 1979–1980 (1996).
T. A. Ell, Hypercomplex Spectral Transformations (Univ. of Minnesota, 1992).
W. R. Hamilton, Elements of Quaternions (Longmans, Green & Company, 1866).
The Moving Picture Experts Group (MPEG). http://www.chiariglione.org/mpeg. Cited Jan. 12, 2009.
A. Amanatiadis, V. G. Kaburlasos, A. Gasteratos, and S. E. Papadakis, “Evaluation of shape descriptors for shape-based image retrieval,” Image Processing 5, 493–499 (2011).
C. S. Pooja, “An effective image retrieval system using region and contour based features,” in Proc. IJCA Int. Conf. on Recent Advances and Future Trends in Information Technology (Patiala, 2012), pp. 7–12.
K. M. Hosny, “Exact and fast computation of geometric moments for gray level images,” Appl. Math. Comput. 189, 1214–1222 (2007)
S. Liao, M. W. Law, and A. Chung, “Dominant local binary patterns for texture classification,” IEEE Trans. Image Processing 18 (5), 1107–1118 (2009).
C. Y. Wee and R. Paramesran, “On the computational aspects of Zernike moments,” Image Vision Comput. 25, 967–980 (2007).
C. Singh and R. Upneja, “Error analysis in the computation of orthogonal rotation invariant moments,” J. Math. Imaging Vision 49, 251–271 (2014).
A. Khatabi, A. Tmiri, and A. Serhir, “A novel approach for computing the coefficient of ART descriptor using polar coordinates for gray-level and binary images,” in Advances in Ubiquitous Networking (Springer, 2016), pp. 391–401.
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Abderrahim Khatabi (born 1987) received a master’s degree of networks and telecommunications from Chouaib Doukkali University Faculty of Science EI Jadida, Morocco in 2011. He is currently pursuing his Ph.D. degree (Computer Science) at the Chouaib Doukkali University Faculty of Science, Jadida, Morocco. His research interests include Medical Image Processing.
Amal Tmiri is currently a professor in Chouaib Doukkali University Faculty of Science, Department of Computer science, Laboratory LAROSERI, EI Jadida, Morocco. His research interests include Medical Image Processing.
Ahmed Serhir is professor in Chouaib Doukkali University Faculty of Science, Department of Math, Laboratory of Fundamental mathematics, EI Jadida, Morocco. His research interests Algebra and fundamental Mathematics.
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Khatabi, A., Tmiri, A. & Serhir, A. Quaternion angular radial transform and properties transformation for color-based object recognition. Pattern Recognit. Image Anal. 26, 705–713 (2016). https://doi.org/10.1134/S1054661816040064
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DOI: https://doi.org/10.1134/S1054661816040064