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Volume 6 Issue 4
Jul.  2019

IEEE/CAA Journal of Automatica Sinica

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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

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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  • 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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