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Volume 6 Issue 4
Jul.  2019

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2019  >  6(4): 1036-1051
Bing He, Jiangtao Cui, Bin Xiao and Xuan Wang, "Image Analysis by Two Types of Franklin-Fourier Moments," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1036-1051, July 2019. doi: 10.1109/JAS.2019.1911591
Citation: Bing He, Jiangtao Cui, Bin Xiao and Xuan Wang, "Image Analysis by Two Types of Franklin-Fourier Moments," IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 1036-1051, July 2019. doi: 10.1109/JAS.2019.1911591
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Image Analysis by Two Types of Franklin-Fourier Moments

doi: 10.1109/JAS.2019.1911591
Funds:  This work was supported by the National Natural Science Foundation of China (61572092, 61702403), the Fundamental Research Funds for the Central Universities (JB170308, JBF180301), the Project Funded by China Postdoctoral Science Foundation (2018M633473), the Basic Research Project of Weinan Science and Technology Bureau (ZDYF-JCYJ-17), and the Project of Shaanxi Provincial Supports Discipline (Mathematics)
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    Abstract
  • In this paper, we first derive two types of transformed Franklin polynomial: substituted and weighted radial Franklin polynomials. Two radial orthogonal moments are proposed based on these two types of polynomials, namely substituted Franklin-Fourier moments and weighted Franklin-Fourier moments (SFFMs and WFFMs), which are orthogonal in polar coordinates. The radial kernel functions of SFFMs and WFFMs are transformed Franklin functions and Franklin functions are composed of a class of complete orthogonal splines function system of degree one. Therefore, it provides the possibility of avoiding calculating high order polynomials, and thus the accurate values of SFFMs and WFFMs can be obtained directly with little computational cost. Theoretical and experimental results show that Franklin functions are not well suited for constructing higher-order moments of SFFMs and WFFMs, but compared with traditional orthogonal moments (e.g., BFMs, OFMs and ZMs) in polar coordinates, the proposed two types of Franklin-Fourier Moments have better performance respectively in lower-order moments.

     

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    • References(28)
  • [1]
    M. R. Teague, " Image analysis via the general theory of moments,” J. Optical Society of America, vol. 69, no. 8, pp. 1468, 1980.
    [2]
    C. H. Teh and R. T. Chin, " On image analysis by the methods of moments,” IEEE Trans. Pattern Anal. Machine Intell, vol. 10, no. 4, pp. 496–513, 1988. doi: 10.1109/34.3913
    [3]
    C. Kan and M. D. Srinath, " Invariant character recognition with zernike and orthogonal fouriermellin moments,” Pattern Recognition, vol. 35, no. 1, pp. 143C154, 2002.
    [4]
    L. Wang and G. Healey, " Using zernike moments for the illumination and geometry invariant classification of multispectral texture,” IEEE Trans. Image Processing A Publication of the IEEE Signal Processing Society, vol. 7, no. 2, pp. 196–203, 1998. doi: 10.1109/83.660996
    [5]
    D. Zhang and G. Lu, " Evaluation of mpeg-7 shape descriptors against other shape descriptors,” Multimedia Systems, vol. 9, no. 1, pp. 15–30, 2003. doi: 10.1007/s00530-002-0075-y
    [6]
    M. Hu, " Visual pattern recognition by moment invariants,” Information Theory IRE Trans., vol. 8, no. 2, pp. 179–187, 1962. doi: 10.1109/TIT.1962.1057692
    [7]
    J. Flusser, B. Zitova, and T. Suk, Moments and Moment Invariants in Pattern Recognition, Wiley Publishing, 2009.
    [8]
    R. Mukundan and K. R. Ramakrishnan, Moment Functions in Image Analysis-Theory and Applications, World Scientific,, 1998.
    [9]
    H. T. Hu, Y. D. Zhang, C. Shao, and Q. Ju, " Orthogonal moments based on exponent functions: exponent-fourier moments,” Pattern Recognition, vol. 47, no. 8, pp. 2596–2606, 2014. doi: 10.1016/j.patcog.2014.02.014
    [10]
    S. X. Liao and M. Pawlak, " On image analysis by moments,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 3, pp. 254–266, 1996. doi: 10.1109/34.485554
    [11]
    Y. Xin, M. Pawlak, and S. Liao, " Accurate computation of zernike moments in polar coordinates,” IEEE Trans. Image Processing, vol. 16, no. 2, pp. 581–587, 2007. doi: 10.1109/TIP.2006.888346
    [12]
    L. Kotoulas and I. Andreadis, " Accurate calculation of image moments,” IEEE Trans. Image Processing, vol. 16, no. 8, pp. 2028–2037, 2007. doi: 10.1109/TIP.2007.899621
    [13]
    H. Lin, J. Si, and G. P. Abousleman, " Orthogonal rotation-invariant moments for digital image processing.,” IEEE Trans. Image Processing, vol. 17, no. 3, pp. 272, 2008. doi: 10.1109/TIP.2007.916157
    [14]
    Y. Sheng and L. Shen, " Orthogonal fourier-mellin moments for invariant pattern recognition,” J. Optical Society of America A, vol. 11, no. 6, pp. 1748–1757, 1994. doi: 10.1364/JOSAA.11.001748
    [15]
    B. Xiao, L. Li, Y. Li, W. Li, and G. Wang, " Image analysis by fractional-order orthogonal moments,” Information Sciences 382–383: 135–149, 2017.
    [16]
    R. Mukundan, S. H. Ong, and P. A. Lee, " Image analysis by tchebichef moments,” IEEE Trans. Image Processing A Publication of the IEEE Signal Processing Society, vol. 10, no. 9, pp. 1357–64, 2001. doi: 10.1109/83.941859
    [17]
    H. S. A. Barmak and J. Flusser, " Fast computation of krawtchouk moments,” Information Sciences, vol. 288, no. C, pp. 73–86, 2014.
    [18]
    B. Xiao, Y. Zhang, L. Li, W. Li, and G. Wang, " Explicit krawtchouk moment invariants for invariant image recognition,” J. Electronic Imaging, vol. 25, no. 2, pp. 023002, 2016. doi: 10.1117/1.JEI.25.2.023002
    [19]
    W. Chen, Z. Cai, and D. Qi, " Orthogonal franklin moments and its application for image representation,” Chinese J. Computers, vol. 37, no. 121, pp. 1–8, 2014.
    [20]
    P. Franklin, " A set of continuous orthogonal functions,” Mathematische Annalen, vol. 100, no. 1, pp. 522–529, 1928. doi: 10.1007/BF01448860
    [21]
    Z. C. Cai, W. Chen, D. X. Qi, and Z. S. Tang, " A class of general Franklin functions and its application,” Chinese J. Computers, vol. 32, no.10, pp. 2004-2013, 2009.
    [22]
    Y. Meyer and R. D. Ryan, Wavelets: Algorithms and Applications. SIAM, l993.
    [23]
    L. Guo, M. Dai, and M. Zhu, " Quaternion moment and its invariants for color object classification,” Information Sciences, vol. 273, no. 273, pp. 132–143, 2014.
    [24]
    E. G. Karakasis, G. A. Papakostas, D. E. Koulouriotis, and V. D. Tourassis, " Generalized dual hahn moment invariants,” Pattern Recognition, vol. 46, no. 7, pp. 1998–2014, 2013. doi: 10.1016/j.patcog.2013.01.008
    [25]
    H. Zhu, H. Shu, J. Liang, L. Luo, and J. L. Coatrieux, Image analysis by discrete orthogonal racah moments, in Proc. Int. Conf. Image Analysis and Recognition, 2005, pp. 524–531.
    [26]
    B. Xiao, G. Y. Wang, and W. S. Li, " Radial shifted legendre moments for image analysis and invariant image recognition,” Image and Vision Computing, vol. 32, no. 12, pp. 994–1006, 2014. doi: 10.1016/j.imavis.2014.09.002
    [27]
    Y. Chen and X. H. Xu, " Supervised orthogonal discriminant subspace projects learning for face recognition,” Neural Networks, vol. 50, no. 2, pp. 33, 2014.
    [28]
    B. Xiao, J. F. Ma, and X. Wang, " Image analysis by bessel-fourier moments,” Pattern Recognition, vol. 43, no. 8, pp. 2620–2629, 2010. doi: 10.1016/j.patcog.2010.03.013
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