基于偏微分方程和非局部方法的图像处理模型研究

项目名称： 基于偏微分方程和非局部方法的图像处理模型研究

项目编号： No.11271141

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 房少梅

作者单位： 华南农业大学

项目金额： 60万元

中文摘要： 本项目研究基于偏微分方程和非局部方法的图像处理问题。主要研究内容如下：首先，将具有非局部性质的一致锐度算子嵌入到各向异性的非线性扩散方程进行图像处理，针对不同图像处理的实际需求，通过选择参数及扩散控制函数，建立不同的改进模型，希望能在有效控制噪音的同时也能够很好地保持边界信息；其次，将一致锐度算子和分数阶偏微分方程相结合，充分利用分数阶偏微分方程处理纹理丰富的图像非常有效的优点与一致锐度算子对噪音不敏感的特点，寻求合适的方法，使其在噪音有效控制、纹理保持和边界检测与提取等方面达到一致，建立、改进和完善图像（特别是医学图像）处理模型。本项目在对如上问题进行数学理论研究的同时，将针对不同参数配置的模型进行数值模拟，以期达到更好地图像处理效果。本项目的特点是用一致锐度算子和分数阶导数算子这样的非局部方法来处理实际图像问题，这和国际上近年来关于非局部邻域滤波处理图像的非局部思想是相似的。

中文关键词： 偏微分方程；非局部分析；分数阶微分算子；图像处理；算法设计

英文摘要： The research project mainly study the image processing problems based on partial differential equations and nonlocal methods. The research includes two aspects: On one hand, we will introduce and employ the region homogeneity measure operator which behaves the nonlocal properties to the anisotropic nonlinear diffusion partial differential equations for image processing. According to the different applications and requirements in image processing, we will develop different kinds of improved models by selecting parameters and controlling the diffusion functions, in order to achieve a good trade-off between noise removal and edge preservation. On the other hand, considering the advantages of fractional differential equations being better for texture images processing and the region homogeneity measure operator is not sensitive to the noise, we will study the combined methods, establish the basic mathematical models and improve them for image processing, especially for the medical images. We will also analyze these models and reach the compromise among noise removal, texture maintenance and edge detection and extraction. This project also carries out some numerical simulation based on different models and parameters in these models in order to achieve better image processing effect, while analyzing mathematical theo

英文关键词： partial differential equations；nonlocal analysis；fractional differential operator；image processing；algorithm design