基于偏微分方程的图像平滑方法的讨论作者姓名：刘洋 专业班级：信息与计算科学 2025070201 指导老师：王茂芝摘 要在信息化的社会里，图像在信息传播中所起的作用越来越大。所以，消除在图像采集和传输过程中而产生的噪声，保证图像受污染度最小，成了数字图像处理领域里的重要部分，图像平滑作为图像处理中的重要环节，也逐渐受到人们的关注，图像平滑的目的主要是消除噪声。本文详细介绍了图像平滑的进展，图像平滑方法按空间域和频率域的分类及各种方法的特点，由于传统的这些方法在去噪的同时会破坏图像的重要特征从而引出了基于偏微分方程的图像平滑方法。首先介绍图像处理应用时的常用函数及其用法；其次详细阐述了几种去噪算法原理及特点；最后运用 Matlab 软件对一张含噪图片（含高斯噪声或椒盐噪声）进行仿真去噪，本文分别从各向同性扩散方程和各向异性扩散方程对基于偏微分方程的图像平滑方法进行讨论，进一步完善图像平滑方法，以达到平滑效果更理想的目的。关键词：图像平滑；偏微分方程；各向同性扩散；各向异性扩散 Based on partial differential equations for image smoothing methodAbstract In the information society, the role of image in the dissemination of information. Therefore, to eliminate the noise in the image acquisition and transmission process to ensure that an important part of the image contaminated minimum, has become the field of digital image processing, image smoothing as an important link in image processing, but also gradually by the attention, smooth the image main purpose is to eliminate noise.This paper describes the development of image smoothing, image smoothing method according to the classification of the space and frequency domains and the characteristics of the various methods, these methods due to the traditional denoising will also undermine the image of the important characteristics which leads based on partial differential equationsimage Smoothing Method. First introduced the common functions and their usage in image processing applications; elaborate...
