基于分数阶微分的边缘检测方法的研究.doc

毕业设计(论文) 题 目 基于分数阶微分的边缘检测 方法的研究 专 业 信息与计算科学 班 级 2006级1班 学 生 陈 辉 指导教师 汪达成 蒋 伟 目 录 摘 要 I ABSTRACT II 第一章 引 言 1 1.1 课题研究背景和意义 1 1.2 边缘检测的研究现状 1 1.3 本文结构 2 第二章 常用边缘检测方法 3 2.1 经典算子边缘检测 3 2.2 基于小波变换的边缘检测 4 2.3 基于数学形态学的边缘检测 6 2.4 其他学科在边缘检测中的应用 7 2.5 本章小结 8 第三章 基于分数阶微分的边缘检测方法 9 3.1 预备知识 9 3.2 一种新的边缘检测模型 11 3.3 新模型与常用算法的对比实验 13 3.4 本章小结 16 第四章 总结及未来工作 18 4.1总结 18 4.2 未来的工作 18 致 谢 19 参考文献 20 附 录 21 摘 要 图像边缘检测作为数字图像处理的研究热点之一，不仅得到人们广泛的重视和研究，也在实际中得到大量的应用。图像边缘检测效果的好坏直接关系到其后续的图像处理工作，例如图像分割，模式识别等。其目的是提取图像结构信息，剔除不相关的信息。但现有的图像方法还存在一些不足如不能较好的。近年来，基于微分( Differential)的图像的研究受到国内外学者的极大关注，并取得了一系列的成果。采用了分数阶微分方法对图像边缘检测进行了研究，在Sobel算子的基础上，一种模型，并用直接差分法对该模型进行数值仿真关键词 边缘检测，分数阶微分，Sobel算子 ABSTRACT one research topic of the digital image processing, was highly researched and attached by people, and were applied widely in many fields. The quality of image edge detection is directly related to the follow-up image processing tasks such as image segmentation, pattern recognition, and so on. Its purpose is to extract the structure information of images and eliminate the irrelevant information. However, there was many weaknesses in the present methods of image edge detection. For instance，the present methods of image edge detection fails to extract the edge of image better and get a higher Signal Noise Ratio(SNR). In recent years, so many researchers had studied image edge detection based on Fractional Differential, and got a series of success. This paper has discussed the methods of image edge detection based on Fractional Differential Equations, extended and improved the Sobel operator, got a new model of Fractional Differential Equations of Sobel operator. Then we use the direct difference method to simulate the model. The simulation results shows that the new model has the features of high accuracy of image edge and little non-edge noise, got a better effect of edge detection. KEY WORDS edge detecti