Adaptive fourth-order diffusion smoothing via bilateral kernel

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.