【摘要】 基于偏微分方程的图像处理方法在图像去噪方面有着良好的应用效果。合适的特征检测函数可以让基于偏微分方程的图像预处理方法达到良好的噪声去除和边缘特征保留效果。通常的特征检测函数是基于图像全局特征设置，文中从图像局部特征角度出发构建了一种边缘检测函数。针对图像局部特征的差异，自适应地调整图像在法线方向的扩散系数指数。在平坦区域法向扩散系数指数趋于1，此时模型为四阶各向同性扩散，可较好地去除噪声；在图像边缘处法向扩散系数指数趋于2，此时模型为四阶各向异性扩散，可较好地保留边缘特征。通过对Lena和Peppers图像进行仿真实验，结果表明该算法的均方根误差、信噪比和峰值信噪比都优于传统的图像去噪模型，在噪声去除和边缘特征保留之间实现了很好的平衡。更多还原

【Abstract】 The image processing method based on partial differential equation(PDE)has a good application effect in image denoising. An appropriate feature detection function can make the image preprocessing method based on PDE achieve good effects on noise removal and edge feature preservation. The usual feature detection function is based on the global feature setting of the image. A kind of edge detection function is constructed in the perspective of the local feature of the image. For there are differences among local features,the diffusion coefficient index of the image in the normal direction is adjusted adaptively. In the flat region,when the diffusion coefficient index in the normal direction tends to 1,the isotropic fourth-order diffusion(IFOD)is achieved,which can better remove the noise. In the image edge,when the diffusion coefficient index in the normal direction tends to 2,the anisotropic fourth-order diffusion(AFOD)is achieved,which can better preserve the edge features.Simulation experiments on images of Lena and Peppers show that the proposed algorithm is better than the traditional image denoising models in terms of RMSE(root mean square error),SNR(signal-to-noise ratio)and PSNR(peak signal-to-noise ratio),and achieves good balance between noise removal and edge feature preservation.更多还原