基于小波分析的图像边缘检测算法研究

【作者】 龚正；

【导师】 袁修贵；

【作者基本信息】 中南大学 ， 计算数学， 2009， 硕士

【摘要】 边缘检测是图像处理领域的重要课题,小波分析是继Fourier分析、短时Fourier分析之后的新的信号分析技术。在本文中,首先简要介绍了小波理论的发展及图像的边缘检测的定义；然后给出了一些传统的边缘检测方法,并回顾了一些经典的边缘检测算子,通过实验得出这些方法对不含噪声的图像的边缘检测效果较好,但用于含有噪声的图像则并不理想；从而引入了多尺度小波边缘检测方法,但该方法会导致边缘细节的损失且边缘位置会发生偏移,即在小尺度下存在噪声剔除不干净的情况,随着尺度的增加,在去除噪声的同时把图像的边缘细节也给去掉了,针对这种情况,提出了基于边缘方向性的小波边缘检测算法,该算法先对图像进行基于边缘方向性的平滑,在处理边缘像素时可自动搜索边缘方向进行平滑,然后再用小波变换提取边缘；通过对一系列图像进行仿真实验有力地证明了该方法的有效性；形态学边缘检测算子具有抗噪性不佳的特点,本文构造了一种新的形态学滤波器,并用该滤波器和小波方法结合起来进行边缘检测,仿真实验结果证明了该算法十分有效。更多还原

【Abstract】 Edge detection is an important topic in the field of image processing. Wavelet transform is a new signal analysis technology after the Fourier transform and short-time Fourier transform. In this thesis, we briefly introduce the development of wavelet theory and the fundamental theories of edge detection firstly, then several traditional methods of edge detection used usually are described and some classical edge detectors are reviewed.Those edge detectors have high performance in detecting the edges when there is no noise in those images, but can not deal well with noisy images, so we introduce the edge detectors based on wavelet transform that can deal well with noisy images, but it may loss some details of the edge and have the drift of edge position across different scale,the algorithm can not clear all the noise of image at small scale,with the increase of the scale,the details of the edge go with the noise, under this situation,we present a wavelet transform-based edge detection algorithm based on edge direction,this method smooth the image based on edge direction firstly,the smoothing algorithm smooth the image on the direction of the edge,then detect the image, a series of experiments for edge detection show that the algorithm is more effective.The edge detector based on morphology can not deal well with noisy images,a new morphology filter is presented in this paper,and we detect the image edge with this filter and wavelet transform,the experimental results show that the proposed alogrithm is very reliable and efficient.更多还原