高阶伪希尔伯特变换在边缘检测中的应用

High-Order Pseudo Hilbert Transform and Application in Edge Detection

在图像边缘检测中,为了克服传统希尔伯特变换提取的边缘质量差、边缘分辨率较低且不变的问题,构造了一种用于图像边缘检测的高阶伪希尔伯特变换,它吸收了短时傅里叶变换和传统希尔伯特变换的思想,利用窗函数宽度和指数的调节实现不同的输出。通过边缘模型仿真,阐述了时窗宽度和指数对边缘的分辨率以及幅值的影响。在实际图像的处理中,高阶伪希尔伯特变换检测到的边缘完整准确、分辨率高,边缘的分辨率与参数有关,证明了它在图像边缘检测中应用的有效性和灵活性。

To avoid the poor edge quality,and the less and unchangeable edge resolution from using Hilbert transform（HT） in the image edge detection,a high-order pseudo Hilbert transform（HOPHT） is presented.HOPHT combines the time-frequency localization property of short time Fourier transform（STFT） and implementation of traditional HT.Its output depends on the width adjustment of the window function and the order.The effect of the width of window function and the order on the edge resolution as well as the amplitude is illustrated by the simulation of edge model processing.The real image processing demonstrates that HOPHT-based edge detection has effectiveness and flexibility with higher edge resolution and quality,compared with HT.