基于二维再生核理论的图像平滑方法

An Image Smoothing Method Based on Two-Dimensional Reproducing Kernel Theory

本文给出了应用扩散方程进行图像平滑的再生核方法．基于再生核理论进行图像平滑，由于再生核函数的导数是小波函数，具有良好的局部性，与常规的对扩散方程差分化进行求解相比，用再生核方法求解扩散方程具有精度高，误差传播速度慢，对时间步长不敏感等优点．同时本文给出了用W2空间再生核求解Alvarez模型的方法．实验表明该方法具有图像清晰、图像平滑效果好等优点，本文的求解方法是有效的．

The paper proposes an image smoothness method with reproducing kemel.A smoothness method based on reproducing kemel theory is introduced. The differential coefficient of reproducing kemel function also is wavelet function. Compared with other general methods, wavelet function possess better partial character,reproducing kemel method has higher precision, slower speed of error diffusion, and not sensitivity to time interval. At last, A method to get the answer of Alvarez model based on W2 space reproducing kernel is presented. The experiment shows the method has many strongpoints such as clearer image, better effect.