基于梯度和拉普拉斯算子的图像扩散变分模型

采用图像扩散的变分方法可以有效地设计边缘保持或增强的图像恢复模型。传统的模型往往基于图像强度的梯度,所得到的结果在本该光滑的区域具有明显的阶梯效应。为此,提出了基于梯度和拉普拉斯算子的图像扩散变分模型,以期实现在对图像进行噪声去除的同时,保持或增强图像的边缘,并消除单纯基于梯度模型导致图像光滑区域的阶梯效应。对变分模型中光滑项的设计,首先针对一维模型的分析得出基于梯度和拉普拉斯算子模型向前、后扩散的条件,然后将其推广到二维图像扩散,并在设计的有限差分方法基础上,对所提模型的有效性进行了实验验证,效果良好。

Variational models for image diffusion based on gradient and Laplacian

Variational methods for image diffusion have been widely applied to image restoration with edge preserving or enhance-ment.The traditional models based only on gradients of image intensity can result in staircase effects beyond edges.So a hybrid variational image diffusion model using gradient and Laplacian was presented to reduce staircasing during image diffusion with edge preservation or enhancement.For the design of smooth terms in a diffusion model,forward and backward diffusion conditions for a one-dimension model based on first and second derivatives were first derived,which were extended to two-dimension image space.Some numerical results validated the model using a finite difference scheme.