图像滤波中P-M方程的两层格式算法

基于偏微分方程方法的图像处理是近十多年来发展起来的新兴领域,近年来,偏微分方程在刻画图形演化和进行特征分析等方面取得了非凡的效果,然而使用这些方法却面临着计算效率低下的问题,如何大规模提高图像处理中所涉及微分方程的快速数值计算成为一个数字图像处理里面的重要问题。在经典的Perona Malik(P-M)方程的图像处理方法基础上,构造显、隐式相结合的两层有限差分格式来提高求解的速度。仿真结果表明,构造的两层格式简单有效。

Two Layers Format Algorithm of P-M Equation in Image Filtering

The image processing based on PDE method is an emerging field developed over the past decade.In recent years,the partial differential equations have achieved extraordinary effect in the characterization of graphics evolution,feature analysis and other aspects,while the problem of low calculation efficiency has appeared in the use of these methods.Therefore,how to massively improve the fast numerical calculation of differential equation involved in image processing becomes an important problem in digital image processing.Based on the classical image processing method of Perona Malik（ PM） equation,the two layers finite difference scheme is constructed by combing the explicit and implicit expression to improve the speed of solving.A large number of numerical results show that the two layers constructed is simple and effective.