基于颜色降维的彩色图像边缘检测研究
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摘要
边缘作为图像最基本的特征,存在于图像的不规则结构和不平稳现象中,即存在于信号的突变点处,这些点不仅传递了大部分的图像信息并且给出了图像轮廓的具体位置,而这些轮廓又是图像处理时所需要的非常重要的信息。在计算机视觉中,边缘检测是获取图像中物体的重要特性的过程。图像的边缘检测大幅度地减少了数据量,并且剔除了不相关的信息,保留住了图像中重要的结构属性,为后续的图像处理工作奠定了基础。边缘检测作为图像分析和理解的基本步骤,其结果的准确性和可靠性使得机器视觉系统对客观世界的理解产生直接影响。目前提出的边缘检测算子大多数是针对灰度图像的,对彩色图像的边缘检测算法的研究还远没有灰度图像边缘检测发展的成熟。
本文首先综述了边缘检测的相关算法的研究,对经典边缘检测算子进行了分析比较；在介绍了彩色空间的基础上,对彩色图像边缘检测的方法如经典边缘检测算子方法,多维度梯度方法,向量空间法等进行了分类研究,在此基础上本文开展了如下的研究工作：
(1)RGB空间是最常用的一种彩色信息表达空间,彩色图像通常是以RGB的方式存储与表达,根据RGB颜色空间的特性,本文利用像素点的颜色坐标r,g,b构建像素的颜色三角形,计算该三角形的周长和内角。将周长和内角作为像素点的信息量的度量。通过像素点在相关邻域上的信息量的计算,确定该像素点是否为彩色图像的边缘点。这种边缘检测方法,将三维空间的颜色信息转换到二维空间进行考虑,在二维空间中定义出像素点的颜色信息量。实验结果表明,与传统方法相比,该方法能检测出更多的边缘,并且算法实现简单,检测出的边缘清晰。
(2)HSI色彩空间是从人的视觉系统出发,用色调、饱和度、和亮度来描述色彩,它比RGB色彩空间更符合人的视觉特性。在图像处理和计算机视觉中大量算法都可以在HSI色彩空间中方便地使用,这三个分量可以分开处理并且是相互独立的。通过分析HSI空间的特点提出了以下方法：利用像素点的颜色坐标H,S,I构建像素的颜色三角形,S和I为三角形的两条边,H为两边的夹角,从而确定该三角形的面积和边长。任意改变H,S,I的值即改变颜色,同时三角形的面积和形状也会发生相应的改变,从而可以用面积和周长为信息量判断该像素点是否为彩色图像的边缘点。文中算法检测出的图像边缘与经典边缘算子提取的图像边缘相比较,结果更加清晰完整。
Edge is the most fundamental characteristic of the image which exists in irregular structure and unstable phenomenon.In other words, it exists in the abrupt change of signal. These points not only transferred most image information but also gave an concrete location of image outline. These outlines are very important in image processing. In computer vision, edge detection is an essential step in gaining the important characteristics of objects. Edge detection has decreased data amount by a large margin, got rid of the irrelevant information, reserved the important structure attribute of image, and established a basis for future work. As the fundamental step of the image analysis and understanding, the accuracy and reliability of edge detection make the computer vision affect the understanding of the objective world directly. At present, most of the old methods applied to grayscale images, the research of edge detection algorithm for color image is far from mature than gray ones.
This thesis first summarized the methods of edge detection and make a contrast among these classical edge detection operators. On the basis of introduction of the color space, we classify the methods into many categories, such as classical edge detection operators method, multi-dimension grads method, vector space method and so on, then make a research on them. On the basis of theses, the main works are as follows:
(1) RGB space is the most common space for expressing the color information. Color image is usually stored and expressed in the form of RGB. According to the characteristics of RGB color space, we constructed the color triangle of a pixel using its color coordinates, and consequently calculate the perimeter and the internal angle of the color triangle. The perimeter and the internal angle of the triangle can be seen as the information measurement of a pixel. It can determine whether a pixel is the edge point of a color image by computing the information quantity of a pixel in its neighborhood. We transformed the color information from three-dimensional space to two-dimensional space, defined the measure of color information of pixel in two-dimensional space. Experimental results indicate that the method in this paper can be realized easily, and can detect more legible edges than the traditional method.
(2) HSI color space starts from human visual system, uses hue, saturation, and intensity to describe color. HSI color space is more suitable for human visual properties than RGB color space. A large number of algorithms can be used in HSI color space conveniently. This three components are independently and can be treated separately. Through analyzing the characteristics of HSI space, we proposed a method as follows:It can construct the color triangle of a pixel using its color coordinates. S and I are two edges of the triangle. H is an angle between the two edges. Then we can gain the triangle area and edge length. The color, triangle area and shape can change with any change of H, S, I value. It can determine whether a pixel is a edge point of color image by the information of area or edge length. Compared with the picture edge classical edge operator, the new one is clearer and more intact.
本文首先综述了边缘检测的相关算法的研究,对经典边缘检测算子进行了分析比较；在介绍了彩色空间的基础上,对彩色图像边缘检测的方法如经典边缘检测算子方法,多维度梯度方法,向量空间法等进行了分类研究,在此基础上本文开展了如下的研究工作：
(1)RGB空间是最常用的一种彩色信息表达空间,彩色图像通常是以RGB的方式存储与表达,根据RGB颜色空间的特性,本文利用像素点的颜色坐标r,g,b构建像素的颜色三角形,计算该三角形的周长和内角。将周长和内角作为像素点的信息量的度量。通过像素点在相关邻域上的信息量的计算,确定该像素点是否为彩色图像的边缘点。这种边缘检测方法,将三维空间的颜色信息转换到二维空间进行考虑,在二维空间中定义出像素点的颜色信息量。实验结果表明,与传统方法相比,该方法能检测出更多的边缘,并且算法实现简单,检测出的边缘清晰。
(2)HSI色彩空间是从人的视觉系统出发,用色调、饱和度、和亮度来描述色彩,它比RGB色彩空间更符合人的视觉特性。在图像处理和计算机视觉中大量算法都可以在HSI色彩空间中方便地使用,这三个分量可以分开处理并且是相互独立的。通过分析HSI空间的特点提出了以下方法：利用像素点的颜色坐标H,S,I构建像素的颜色三角形,S和I为三角形的两条边,H为两边的夹角,从而确定该三角形的面积和边长。任意改变H,S,I的值即改变颜色,同时三角形的面积和形状也会发生相应的改变,从而可以用面积和周长为信息量判断该像素点是否为彩色图像的边缘点。文中算法检测出的图像边缘与经典边缘算子提取的图像边缘相比较,结果更加清晰完整。
Edge is the most fundamental characteristic of the image which exists in irregular structure and unstable phenomenon.In other words, it exists in the abrupt change of signal. These points not only transferred most image information but also gave an concrete location of image outline. These outlines are very important in image processing. In computer vision, edge detection is an essential step in gaining the important characteristics of objects. Edge detection has decreased data amount by a large margin, got rid of the irrelevant information, reserved the important structure attribute of image, and established a basis for future work. As the fundamental step of the image analysis and understanding, the accuracy and reliability of edge detection make the computer vision affect the understanding of the objective world directly. At present, most of the old methods applied to grayscale images, the research of edge detection algorithm for color image is far from mature than gray ones.
This thesis first summarized the methods of edge detection and make a contrast among these classical edge detection operators. On the basis of introduction of the color space, we classify the methods into many categories, such as classical edge detection operators method, multi-dimension grads method, vector space method and so on, then make a research on them. On the basis of theses, the main works are as follows:
(1) RGB space is the most common space for expressing the color information. Color image is usually stored and expressed in the form of RGB. According to the characteristics of RGB color space, we constructed the color triangle of a pixel using its color coordinates, and consequently calculate the perimeter and the internal angle of the color triangle. The perimeter and the internal angle of the triangle can be seen as the information measurement of a pixel. It can determine whether a pixel is the edge point of a color image by computing the information quantity of a pixel in its neighborhood. We transformed the color information from three-dimensional space to two-dimensional space, defined the measure of color information of pixel in two-dimensional space. Experimental results indicate that the method in this paper can be realized easily, and can detect more legible edges than the traditional method.
(2) HSI color space starts from human visual system, uses hue, saturation, and intensity to describe color. HSI color space is more suitable for human visual properties than RGB color space. A large number of algorithms can be used in HSI color space conveniently. This three components are independently and can be treated separately. Through analyzing the characteristics of HSI space, we proposed a method as follows:It can construct the color triangle of a pixel using its color coordinates. S and I are two edges of the triangle. H is an angle between the two edges. Then we can gain the triangle area and edge length. The color, triangle area and shape can change with any change of H, S, I value. It can determine whether a pixel is a edge point of color image by the information of area or edge length. Compared with the picture edge classical edge operator, the new one is clearer and more intact.
引文
[1]姚敏等.数字图像处理[M].北京：机械工业出版社,2006.
[2]L.G Roberts. Machine Perception of Three Dimension Solids[A]. In Optical And Electro-Optical Information Processing. Cambridge, Mass:Mit Press,1965,159-197.
[3]高赞,姜威,朱孔凤等.基于Roberts梯度的自动聚焦算法[J].红外与激光工程,2006,35(1)：117-121.
[4]Sobel L. Camera models and machine Perception[D]. Stanford University, CA,1970.
[5]章毓晋.图像分割[M].北京：科学出版社,2001.
[6]韩君君.彩色图像边缘检测算法研究[D].曲阜师范大学,2009.
[7]余松煜,周源华,张瑞编.数字图像处理[M].上海：上海交通大学出版社,2007.
[8]孙正军.基于图像边缘提取的电池极片瑕疵检测研究[D].中南大学,2009.
[9]Canny J. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence,1986,8(6):679-698.
[10]John Canny. Finding edges and Lines in Images, MIT Artificial Intelligence Laboratory,1983.
[11]Chang. S.H, Leiguang Gong, Maoqing Li, etal. Small Retinal Vessel Extraction Using Modified Canny Edge Detection[C], IEEE ICALIP'08 Shanghai, China,2008,1255-1259.
[12]张昌林,苏小英.基于复合型数学形态学的中医学图像边缘处理方法的研究[J].计算机应用与软件,2008,25(9)：78-80.
[13]成晓倩,马洪超.一种基于数学形态学的边缘检测算子[J].四川测绘,2008,31(4)：174-176.
[14]Zhao YU-qian, Gui Wei-hua, Chen Zheng-cheng, etal. Medical Images Edge Detection Based on Mathematical Morphology[C]. Proceedings of the 2005 IEEE, Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China,2005:6492-6495.
[15]Rosenfeld.A, Thurston.M. Edge and curve detection for visual scene analysis[J]. IEEE Trans Computer,1971,20:512-519.
[16]Marr D, Hidreth E. Theory of Edge Detection[J]. Proc Roy Soc,1980,207(B):187-217.
[17]A.P. Witkin. Scale-Space Filtering[C]. In Proceedings of IJCAI, Karlsruhe,1983:1019-1021.
[18]Mallat S, Zhong S. Characterization of signals from multiscale edges [J]. IEEE Transaction on Pattern Analysis and Machine Intelligence,1992,14(7):710-732.
[19]赵登峰,许纯新.小波分析及其在数字图像处理中的应用[J].同济大学学报,2001,29(9)：1054-1057.
[20]孙延奎.小波分析及其应用[M].北京：机械工业出版社,2005.
[21]徐立章,王显仁.基于小波变换的多尺度边缘检测用于稻谷内部损伤的检测[J].中国粮油
学报,2008,23(4)：202-204.
[22]杨建国,林波,周瑞.基于分形的汽油机爆震边缘检测[J].内燃机学报,2006,24(1)：78-82.
[23]崔旭东,邱春蓉,刘瑞根.用标记松弛方法检测闪光图像边缘[J].光电工程,2001,28(4)：42-45.
[24]P. Kanungo, P.K. Nanda and U.C.Samal. Image Segmentation Using Threshold and Genetic Algorithm[J]. IEEE,2006:1-10.
[25]陈立英,裴喜春,侯振杰.基于遗传算法的血液细胞图像的分割方法研究[J].计算技术与自动化,2008(02).
[26]周龙,卢亚玲,谢兆鸿.模糊边缘检测算法在储粮害虫图像中的应用[J].微计算机信息,2005(05)：201-202.
[27]吕明忠,罗鹏等.一种基于色差的彩色图像的边缘检测方法[J].华东理工大学学报.2001,27(5).
[28]李文举,梁德群等.基于方向区域距离测度的彩色边缘检测方法[J].计算机用,2003,23(1).
[29]R.Nevatia. A Color Edge Detector and Its Use in Scene Segmentation[J]. IEEE Trans. Systems, Man, and Cybernetics,1977,7 (11):820-826.
[30]M.H.Hueckel. An Operator which Locates Edges in Digitized Pictures[J]. ACM,1971, 18(1):113-125.
[31]ScharcanskiJ, Venetsanopoulos A.N. Edge Detection of Color Images Using Directional operators[J]. IEEE Transactions on Circuits and Systems for Video Technology,1997, 7(2):397-401.
[32]R.D.Dony, S.Wesolkowski. Edge Detection on Color Images Using RGB Vector Angles[C]. IEEE Canadian Conference on Electrical and Computer Engineering. Edmonton, Alta, Canada: IEEE,19992,2:687-692.
[33]C.L.Novak, S.A.Shafer. Color Edge Detection[C]. In Proe.DARPA Image Understanding Workshop,1987,1:35-37.
[34]S.Di Zenzo. A Note on the Gradient of a Multi-Image[J]. Computer Vision, Graphics and Image Processing,1986,33(1):116-125.
[35]A.Cumani. Edge Detection in Multispectral Images[J]. CVGIP:Graphical Models and Image Proeessing,1991,53(1):40-51.
[36]T.L.Huntsberger, M.F.Descalzi. Color Edge Detection[J]. Pattern Recognition Letters,1985, 3(3):205-209.
[37]M.Pietikainen,D.Harwood. Edge Information in Color Images Based on Histograms of Differences[C]. Proc.Int'l Conf. Pattern Recognition,1986:594-596.
[38]C.K.Yang, W.H.Tsai. Reduction of Color Space Dimensionality by Moment-Preserving
Thresholding and its Application for Edge-Detection in Color Images[J]. Pattern Recognition Letters,1996,17(5):481-490.
[39]Djuric.P.M, Fwu.J.K. On the Detection of Edges in Vector Images[J]. IEEE Transactions on Image Processing,1997,6(11),1595-1601.
[40]P.E.Trahanias and A.N.Venetsanopoulos. Color edge detection using vector order statistics[J]. IEEE Trans.ImageProcessing,1993,2(2):259-264.
[41]Prewitt J, Mendelsohn M. The analysis of cell images[J]. Annals of the N.Y.Academy of Sciences,1966,128:1035-1053.
[42]万力,易昂,傅明.一种基于Canny算法的边缘提取改善方法,计算机技术与自动化.2003,22(1)：24-26.
[2]L.G Roberts. Machine Perception of Three Dimension Solids[A]. In Optical And Electro-Optical Information Processing. Cambridge, Mass:Mit Press,1965,159-197.
[3]高赞,姜威,朱孔凤等.基于Roberts梯度的自动聚焦算法[J].红外与激光工程,2006,35(1)：117-121.
[4]Sobel L. Camera models and machine Perception[D]. Stanford University, CA,1970.
[5]章毓晋.图像分割[M].北京：科学出版社,2001.
[6]韩君君.彩色图像边缘检测算法研究[D].曲阜师范大学,2009.
[7]余松煜,周源华,张瑞编.数字图像处理[M].上海：上海交通大学出版社,2007.
[8]孙正军.基于图像边缘提取的电池极片瑕疵检测研究[D].中南大学,2009.
[9]Canny J. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence,1986,8(6):679-698.
[10]John Canny. Finding edges and Lines in Images, MIT Artificial Intelligence Laboratory,1983.
[11]Chang. S.H, Leiguang Gong, Maoqing Li, etal. Small Retinal Vessel Extraction Using Modified Canny Edge Detection[C], IEEE ICALIP'08 Shanghai, China,2008,1255-1259.
[12]张昌林,苏小英.基于复合型数学形态学的中医学图像边缘处理方法的研究[J].计算机应用与软件,2008,25(9)：78-80.
[13]成晓倩,马洪超.一种基于数学形态学的边缘检测算子[J].四川测绘,2008,31(4)：174-176.
[14]Zhao YU-qian, Gui Wei-hua, Chen Zheng-cheng, etal. Medical Images Edge Detection Based on Mathematical Morphology[C]. Proceedings of the 2005 IEEE, Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China,2005:6492-6495.
[15]Rosenfeld.A, Thurston.M. Edge and curve detection for visual scene analysis[J]. IEEE Trans Computer,1971,20:512-519.
[16]Marr D, Hidreth E. Theory of Edge Detection[J]. Proc Roy Soc,1980,207(B):187-217.
[17]A.P. Witkin. Scale-Space Filtering[C]. In Proceedings of IJCAI, Karlsruhe,1983:1019-1021.
[18]Mallat S, Zhong S. Characterization of signals from multiscale edges [J]. IEEE Transaction on Pattern Analysis and Machine Intelligence,1992,14(7):710-732.
[19]赵登峰,许纯新.小波分析及其在数字图像处理中的应用[J].同济大学学报,2001,29(9)：1054-1057.
[20]孙延奎.小波分析及其应用[M].北京：机械工业出版社,2005.
[21]徐立章,王显仁.基于小波变换的多尺度边缘检测用于稻谷内部损伤的检测[J].中国粮油
学报,2008,23(4)：202-204.
[22]杨建国,林波,周瑞.基于分形的汽油机爆震边缘检测[J].内燃机学报,2006,24(1)：78-82.
[23]崔旭东,邱春蓉,刘瑞根.用标记松弛方法检测闪光图像边缘[J].光电工程,2001,28(4)：42-45.
[24]P. Kanungo, P.K. Nanda and U.C.Samal. Image Segmentation Using Threshold and Genetic Algorithm[J]. IEEE,2006:1-10.
[25]陈立英,裴喜春,侯振杰.基于遗传算法的血液细胞图像的分割方法研究[J].计算技术与自动化,2008(02).
[26]周龙,卢亚玲,谢兆鸿.模糊边缘检测算法在储粮害虫图像中的应用[J].微计算机信息,2005(05)：201-202.
[27]吕明忠,罗鹏等.一种基于色差的彩色图像的边缘检测方法[J].华东理工大学学报.2001,27(5).
[28]李文举,梁德群等.基于方向区域距离测度的彩色边缘检测方法[J].计算机用,2003,23(1).
[29]R.Nevatia. A Color Edge Detector and Its Use in Scene Segmentation[J]. IEEE Trans. Systems, Man, and Cybernetics,1977,7 (11):820-826.
[30]M.H.Hueckel. An Operator which Locates Edges in Digitized Pictures[J]. ACM,1971, 18(1):113-125.
[31]ScharcanskiJ, Venetsanopoulos A.N. Edge Detection of Color Images Using Directional operators[J]. IEEE Transactions on Circuits and Systems for Video Technology,1997, 7(2):397-401.
[32]R.D.Dony, S.Wesolkowski. Edge Detection on Color Images Using RGB Vector Angles[C]. IEEE Canadian Conference on Electrical and Computer Engineering. Edmonton, Alta, Canada: IEEE,19992,2:687-692.
[33]C.L.Novak, S.A.Shafer. Color Edge Detection[C]. In Proe.DARPA Image Understanding Workshop,1987,1:35-37.
[34]S.Di Zenzo. A Note on the Gradient of a Multi-Image[J]. Computer Vision, Graphics and Image Processing,1986,33(1):116-125.
[35]A.Cumani. Edge Detection in Multispectral Images[J]. CVGIP:Graphical Models and Image Proeessing,1991,53(1):40-51.
[36]T.L.Huntsberger, M.F.Descalzi. Color Edge Detection[J]. Pattern Recognition Letters,1985, 3(3):205-209.
[37]M.Pietikainen,D.Harwood. Edge Information in Color Images Based on Histograms of Differences[C]. Proc.Int'l Conf. Pattern Recognition,1986:594-596.
[38]C.K.Yang, W.H.Tsai. Reduction of Color Space Dimensionality by Moment-Preserving
Thresholding and its Application for Edge-Detection in Color Images[J]. Pattern Recognition Letters,1996,17(5):481-490.
[39]Djuric.P.M, Fwu.J.K. On the Detection of Edges in Vector Images[J]. IEEE Transactions on Image Processing,1997,6(11),1595-1601.
[40]P.E.Trahanias and A.N.Venetsanopoulos. Color edge detection using vector order statistics[J]. IEEE Trans.ImageProcessing,1993,2(2):259-264.
[41]Prewitt J, Mendelsohn M. The analysis of cell images[J]. Annals of the N.Y.Academy of Sciences,1966,128:1035-1053.
[42]万力,易昂,傅明.一种基于Canny算法的边缘提取改善方法,计算机技术与自动化.2003,22(1)：24-26.