Image Analysis by Two Types of Franklin-Fourier Moments

作     者：Bing He Jiangtao Cui Bin Xiao Xuan Wang 

作者机构：the School of Computer Science and TechnologyXidian UniversityXi’an 710071China the School of Physics and Electrical EngineeringWeiNan Normal UniversityWeinan 714000China the Key Laboratory of Computational IntelligenceChongqing University of Posts and TelecommunicationsChongqing 400065China the School of Physics and Information TechnologyShaanxi Normal UniversityXi’an 710062China 

出 版 物：《IEEE/CAA Journal of Automatica Sinica》 (自动化学报（英文版）)

年 卷 期：2019年第6卷第4期

页      面：1036-1051页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 

基　　金：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) the Project of Shaanxi Provincial Supports Discipline(Mathematics) 

主　　题：Franklin functions image reconstruction moment invariants object recognition orthogonal moments 

摘      要：In this paper,we first derive two types of transformed Franklin polynomial:substituted and weighted radial Franklin *** 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 *** 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 ***,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 *** 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.