基于数学形态学的图像边缘检测方法

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哈尔滨工业大学理学硕士学位论文
目
录
摘 要 ......................................................................................................................I ABSTRACT ........................................................................................................... II 第 1 章 绪 论 ....................................................................................................... 1 1.1 引言 .............................................................................................................. 1 1.2 数字图像处理概述 ....................................................................................... 1 1.2.1 数字图像处理的发展与应用 ................................................................. 1 1.2.2 数字图像处理的主要内容 ..................................................................... 2 1.3 数学形态学概述 ........................................................................................... 3 1.3.1 数学形态学的发展状况 ........................................................................ 3 1.3.2 数学形态学在图像处理中的应用 ......................................................... 3 1.4 边缘检测概述 ............................................................................................... 4 1.4.1 图像边缘的定义 .................................................................................... 4 1.4.2 边缘检测的发展历程与趋势 ................................................................. 5 1.4.3 理想边缘检测结果的要求 ..................................................................... 6 1.4.4 边缘检测中存在的难题 ........................................................................ 6 1.5 本文的研究内容及安排 ............................................................................... 8 第 2 章 图像边缘检测的常见算法 ........................................................................ 9 2.1 基于梯度的边缘检测算子 ........................................................................... 9 2.1.1 Roberts 算子 ......................................................................................... 10 2.1.2 Sobel 算子 ............................................................................................ 11 2.1.3 Prewitt 算子 .......................................................................................... 11 2.2 基于二阶微分的边缘检测算子 .................................................................. 12 2.2.1 Laplace 算子 ......................................................................................... 13 2.2.2 LOG 算子 ............................................................................................. 13 2.2.3 Canny 算子 ........................................................................................... 14 2.3 新兴的边缘检测算法 ................................................................................. 15 2.3.1 小波分析 .............................................................................................. 15 2.3.2 模糊算法 .............................................................................................. 16 2.3.3 人工神经网络 ...................................................................................... 16 2.4 实验结果分析 ............................................................................................. 16 2.4.1 无噪声时的边缘检测结果分析 ........................................................... 16
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哈尔滨工业大学理学硕士学位论文
can be seen from the results that the improved operators are better on the effect of edge detection and denoising performance, and can be used widely in the later image processing. Keywords: Mathematical morphology, Edge detection, Structuring element, Denoising performance
国内图书分类号： O175 国际图书分类号： 519.7
学校代码： 10213 密级：公开
理学硕士学位论文
基于数学形态学的图像边缘检测方法
硕 士 研 究 生 ： 曹晓琳 导 申 学 所 答 在 辩 单 日 请 学 师 ： 高广宏副教授 位 ： 理学硕士 科 ： 计算数学 位 ： 理学院数学系 期 ： 2012 年 7 月
授 予 学 位 单 位 ： 哈尔滨工业大学
Classified Index: O175 U.D.C.: 519.7
Dissertation for the Master Degree in Science
IMAGE EDGE DETECTION METHOD BASED ON MATHEMATICAL MORPHOLOGY
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哈尔滨工业大学理学硕士源自文库位论文
Abstract
Image edge is one of the most basic characteristics of the image, and edge detection is an important link of image pre-processing and analysis, with a wide range of theoretical and practical significance. Compared with traditional edge detection methods, image edge detection based on mathematical morphology is better, since it can change the scale of the morphological structuring element to overcome the effect of noise, and change the structure and orientation of structuring element to detect richer edges. This method can not only meet the real-time requirements, but also be easily to implemented in hardware. This paper first introduces the basic concepts and development status of mathematical morphology and edge detection, elaborates traditional edge detection methods, performs the experimental analysis of the image with and without noise, simultaneously, and then introduces some new emerging edge detection methods briefly. Since the method of edge detection in this paper is that based on mathematical morphology, we then introduce the basic theory of mathematical morphology, present some basic morphological operator formulas, and simulate in the case with and without noise and carry out a detailed analysis and summary. According to the characteristics of morphological operators and the disadvantages of selecting single structuring elements, this paper gives two improved morphological edge detection operators. The first improved operator is the formula constructed based on the characteristics of erosion, dilation, opening and closing operations to. In the images with noise, by using the open-close operation of this formula repeatedly to filter, we can effectively suppress noise. At the same time, since the selected structuring elements have the characteristic of multi-directional, this method can detect the edge information in different directions to ensure the integrity of the edge information. The second improved operator uses different structuring elements on the basis of the first improved operator, and has the characteristics of multi-structure, multi-scale and multi-direction. The multi-structuring element can detect various types of image edges, while rational combination of the multi-scale structuring element can suppress noise effectively, and simultaneously detect better edge details. Finally, this paper experiments with the two improved operators above, and compares with the previous morphological operators and traditional operators. It
Candidate： Supervisor： Academic Degree Applied for： Speciality： Affiliation： Date of Defence： Degree-Conferring-Institution：
Cao Xiaolin A.P. Gao Guanghong Master of Science Computational Mathematics Department of Mathematics July, 2012 Harbin Institute of Technology
哈尔滨工业大学理学硕士学位论文
摘 要
图像边缘是图像的一个最基本特征，图像边缘检测是图像预处理与分析的 重要环节之一，具有广泛的理论与实际意义。与传统的边缘检测方法相比，基 于数学形态学的图像边缘检测方法更好，它可以通过使形态结构元素的尺度发 生改变来克服噪声影响，并可以通过改变结构元素的结构和方向来检测到更加 丰富的边缘，此方法既能满足实时性的要求，又容易硬件实现。 本文首先介绍了形态学与边缘检测的基本概念及发展现状，对传统边缘检 测方法进行了阐述，并进行了有无噪声图像的实验分析，同时还简单介绍了新 兴的一些边缘检测方法。本文采用的边缘检测方法是基于数学形态学的图像边 缘检测方法，因而首先介绍了数学形态学的基本理论，给出了几种基本形态学 算子公式及在有无噪声情况下的图像仿真模拟，并进行了详细的分析与总结。 根据形态学算子的特点及选取单一结构元素的缺点，本文提出了两种改进的形 态学边缘检测算子。 改进算子一是根据开闭运算与膨胀腐蚀运算的特点构造的公式。在含有噪 声的图像中，利用此公式的反复开闭运算进行滤波，可以有效的抑制噪声。同 时采用的结构元素具有多结构和多方向的特点，这样既可以检测到多种类型的 图像边缘，又能检测出不同方向的边缘信息，以确保边缘信息的完整性。 改进算子二在改进算子一的基础上采用了不同的结构元素，其特点是具有 多结构、多尺度及多方向性。多尺度结构元素的合理组合，能够有效地抑制噪 声的同时检测到更好的边缘细节。 本文最后对两种改进算子进行了实验，并与之前的形态学算子和传统算子 进行比较，可以看出改进算子的边缘检测效果及抗噪性能都较更好，在以后的 图像处理中可以广泛应用。 关键词： 数学形态学；边缘检测；结构元素；抗噪性能