基于四元数尺度函数的边缘检测方法  

The edge detection based on the quaternion scale function

作　　者：胡晓晓[1] 程冬 HU Xiaoxiao;CHENG Dong(The First School of Medicine,School of Information and Engineering,The First Affiliated Hospital of Wenzhou Medical University,Wenzhou Medical University,Wenzhou 325000,Zhejiang Province,China;Research Center for Mathematics and Mathematics Education,Beijing Normal University,Zhuhai,Zhuhai 519087,Guangzhou Province,China)

机构地区：[1]温州医科大学第一临床医学院(信息与工程学院)附属第一医院,浙江温州325000 [2]北京师范大学珠海校区数学与数学教育研究中心,广州珠海519087

出　　处：《浙江大学学报（理学版）》2022年第5期549-554,共6页Journal of Zhejiang University（Science Edition）

基　　金：温州市科技局资助项目(G2020031);浙江省教育厅一般科研项目(Y202147071);温州医科大学博士启动基金项目(QTJ18012);广东省基础与应用基础研究基金项目(2019A1515111185)。

摘　　要：四元数解析信号是解析信号在四元数意义下的推广,其由原信号、四元数方向Hilbert变换和四元数交叉项Hilbert交换构成。通过四元数解析信号的极坐标表示,可得信号的特征表示,如局部相位角和局部振幅,其中局部相位角包含信号的结构信息。研究了右四元数解析信号,给出了其二维延拓定理,得到右四元数尺度函数,并将其局部特征应用于彩色图像的边缘检测,提出了基于局部相位角和局部振幅的边缘检测方法,通过对比实验,证明了基于局部相位角的边缘检测方法在抗噪上具有鲁棒性。The quaternion analytic signal is a generalization of analytic signal in the quaternion sense. It is constructed by an original signal and its quaternion partial and total Hilbert transforms. The signal feature representation can be provided by the polar form of the quaternion analytic signal, such as the local amplitude and local phase angle, the latter includes the structural information of the original signal. The aim of this work is to study the quaternion analytic signal associate with right-sided quaternion Fourier transform and it applications. Firstly, quaternion analytic signal associate with right-sided quaternion Fourier transform is defined. By using Possion operator, the quaternion analytic signal is extended to the quaternion scale function. The quaternion scale function provides the signal features representation. At last, three novel types of phase and amplitude-based edge detectors are proposed. Comparisons with competing methods on real-world images consistently show the superiority of the proposed methods.

关 键 词：右边四元数傅里叶变换(QFT) 解析信号 局部相位角 局部衰减 泊松算子 

分 类 号：O29[理学—应用数学]