基于反热传导方程与Sobel算子的图像锐化方法  

An Image Sharpening Method Based on Anti-Heat Conduction Equations and Sobel operator

作　　者：赵恩良[1] 孙丽华[1] 周巧姝[2] 徐英祥[3] 

机构地区：[1]沈阳建筑大学理学院,辽宁沈阳110168 [2]长春师范学院学报编辑部,吉林长春130032 [3]东北师范大学数学与统计学院,吉林长春130024

出　　处：《沈阳建筑大学学报（自然科学版）》2009年第6期1221-1224,共4页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家自然科学基金项目(10701038)

摘　　要：目的应用偏微分方程理论与经典的图像锐化算子,研究图像锐化的有效方法.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,推导出反热传导方程,在满足模糊图像是原图像被热传导滤波器作用的结果和参数t足够小的情况下,建立图像锐化模型,利用Sobel算子求解偏微分方程,实现图像锐化.结果数值实验显示应用笔者所提方法对图像进行锐化,得到了相对清晰的图像,锐化后的图像没有信息偏移现象,而且不会出现噪声.同时对图像的边缘和细节特征保持较好.结论笔者所提算法具有长时间计算的稳定性,锐化图像不会随着迭代次数的增加而变得模糊,是一种有效的图像锐化方法.The paper studies effective ways to sharpen images by using partial differential equations and the classical image sharpening operators. Based on the physical meaning of heat equation, and regarding the values of an image as the temperature on a flat object, a model of the inverse heat equation is obtained. Under the assumptions that the blurred image is the result of the original image filtered by the heat equation and the time t is small enough, a model for image sharpening is established, which is solved by means of Sobel operator. The results of numerical experiments show that the method can make the images much sharper and obtain clearer image. Sharpened image hasn＇t moved information, and at the same time denoising doesn＇t appear. It does keep the edges and details in the original image. The algorithm maintains stable over a long time, and the sharpened image is not blurred with the increase of the number of iterations.

关 键 词：偏微分方程 图像锐化 SOBEL算子 反热传导方程 

分 类 号：TN911.73[电子电信—通信与信息系统]