文献类型：期刊文献

英文题名：Image analysis by generalized Chebyshev-Fourier and generalized pseudo-Jacobi-Fourier moments

作者：Zhu, Hongqing[1];Yang, Yan[1];Gui, Zhiguo[2];Zhu, Yu[1];Chen, Zhihua[1]

机构：[1]E China Univ Sci & Technol, Sch Informat Sci & Engn, Shanghai 200237, Peoples R China;[2]North Univ China, Natl Key Lab Elect Measurement Technol, Taiyuan 030051, Peoples R China

年份：2016

卷号：51

起止页码：1

外文期刊名：PATTERN RECOGNITION

收录：;EI(收录号：20155201712360);WOS:【SCI-EXPANDED(收录号:WOS:000367633400001)】；

基金：The authors would like to thank the anonymous reviewers and the associate editor for their insightful comments that significantly improved the quality of this paper. This work was supported by the National Natural Science Foundation of China under Grants 61371150, 61271357, and 61370174.

语种：英文

外文关键词：Generalized radial polynomial; Jacobi polynomial; Recurrence relation; Rotation invariant; Chebyshev-Fourier moment; Pseudo Jacobi-Fourier moment

摘要：In this paper, we present two new sets, named the generalized Chebyshev-Fourier radial polynomials and the generalized pseudo Jacobi-Fourier radial polynomials, which are orthogonal over the unit circle. These generalized radial polynomials are then scaled to define two new types of continuous orthogonal moments, which are invariant to rotation. The classical Chebyshev-Fourier and pseudo Jacobi-Fourier moments are the particular cases of the proposed moments with parameter alpha = 0. The relationships among the proposed two generalized radial polynomials and Jacobi polynomials, shift Jacobi polynomials, and the hypergeometric functions are derived in detail, and some interesting properties are discussed. Two recursive methods are developed for computing radial polynomials so that it is possible to improve computation speed and to avoid numerical instability. Simulation results are provided to validate the proposed moment functions and to compare their performance with previous works. (C) 2015 Elsevier Ltd. All rights reserved.