中文摘要：

针对传统小波变换对含噪图像边缘检测的不足，结合全向小波和Hausdorff距离的知识，提出了一种改进的边缘检测算法。首先，对图像做全向小波变换，同时做改进的灰度图形态学处理；然后在一定的窗口下求处理后图像间的Hausdorff距离，并将其大小作为图像边缘检测的像素值。最后将该算法与Sobel算法、Canny算法做比较，实验结果表明该方法提取的边缘清晰度优于其他方法，且可以很好地抑制噪声。

英文摘要：

In order to overcome the weakness of the traditional wavelet transform at the edge detection of noisy image, an improved edge detection algorithm based on the omni-directional wavelet and Hausdorff distance is proposed. Firstly, the Omni-directional wavelet transform detects the edge of the image, at the same time the method of improved gray morphology also detects the edge. Then, the Hausdorff distance can be calculated between two processed images under a certain window, and the value of distance is regarded as the pixel value of image edge detection. Finally, experimental comparison of the algorithm with Sobel algorithm and Canny algorithm. And the results prove that this method is better than others in image edge definition. Furth more the noise can be restrained well.