This paper presents a flexible and adaptive fourth-order diffusion model for image noise removal. A flexible fourth-order diffusion equation is first presented. Then, an efficient and robust contextual discontinuity indicator based on the bilateral kernel is constructed and combined with the local discontinuity indicator (local spatial gradient) to get the desired adaptive fourth-order diffusion model. The proposed model degenerates to an anisotropic equation which performs the tangent smoothing for sharpening the inter-object boundaries and reduces to an isotropic equation which implements the fast smoothing in the homogenous regions for noise removal. Moreover, it is able to overcome the staircase artifacts arisen by most of second-order diffusion models. Experimental results are provided to validate the effectiveness of the proposed model with regard to objective evaluation metrics and visual performance which outperform those of some benchmark models.

本文提出了一种灵活的自适应四阶扩散模型来去除图像噪声。首先提出了一个灵活的四阶扩散方程。然后，构造了基于双边核的有效且健壮的上下文不连续性指示符，并将其与局部不连续性指示符（局部空间梯度）组合以获得所需的自适应四阶扩散模型。提出的模型退化为各向异性方程，该方程执行切线平滑以锐化对象间边界，并简化为各向同性方程，该方程在均质区域中实现快速平滑以去除噪声。而且，它能够克服大多数二阶扩散模型产生的阶梯伪像。