改进的自适应四阶偏微分方程的图像恢复算法-《计算机技术与发展》

文章信息/Info

Title:: An Improved Image Restoration Algorithm Based on Adaptive Four-order Partial Differential Equation

Author(s):: WANG Jun-feng; HE Ya-ru; Department of Application Mathematics,School of Science,Xi’an University of Technology,Xi’an 710054,China

Keywords:: four-order partial differential equation; isotropic diffusion; anisotropic diffusion; edge detection function; diffusion function

摘要:: 为了克服各项同性扩散和各项异性扩散模型使图像平滑过渡造成图像模糊、扩散不均匀出现“阶梯效应”等不足,提出了一种新的自适应四阶偏微分方程图像恢复算法。首先采用梯度模值构造边缘检测函数,区分出图像的边缘区、平坦区,再构造边缘扩散函数,根据图像的信息特征,使得该算法在图像梯度方向及其法向自适应地选取扩散方式,从而在平坦区域采用各项同性扩散更好地去除噪声,在边缘区域采用各项异性扩散保留边缘信息。实验结果表明,该算法在去噪和保留边缘的同时,保留了细节信息,提高了图像的峰值信噪比。

Abstract:: In order to overcome the shortcomings like ladder effect caused by image blur and uneven diffusion by image smoothing of the isotropic and anisotropic diffusion model,we propose a new image restoration algorithm of adaptive four-order partial differential equation. First,we use the gradient modulus to build the edge detection function to distinguish the edge of the image area and flat area,and then construct the edge diffusion function. According to the characteristics of image,it makes the algorithm to adaptively select the diffusion mode in gradient and its normal direction. Therefore in the flat area,the kind of isotropic diffusion is used to remove the noise,and in the edge region,the kind of anisotropic diffusion is used to preserve the edge information. The experiments show that the proposed algorithm can preserve the details while removing the noise and preserving the edges,and improve the peak signal to noise ratio of the image.