一种基于偏微分方程的图像放大方法

目的结合偏微分方程理论,研究图像放大的有效方法.方法根据热传导方程的物理意义,把图像的灰度值视为平面物体的温度,以原图像的某种插值结果作为异性扩散方程的初值,利用数值方法对方程进行求解,所得结果作为预估值.将预估结果中相应于原图像位置的像素值以原图像替换,所得结果作为校正值.校正值将作为下一步预估计算的初值.利用有限差分法求解偏微分方程,实现预估-校正迭代.结果数值实验显示笔者所提算法与传统的插值放大算法相比放大后图像没有明显的斑点及亮度偏移现象;与已有基于偏微分方程的图像放大算法相比,该算法能够较好地保持图像的边缘特征和细节信息.结论笔者所提算法具有长时间计算的稳定性,放大图像不会随着迭代次数的增加而变得模糊,是一种有效的图像放大方法.

An Image Zooming Method Based on Partial Differential Equations

The paper is devoted to give out a new algorithm for image zooming based on the partial differential equations and the idea of prediction-correction method.We regarded the process of image zooming as the diffusion process of the temperature on a plane object.By taking some kind of interpolation of the original image as the initial value of an anisotropic diffusion equation,we obtained our prediction value via certain numerical method.To replace the pixel value by the original image correspondingly,we obtained our correction value,which was taken as initial value in the next step of prediction-correction process.Furthermore,the numerical experiments we carried out show that the algorithm is stable;it does keep the edges and details in the original image.It is concluded that the algorithm in our paper is a good method for image zooming.