一种改进的偏微分方程图像平滑方法

针对退化扩散方程在图像平滑时对角点的圆弧化，提出由梯度及其正交方向上的二阶方向导数共同决定扩散速度。在图像的角点位置上，扩散速度趋于零，在线条点位置上，扩散速度由梯度的模值来决定，并在与梯度正交的方向上进行平滑，在灰度变化不大的区域上，采用传导系数为常数的热方程进行平滑。文中的理论上说明了扩散速度的构造方法。实验结果表明，该扩散模型在对图像进行平滑的同时，对特征点的保留是明显的。

Improved Partial Differential Equations Smoothing Method

As a cornen in an image is rounded when using degenerate diffusion equation to smooth the image, it proposed to use both the gradient and the second order directional derivative in the direction orthogonal to the gradient to control the diffusion velocity. This diffusion velocity is about zero at the corner position. At the position of the edge it is dominated by the gradient, and the smoothing is executed on the direction orthogonal to the gradient. In the area where the intensity of the image is changed small the image is smoothed by the heat equation whose conduction coefficient is constant. A method was given to construct the diffusion velocity in theory. The experiment shows that this method is valid on the image smoothing while preserving the features.