基于 Cauchy-Riemann方程的图像边缘检测方法

摘要

For edge detection problem, we put forward a complex function-based finite difference method, it conducts edge detection using analytical signal;Through solving the Cauchy-Riemann equations, the method constructs the conjugate image of the original image and obtains the edge detection image.After preprocessing and refined processing on conjugate image, better edge detection effect can be achieved.It is shown by digital images experiments that the method proposed is very useful, and the complex background contour will not interfere the recog-nition of main object due to relatively poor connectivity of the algorithm.This advantage shows that the method is a direction deserving further research.%针对边缘检测问题，提出一种基于复变函数的有限差分法，利用解析信号来进行边缘检测；通过求解Cauchy-Riemann方程，构造原图的共轭图像，并得到边缘检测图。对共轭图像进行预处理与细化处理后，获得更好的边缘检测效果。数字图像实验表明，该方法实用性强，且因为连接性较差而使得复杂的背景轮廓不会干扰到主对象的识别。这一优势表明，该方法是一个值得深入的研究方向。