保护角点的非线性扩散滤波

Nonlinear Diffusion Filter with Corner Preserving Characteristics

基于偏微分方程的非线性扩散滤波可以有效去除噪声,同时很好地保护边缘信息,但角点在其滤波过程中逐渐变得圆滑甚至消失。通过设计扩散系数为梯度模及曲率的函数,提出了一种保护角点的非线性扩散滤波模型。该模型在区域内部为普通的高斯滤波,而在边缘处滤波效果降低,在角点处滤波效果进一步降低,从而在滤波过程中角点信息可以得到较好的保留,还可能出现角点及边缘相对增强的效果。实验结果的视觉效果及数据分析都表明,新模型可以同时保护边缘及角点信息。

Nonlinear diffusion filters based on partial differential equations can well preserves the edge information while de-noise effectively, but the corners gradually become rounded and vanish while filtering. A corner preserving nonlinear diffusion filter is proposed, whose diffusion coefficient is the function of the gradient and the curvature. The new model behaves as a Gaussian filter inside the regions and smoothes less across regions; and the smoothing effect is even decreased in the corner points. These effects ensure better preservation of the corner. Visual effect with data analysis of the experiment result proves simultaneous protection of the edge and corner information.