基于数学形态学的边缘检测研究
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摘要
图像的边缘是图像的基本特征之一,它包含了图像的位置、轮廓等重要信息,因此对图像的边缘进行检测是图像处理和分析中重要的过程。由于图像测量、图像压缩、图像分割、以及图像识别都是以图像检测为基础的,因此对图像进行边缘检测有极其重要的意义。一些经典的边缘检测方法大都是基于微分运算,其中包含Sobel算子、Prewitt算子、Robert算子、LOG算子、Canny算子等。目前也有一些新的算法,例如:统计判决法、边缘连接法、小波边缘检测法、基于模糊学的边缘检测等。但这些方法都其局限性及适用范围。针对上述方法的缺点,本文提出了一种多尺度、多结构的结构元素形态学的边缘检测方法。
本文首先介绍了图像边缘、边缘检测的定义,以及边缘检测的意义。然后进一步介绍了各种经典的边缘检测算法,以及其他新的边缘检测方法。并且通过仿真实验讨论了其中部分算法的优缺点。接着介绍了数学形态学中二值形态学与灰度形态学的基本知识与性质以及数学形态学在图像处理中的应用,介绍了现有的基于形态学边缘检测的方法。最后在现有的算法基础上提出一种新的边缘检测算法。该方法是在传统的数学形态学边缘检测算子上加以改进,能有效的提取图像的边缘,对椒盐噪声和高斯噪声都有很好的抑制作用,而且简单实用。该方法是一种多尺度和多结构的结构元素结合的形态学边缘检测法,在边缘检测问题上取得了较好的效果。
Edge is one of basic traits of image, it contains some important information, for example place of image, figure and so on. Thence, edge detection is an important process of image processing and analyze. Edge detection is the foundation technology of image processing that contains image measuring, image segmentation, image compressing, and image recognition, so it is very important. There are many classic methods about edge detection that based on differential coefficient, for example, Sobel operator based grads, Prewitt operator, Robert operator, Laplace operator, LOG operator, Canny operator and so on. Now there are some new methods, such as statistical, edge connecting, edge detection based on micro-wavelet. However, these methods only use in some limitation area. Through analyze merits and drawbacks of these methods,and then create a new edge detection which based on mathematical morphology.
Firstly,present definition of digital image,image detection and its functions and significance. Secondly, present some classic and new edge detection methods, and then summarize their merits and drawbacks by experiments. In succession, summarize basic knowledge and properties of binary morphology and gray morphology, and clarify purposes of these morphology operators in image processing. Finally, create a new edge detection method based on existent mathematical morphology. Multi-scale and multi-frame frame elements are used in the method. The method that improves those traditional methods, can detect better edge details, and can resist salt and pepper noise and Gaussian noise, and it is easy and useful. The method based on mathematical morphology which is a combination of multi-scale and multi-structure structure elements. It is good for image edge detection.
本文首先介绍了图像边缘、边缘检测的定义,以及边缘检测的意义。然后进一步介绍了各种经典的边缘检测算法,以及其他新的边缘检测方法。并且通过仿真实验讨论了其中部分算法的优缺点。接着介绍了数学形态学中二值形态学与灰度形态学的基本知识与性质以及数学形态学在图像处理中的应用,介绍了现有的基于形态学边缘检测的方法。最后在现有的算法基础上提出一种新的边缘检测算法。该方法是在传统的数学形态学边缘检测算子上加以改进,能有效的提取图像的边缘,对椒盐噪声和高斯噪声都有很好的抑制作用,而且简单实用。该方法是一种多尺度和多结构的结构元素结合的形态学边缘检测法,在边缘检测问题上取得了较好的效果。
Edge is one of basic traits of image, it contains some important information, for example place of image, figure and so on. Thence, edge detection is an important process of image processing and analyze. Edge detection is the foundation technology of image processing that contains image measuring, image segmentation, image compressing, and image recognition, so it is very important. There are many classic methods about edge detection that based on differential coefficient, for example, Sobel operator based grads, Prewitt operator, Robert operator, Laplace operator, LOG operator, Canny operator and so on. Now there are some new methods, such as statistical, edge connecting, edge detection based on micro-wavelet. However, these methods only use in some limitation area. Through analyze merits and drawbacks of these methods,and then create a new edge detection which based on mathematical morphology.
Firstly,present definition of digital image,image detection and its functions and significance. Secondly, present some classic and new edge detection methods, and then summarize their merits and drawbacks by experiments. In succession, summarize basic knowledge and properties of binary morphology and gray morphology, and clarify purposes of these morphology operators in image processing. Finally, create a new edge detection method based on existent mathematical morphology. Multi-scale and multi-frame frame elements are used in the method. The method that improves those traditional methods, can detect better edge details, and can resist salt and pepper noise and Gaussian noise, and it is easy and useful. The method based on mathematical morphology which is a combination of multi-scale and multi-structure structure elements. It is good for image edge detection.
引文
[1]冈萨雷斯.数字图像处理[M].北京:电子工业出版社,2003,471-474.
[2]陈书海,傅录祥.实用数字图像处理[M].北京:科学出版社,2005:120-121.
[3]胡学龙,徐开字.数字图像处理[M].北京:北京工业出版社,2003:180-184.
[4]杨帆等.数字图像处理与分析[M].北京:北京航空航天出版社, 2007.
[5]王坤.多尺度结构元素的数学形态边缘检测新方法[J].东北大学学报,2008,4(29):473-476 .
[6]张德丰. MATLAB数字图像处理[M].北京:机械工业出版社,2009:120-121.
[7]白相志.基于改进形态学算子的多尺度边缘检测[J].中国图象图形学报,2007,9(9):1612-1613 .
[8] William K.Pratt.数字图像处理[M].北京:机械工业出版社,2005:120-121.
[9]傅茂名.基于形态灰度边缘检测算法的一种改进[J].电子科技大学学报,2005,2(34):206-209 .
[10]蔡友杰.基于形态学的边缘检测[J].计算机应用与软件,2009,5(26):213-214.
[11]顾茂松.基于局部差别的形态学边缘检测方法研究[J].红外与激光工程,2006,35(10):276-279.
[12]范立南,韩晓波,张广渊.数字图像处理与模式识别[M].北京:科学出版社,2007:120-121.
[13]杨淑莹. VC++图像处理程序设计[M].北京:清华大学出版社,2005:120-121.
[14]杨述斌.交替滤波的加权形态学边缘检测算法[J].武汉工程大学学报,2009,7(31):88-90 .
[15]朱柱.边缘检测技术研究[D].苏州大学,2010.
[16]陈宇云.灰度图像的边缘检测研究[D].电子科技大学,2009.
[17]何俊峰.基于视觉原理的图像的边缘检测算子研究[D].华中科技大学,2006.
[18]方磊.基于数学形态学的边缘检测[D].昆明理工大学,2010.
[19]王咏胜.基于数学形态学的灰度图像的边缘检测技术研究[D].哈尔滨工程大学,2005.
[20]赵慧.基于数学形态学的图像边缘检测方法研究[D].大连理工大学,2010.
[21] D.Marr, E.Hildreth. Theory of edged detection. [J] Computer Vision,2006,77-107.
[22]姚进.基于数学形态学的边缘检测研究[D].山东师范大学,2010.
[23]蔡正涛.基于双结构元数学形态学边缘检测方法[D].西北工业大学,2009.
[24]沈阳.基于形态学的边缘检测技术研究[D].电子科技大学,2008.
[25]杨平先.一种改进多尺度形态学边缘检测算法[J].光电工程,2005,11(32):73-75.
[26]尚俊娜.一种改进柔性形态学边缘检测算法[J].杭州电子科技大学学报,2009,29(5):75-78.
[27]黄剑玲.一种基于形态学的多结构多尺度图像边缘检测算法[J].微电子学与计算机,2009,8(62):76-79 .
[28] SOILLEP,PESARESIM .Advances in mathematical morphology applied to geoscience and Remote Sensing[J]. IEEE Trans on Geosci Remote Sensing,2008,40(9):2043一2055.
[29] PESARESL M,BENEDIKTSSON J. A new approach for the morphological segmentation of high resolution satellite imagery[J].IEEE Trans on Geosei Remote Sensing,2007,39:309-320.
[30]杨凡.一种新的多方向模糊形态学边缘检测算法[J].图像处理,2009,1(3):14-19.
[31]汪林林.自适应多方向模糊形态学边缘检测算法[J].计算机应用与研究,2009,26(3):1177-1179.
[32]李峰.自适应多结构形态学边缘检测方法[J].湖南有色金属,2009,26(10):263-268.
[33]亢洁.自适应权重形态学边缘检测算法研究[J].计算机工程与应用,2010,46(17):163-168.
[34]任文杰.图像边缘检测方法研究[D].山东大学,2008.
[35]范立南,韩晓微,张广渊.图像处理与模式识别[M].北京:科学出版社,2007:120-121.
[36] James S J Lee, Robert M, Haralick, Linda G Shapiro. Morphologic edge detection [J]. IEE Journal of Robotics and Automation, 2008, RA-3(2): 142-156.
[37] Young, C. Alex. Multi-scale Edge Detection in the Corona [J].Bell System Tech.2008, 4(38):457-469.
[38] Berlemont. Combining local filtering and multi-scale analysis for edge, ridge, and curvilinear objects detection [J]. IEEE Transactions on Image Processing, 2010, 19(1):74-84.
[39] Jiang, J.A. Mathematical-morphology-based edge detectors for detection of thin edges in low-contrast regions [J]. ET Image Processing, 2007,1(3):269-277.
[40] Laligant,Olivier. A Nonlinear Derivative Scheme Applied to Edge Detection[J].IEEE Trans Transactions on Pattern Analysis & Machine Intelligence, 2010,32(2):242-257.
[41]崔艳莉.改进基于模糊集的边缘检测算法[J].图像处理,2009,3(8):47-48.
[42]张喜平.一种改进的基于模糊推理的边缘检测算法[J].计算机应用与软件,2009,5(26):213-214 .
[2]陈书海,傅录祥.实用数字图像处理[M].北京:科学出版社,2005:120-121.
[3]胡学龙,徐开字.数字图像处理[M].北京:北京工业出版社,2003:180-184.
[4]杨帆等.数字图像处理与分析[M].北京:北京航空航天出版社, 2007.
[5]王坤.多尺度结构元素的数学形态边缘检测新方法[J].东北大学学报,2008,4(29):473-476 .
[6]张德丰. MATLAB数字图像处理[M].北京:机械工业出版社,2009:120-121.
[7]白相志.基于改进形态学算子的多尺度边缘检测[J].中国图象图形学报,2007,9(9):1612-1613 .
[8] William K.Pratt.数字图像处理[M].北京:机械工业出版社,2005:120-121.
[9]傅茂名.基于形态灰度边缘检测算法的一种改进[J].电子科技大学学报,2005,2(34):206-209 .
[10]蔡友杰.基于形态学的边缘检测[J].计算机应用与软件,2009,5(26):213-214.
[11]顾茂松.基于局部差别的形态学边缘检测方法研究[J].红外与激光工程,2006,35(10):276-279.
[12]范立南,韩晓波,张广渊.数字图像处理与模式识别[M].北京:科学出版社,2007:120-121.
[13]杨淑莹. VC++图像处理程序设计[M].北京:清华大学出版社,2005:120-121.
[14]杨述斌.交替滤波的加权形态学边缘检测算法[J].武汉工程大学学报,2009,7(31):88-90 .
[15]朱柱.边缘检测技术研究[D].苏州大学,2010.
[16]陈宇云.灰度图像的边缘检测研究[D].电子科技大学,2009.
[17]何俊峰.基于视觉原理的图像的边缘检测算子研究[D].华中科技大学,2006.
[18]方磊.基于数学形态学的边缘检测[D].昆明理工大学,2010.
[19]王咏胜.基于数学形态学的灰度图像的边缘检测技术研究[D].哈尔滨工程大学,2005.
[20]赵慧.基于数学形态学的图像边缘检测方法研究[D].大连理工大学,2010.
[21] D.Marr, E.Hildreth. Theory of edged detection. [J] Computer Vision,2006,77-107.
[22]姚进.基于数学形态学的边缘检测研究[D].山东师范大学,2010.
[23]蔡正涛.基于双结构元数学形态学边缘检测方法[D].西北工业大学,2009.
[24]沈阳.基于形态学的边缘检测技术研究[D].电子科技大学,2008.
[25]杨平先.一种改进多尺度形态学边缘检测算法[J].光电工程,2005,11(32):73-75.
[26]尚俊娜.一种改进柔性形态学边缘检测算法[J].杭州电子科技大学学报,2009,29(5):75-78.
[27]黄剑玲.一种基于形态学的多结构多尺度图像边缘检测算法[J].微电子学与计算机,2009,8(62):76-79 .
[28] SOILLEP,PESARESIM .Advances in mathematical morphology applied to geoscience and Remote Sensing[J]. IEEE Trans on Geosci Remote Sensing,2008,40(9):2043一2055.
[29] PESARESL M,BENEDIKTSSON J. A new approach for the morphological segmentation of high resolution satellite imagery[J].IEEE Trans on Geosei Remote Sensing,2007,39:309-320.
[30]杨凡.一种新的多方向模糊形态学边缘检测算法[J].图像处理,2009,1(3):14-19.
[31]汪林林.自适应多方向模糊形态学边缘检测算法[J].计算机应用与研究,2009,26(3):1177-1179.
[32]李峰.自适应多结构形态学边缘检测方法[J].湖南有色金属,2009,26(10):263-268.
[33]亢洁.自适应权重形态学边缘检测算法研究[J].计算机工程与应用,2010,46(17):163-168.
[34]任文杰.图像边缘检测方法研究[D].山东大学,2008.
[35]范立南,韩晓微,张广渊.图像处理与模式识别[M].北京:科学出版社,2007:120-121.
[36] James S J Lee, Robert M, Haralick, Linda G Shapiro. Morphologic edge detection [J]. IEE Journal of Robotics and Automation, 2008, RA-3(2): 142-156.
[37] Young, C. Alex. Multi-scale Edge Detection in the Corona [J].Bell System Tech.2008, 4(38):457-469.
[38] Berlemont. Combining local filtering and multi-scale analysis for edge, ridge, and curvilinear objects detection [J]. IEEE Transactions on Image Processing, 2010, 19(1):74-84.
[39] Jiang, J.A. Mathematical-morphology-based edge detectors for detection of thin edges in low-contrast regions [J]. ET Image Processing, 2007,1(3):269-277.
[40] Laligant,Olivier. A Nonlinear Derivative Scheme Applied to Edge Detection[J].IEEE Trans Transactions on Pattern Analysis & Machine Intelligence, 2010,32(2):242-257.
[41]崔艳莉.改进基于模糊集的边缘检测算法[J].图像处理,2009,3(8):47-48.
[42]张喜平.一种改进的基于模糊推理的边缘检测算法[J].计算机应用与软件,2009,5(26):213-214 .
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