基于改进二维离散希尔伯特变换的图像边缘检测方法  

The Modified Algorithm of Image Edge Features Detection Based on 2-D Discrete Hilbert Transform

作　　者：王珂[1,2] 肖鹏峰[1] 冯学智[1] 吴桂平[1] 李晖[1] 

机构地区：[1]南京大学地理与海洋科学学院地理信息科学系,江苏南京210093 [2]中国科学院遥感应用研究所,北京100101

出　　处：《测绘学报》2012年第3期421-427,433,共8页Acta Geodaetica et Cartographica Sinica

基　　金：国家863计划(2008AA12Z106);国家自然科学基金(40801166;40771137)

摘　　要：提出一种新的基于二维希尔伯特变换的边缘检测方法。对于频域信号而言,希尔伯特变换不改变信号的幅值,而仅仅改变其相位,即负频率的相位作+90°相移,而正频率作-90°相移。经由傅里叶变换后,边缘特征呈极值状态,因此本文利用二维离散希尔伯特变换实现边缘检测。由于二维离散希尔伯特变换结果具有方向性,提出利用两个呈正交性的二维离散希尔伯特变换的幅度平方和来检测图像边缘特征。此外将高斯核函数引入到希尔伯特变换中,以减少图像噪声对检测结果的影响,并根据PSNR(峰值信噪比)来确定最佳参数σ,从而得到理想的边缘检测效果。为验证该方法的检测结果,将所提方法与传统边缘检测算子的检测效果进行了比较分析,并将该方法运用于卫星遥感图像中,结果表明该方法可以有效地应用于边缘检测工作中。A novel algorithm is proposed based on 2-D discrete Hilbert transform. It has been verified that Hilbert transform can be used to detect the edge features from images. The magnitude of signal is not changed, and the phase is shifted in frequency domain after transforming byHilbert transform. Namely, when the signal is negative, the phaseshift is4-90°; when it is positive, thephaseshifit is -90°. There are peaks and valleys on features of signal after Hilbert transform. Thus, the2-DdiscreteHilbert transform to detect image edges is proposed. Because of the directionality of the 2-D discrete Hilbert transform in edge detection, the quadratic sum of two orthogonal 2-D dis- creteHilbert transform is calculated to complete the edge detection. Furthermore, Gaussian function is introduced into the 2-D discrete Hilbert transform to reduce the influence from noises, and PSNR （peak signal to noise ratio） is used to determine the optimal parameter a. An evaluation between the proposed algorithm and the others is realized to verify the result of edge detection. Remotely sensed imageries are chosen as test data in edge features detection. The results of detection show that the proposed algorithm is effective in edge features detection.

关 键 词：二维离散希尔伯特变换 高斯函数 边缘检测 傅里叶变换 频域 

分 类 号：TP751.1[自动化与计算机技术—检测技术与自动化装置]