运用偏微分方程进行图像平滑的过程中，迭代的最佳停止次数一直都是研究重点.利用随机变量之间的独立性，提出一个基于核密度估计的最优停止准则.该准则能获得准确的最佳停止次数,且不需要预知图像中的噪声水平.数值实验结果表明，该准则所得到的最佳停止次数非常接近于均方差（mean square error，MSE）方法所得到的最佳停止次数,且适用于多种噪声水平.

Optimal stopping has been an important issue in image smoothing based on partial differential equations. According to the independence of random variables and the kernel density estimation, a novel optimal stopping criterion is proposed, which can be used without knowing the noise variance. Numerical experiments show consistency between the results obtained with the proposed method and that of the mean square error (MSE) method. The criterion is applicable at various noise levels.