各向异性扩散的最大特点在于它是有选择性的平滑过程,这种平滑过程在均匀的区域不受限制,而在跨越边界部分被抑制,因此噪声和一些无关的细节被平滑掉了,从而能够有效地实现图像保边缘平滑。在现有各向异性扩散模型中,偏微分扩散方程解的适定性和扩散系数中的梯度阈值的合理估计是尚未很好解决的问题。为此利用最小描述长度(MDL)原则发展了一种各向异性扩散模型,并与Lyapunov函数的p-范数相结合,改善了各向异性扩散模型中梯度阈值的估计方法,形成了一种性能较好的各向异性扩散非线性滤波技术。实验结果表明,该方法不仅能够更有效地识别噪声图像中的细节边缘,而且还保证了各向异性扩散模型的稳定性;改进的扩散模型,滤波效果优于传统的各向异性扩散模型,是一种较为理想的保边缘滤波方法。

The anisotropic diffusion is a selective smoothing technique that effectively employs intra-region smoothing without limitation while inhibits inter-region smoothing.With this technique,noise is smoothed out and the edge-preserving smoothing can be effectively implemented.Two problems in anisotropic diffusion schemes have still not been solved.One is existence and uniqueness of the solution of the partial derivative diffusion equation;the other is reasonable estimate of gradient threshold in diffusion coefficients.The algorithm proposed in this paper is developed on the basis of minimal description length criterion and incorporated with one alternative method for setting gradient threshold based on the simple calculation of the p-norm.The improved model not only detects effectively the detailed edges in images,but also preserves the stability of anisotropic diffusion.Experimental results show that this method has superiority over the previous anisotropic diffusion models and is an ideal edge-preserving filtering method.