摘  要：图像的边缘是图像的重要基本特征之一，它包含着图像的重要信息，广泛应用于图像压缩、图像去噪、图像增强、图像融合和图像边缘检测。随着时代的发展和进步，对于图像边缘的提取和分析已经成为一个热门话题。

目前，对于图像的边缘检测已经有很多的实现方法，但是因为问题本身的复杂性和技术手段的限制，图像的边缘检测一直没有得到完美的处理方法。

对于图像的边缘检测，使用传统的滤波方法检测图像边缘时会导致边缘模糊化等问题，而且对于细节较多的图像处理效果不佳。小波变换作为一种时频局部化方法，他的窗口是可变的，也就是说，小波变换在低频处频率细分，在高频处时间细分，具有局部分析的能力，对信号具有自适应性，因而十分适合于图像的边缘检测。

本文首先介绍了边缘检测技术和小波变换技术的发展状况，之后介绍了五种经典的边缘检测算子并分别用这五种边缘检测算子对无噪和加噪的图像进行边缘检测，并对比检测结果，分析了每种边缘检测算子的特性。然后介绍了小波变换一系列的基本概念，最后基于小波变化和小波包变化对图像的边缘进行了检测，并得出结论：在小波变换对于图像边缘的检测中，在尺度较大时，边缘比较稳定，对噪声不敏感，但是对于边缘检测的准确度不高；然而在尺度较小时，对于边缘检测的准确度高，但是此时又对噪声很敏感，影响了边缘检测的效果。因此在多尺度边缘提取中，应利用多尺度的优点，对不同尺度下的边缘图像分析处理，这样得出的边缘检测效果更佳。

关键词：小波变换；图像边缘检测；多分辨率分析；B样条小波

Abstract：The edge of the image is one of the important basic features of the image, it contains important information of the image, widely used in image compression, image denoising, image enhancement, image fusion and image edge detection. With the development and progress of the times, for the edge of the image extraction and analysis has become a hot topic.

   At present, there are a lot of ways to realize the edge detection of the image, but because of the complexity of the problem itself and the limitation of the technical means, the edge detection of the image has not been the perfect way to deal with it.

   For the edge detection of the image, using the traditional filtering method to detect the edge of the image can cause the edge blur, and the effect of image processing with more detail is poor. Wavelet transform is a time-frequency localization method, his window is variable, that is, wavelet transform in the low frequency pision frequency subpision, at the high frequency of time subpision, has the ability of local analysis, the signal is adaptive, so it is very suitable for the edge detection of the image.

   In this paper first introduces the development of edge detection technology and wavelet transform technology, then introduces five classical edge detection operators and uses these five edge detection operators to detect the edge detection of the image without noise and noise, and compares the detection results, and analyzes the characteristics of each edge detection operator. Then, a series of basic concepts of wavelet transform are introduced. finally, the edge of image is detected based on wavelet transform and wavelet packet change. conclusion: in the detection of image edge, the edge is stable and is not sensitive to noise, but the accuracy of edge detection is not high. However, in the small scale, the accuracy of edge detection is not high, but at this time it is sensitive to noise, which affects the effect of edge monitoring. Therefore, in multi-scale edge extraction, multi-scale advantage should be used to analyze the edge image under different scales, so the edge detection result is better.