一种基于小波子带各向异性扩散方程的图像平滑方法

Smoothing Method Using Anisotropic Diffusion Equations Based on Wavelet Subbands

根据小波变换对图象的多分辨率表示的同时将不同边缘归结到不同的小波子带，文章提出了将改进的退化扩散方程结合图象的不同小波子带的图象平滑方法。这样，对高频子带，扩散方向由子带方向确定，扩散速度由梯度幅值和二阶导数决定； 而在灰度变化不大的低频子带，采用传导系数为常数的热方程进行平滑。实验证明，该方法在对图象进行平滑的同时，较好地保留了图象的线条边缘特征和角点特征，同时算法复杂性大为降低。

： Considering different edges in an image can be classified into different wavelet subbands when using multiple resolution representation with wavelet transform，this paper proposes a smoothing method combined wavelet subband with anisotropic diffusion equations．At the higher frequency subbands，both the gradient and second order directional derivative are used to control the diffusion velocity，while the diffusion direction dominated by the subband．At the low frequency subband，the smoothing is excuted by the heat equation whose conduction coefficient is constant．The experiments shows this method is good at the image smoothing and preserves the features，while saving the complexity of algorithm．