本文主要研究的是偏微分方程在数字图像处理方面的应用。文章首先详细阐

述了尺度空间的概念和性质，并以热传导方程所确定高斯尺度空间为例给出了连

续尺度空间与偏微分方程的联系。接着文章由简单的线性扩散方程开始，介绍了

非线性同质扩散和非线性异质扩散，不仅给出了相应的具体扩散方程模型，而且

对它们在图像处理中的不同效果作了比较。-This paper studies the partial differential equations in the digital image processing applications. The article first elaborates the concept of scale space and nature, and to determine the heat conduction equation by the Gaussian scale space is given as an example a continuous scale space with the associated partial differential equations. Then a simple article from the beginning of the linear diffusion equation, introduce a non-linear homogeneous proliferation and the proliferation of non-linear heterogeneous, not only the corresponding specific diffusion equation model, but also for them to deal with different image effects were comparison.