基于小波和奇异值分解的图像边缘检测

Image Edge Detection Based on Wavelet and Singular Value Decomposition

针对传统图像边缘检测抑制噪声能力弱的问题,给出了一种小波变换和局部梯度场内奇异值分解相结合的边缘检测方法。首先在图像预处理阶段,为了提取准确的边缘特征,文中利用小波变换的时频局部化特性,对图像进行小波变换。该文对用小波求取的梯度场使用局部梯度奇异值分解的方法;利用奇异值的特性和良好的稳定性,使提取的边缘特征更加突出并且能够达到抑制噪声的目的。实验证明该文方法既能在无噪声影响的图像中提取出清晰完整的单边缘,又能在有噪声干扰的情况下提取出理想的边缘。

Traditional image edge detection algorithms do not perform well in noise suppression. For solving the problem, this paper presents a new method based on wavelet and local gradient field singular value decomposition to detect image edge. First, the wavelet transform （WT） is applied to the image in order to utilize the time-frequency localization characteristic of WT to extract the accurate edge character. Then the local gradient field singular value decomposition （SVD） is used to the gradient field calculated by the wavelet. The feature and good stability of the singular values （SVs） enhance edge character and suppress noise. The experimental results of edge detection illustrate that the proposed method can not only extract clear and complete single-pixel edge in the images without noise, but also find ideal edge from noised images.