精确直方图规定化
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摘要
图像增强是图像处理领域的一个基本的、重要的研究课题。图像增强的主要目的是改善图像的视觉效果,使处理后的图像比原始图像更适用于特定应用。直方图修正技术就是其中一种常用的方法。直方图修正技术通常有直方图均衡化和直方图规定化两类。直方图均衡化是一种最早也是最常用的图像增强方法,经过直方图均衡化处理后,可以产生更均衡有较好对比度的图像。直方图规定化也是常用的图像增强方法,它用于获得处理后具有特殊直方图的图像,推广了直方图均衡化的情况。
本文首先介绍了直方图的基本原理、性质和用途,以及直方图均衡化和直方图规定化算法的基本原理。在连续的情况下,直方图均衡化或规定化的统计模型可以产生精确结果,但是相应的离散情形却没有这样的结果。到目前为止,在离散情况下,对直方图均衡化可能已经很清楚了,但直方图规定化在大多数时候都是试凑过程。文中介绍了一些常见的直方图规定化方法,所提到的几种映射规则虽然可以从不同角度改善图像,但只能给出近似结果。这是由于在一个图像中像素的数量通常要比灰度级的数量大很多,在离散情况下累积分布函数是阶梯函数,除了当像素取不同的值这种情况以外,它是不可逆的。
基于上述问题,本文接下来介绍了一种基于排序理论的精确直方图规定化算法。该算法首先给出了精确直方图规定化的原理,即在图像像素上定义的排序关系,它可诱导出几乎严格排序。然后讨论了图像像素严格排序的导出方法,即通过利用向量算子把一个向量和每个像素相联系,问题从标量图像转换到了K维空间,利用字典方式给向量排序,并且进一步在图像像素中诱导出一个严格排序,从而得到一个可逆的累积分布函数。接下来又对这个排序的存在性进行了理论分析,并给出了实验结果和诱导排序的统计模型。一旦得到这样的排序,像素马上就被分类并且分配给一个期望的灰度级。所提到的严格排序和自然排序是一致的,这样图像的信息内容基本上都被保留了。
在本文的最后讨论了精确直方图规定化在图像增强,图像标准化,直方图规定化反演,水印等方面的应用。
Image enhancement is a fundamental but important topic in image processing field. The main aim of image enhancement is to improve visual effects such that the processed image is more applicable to specific use than the original one. Histogram correction technique is one of the commonly used methods of image enhancement. In usual, it has two classes of histogram correction technique, histogram equalization and specification. Histogram equalization is the earliest and the most commonly used technique in image processing. By means of histogram equalization yield more balanced and better contrasted images. Histogram specification is also a commonly used technique in image processing and it is used to obtain the image which has special histogram. Histogram specification popularizes histogram equalization.
At first, this paper introduces the fundamental principles、properties and applications of histogram. In addition, the fundamental principles of histogram equalization and histogram specification. In the continuous case, statistical models of histogram equalization/ specification would yield exact results, their discrete counterparts fail. In the case of discrete, although it probably is obvious for histogram equalization by now, histogram specification is a trial-and-error process for the most part. In this paper, we introduce some commonly used methods of histogram specification. Although the introduced mapping laws can improve the image qualities in different aspects, the results are approximate. This is due to the fact that the number of pixels in an image is usually considerably larger than the number of graylevels. In the discrete case, the cumulative distribution functions are staircase function, hence they are not invertible except in the case when pixels take distinct values.
For the above-mentioned topic, we introduce the exact histogram specification, a kind of arithmetic which based on ordering theory. Firstly, we present the principle of exact histogram specification , namely ordering relation defined on image pixel, which can induce almost strict ordering. Then, we discuss the method how to induce such a strict ordering. Speaking specifically, by using a vector operator, the problem is transferred from a scalar image to a K-dimensional space by associating a vector to each pixel by lexicographically ordering. Next, a strict ordering is induced among the image pixels and invertible cumulative distribution function is obtained. Furthermore, we provide the theoretical analysis of the ordering existence. Also, the experimental results、the statistical models of the induced ordering are presented. Once ordering is achieved, pixels are immediately separated into classes and assigned to the desired graylevel. The proposed strict ordering is consistent with the natural one and thus, the information content of images is generally preserved.
Finally, several applications related to exact histogram specification are discussed: image enhancement, normalization, histogram specification inversion, watermarking, etc.
本文首先介绍了直方图的基本原理、性质和用途,以及直方图均衡化和直方图规定化算法的基本原理。在连续的情况下,直方图均衡化或规定化的统计模型可以产生精确结果,但是相应的离散情形却没有这样的结果。到目前为止,在离散情况下,对直方图均衡化可能已经很清楚了,但直方图规定化在大多数时候都是试凑过程。文中介绍了一些常见的直方图规定化方法,所提到的几种映射规则虽然可以从不同角度改善图像,但只能给出近似结果。这是由于在一个图像中像素的数量通常要比灰度级的数量大很多,在离散情况下累积分布函数是阶梯函数,除了当像素取不同的值这种情况以外,它是不可逆的。
基于上述问题,本文接下来介绍了一种基于排序理论的精确直方图规定化算法。该算法首先给出了精确直方图规定化的原理,即在图像像素上定义的排序关系,它可诱导出几乎严格排序。然后讨论了图像像素严格排序的导出方法,即通过利用向量算子把一个向量和每个像素相联系,问题从标量图像转换到了K维空间,利用字典方式给向量排序,并且进一步在图像像素中诱导出一个严格排序,从而得到一个可逆的累积分布函数。接下来又对这个排序的存在性进行了理论分析,并给出了实验结果和诱导排序的统计模型。一旦得到这样的排序,像素马上就被分类并且分配给一个期望的灰度级。所提到的严格排序和自然排序是一致的,这样图像的信息内容基本上都被保留了。
在本文的最后讨论了精确直方图规定化在图像增强,图像标准化,直方图规定化反演,水印等方面的应用。
Image enhancement is a fundamental but important topic in image processing field. The main aim of image enhancement is to improve visual effects such that the processed image is more applicable to specific use than the original one. Histogram correction technique is one of the commonly used methods of image enhancement. In usual, it has two classes of histogram correction technique, histogram equalization and specification. Histogram equalization is the earliest and the most commonly used technique in image processing. By means of histogram equalization yield more balanced and better contrasted images. Histogram specification is also a commonly used technique in image processing and it is used to obtain the image which has special histogram. Histogram specification popularizes histogram equalization.
At first, this paper introduces the fundamental principles、properties and applications of histogram. In addition, the fundamental principles of histogram equalization and histogram specification. In the continuous case, statistical models of histogram equalization/ specification would yield exact results, their discrete counterparts fail. In the case of discrete, although it probably is obvious for histogram equalization by now, histogram specification is a trial-and-error process for the most part. In this paper, we introduce some commonly used methods of histogram specification. Although the introduced mapping laws can improve the image qualities in different aspects, the results are approximate. This is due to the fact that the number of pixels in an image is usually considerably larger than the number of graylevels. In the discrete case, the cumulative distribution functions are staircase function, hence they are not invertible except in the case when pixels take distinct values.
For the above-mentioned topic, we introduce the exact histogram specification, a kind of arithmetic which based on ordering theory. Firstly, we present the principle of exact histogram specification , namely ordering relation defined on image pixel, which can induce almost strict ordering. Then, we discuss the method how to induce such a strict ordering. Speaking specifically, by using a vector operator, the problem is transferred from a scalar image to a K-dimensional space by associating a vector to each pixel by lexicographically ordering. Next, a strict ordering is induced among the image pixels and invertible cumulative distribution function is obtained. Furthermore, we provide the theoretical analysis of the ordering existence. Also, the experimental results、the statistical models of the induced ordering are presented. Once ordering is achieved, pixels are immediately separated into classes and assigned to the desired graylevel. The proposed strict ordering is consistent with the natural one and thus, the information content of images is generally preserved.
Finally, several applications related to exact histogram specification are discussed: image enhancement, normalization, histogram specification inversion, watermarking, etc.
引文
[1]胡学龙,许开宇著,数字图像处理[M].北京:电子工业出版社,2006.9,pp.7-9.
[2]魏世成,邓锋主编,口腔医学信息学[M].四川:四川大学出版社,2003.2,pp.42.
[3]胡学龙,许开宇著,数字图像处理[M].北京:电子工业出版社,2006.9,pp.4-5.
[4]http://blog.sina.com.cn/s/blog_4504388f0100060u.html
[5]高守传等编著,Visual C++实践与提高--数字图像处理与工程应用篇[M].北京:中国铁道出版社,2006.1,pp.2-4.
[6]王慧琴编著,数字图像处理[M].北京:北京邮电学院出版社,2006.11,pp.19-20.
[7]胡学龙,许开宇著,数字图像处理[M].北京:电子工业出版社,2006.9,PP.16-17.
[8]高守传等编著,Visual C-H-实践与提高--数字图像处理与工程应用篇[M].北京:中国铁道出版社,2006.1,pp.5.
[9]R.C.Gonzales and R.E.Woods,Digital Image Processing[M].Upper Saddle River,NJ:Prentice-Hall,2002.
[10]曹雪红,张宗橙,信息论与编码(第一版)[M].北京:北京邮电大学出版社,2002.
[11]A.Rosenfeld and A.Kak,Digital Picture Processing[M].Upper Saddle River,NJ:Prentice-Hall,1982.
[12]A.K.Jain,Fundamentals of Digital Image Processing[M].Upper Saddle River,NJ:Prentice-Hall,1989.
[13]Y.J.Zhang,"Improving the accuracy of direct histogram specification,"[J].Electron.Lett.,vol.28,no.3,pp.213-214,1992.
[14]S.Kundu,"A solution to histogram-equalization and other related problems by shortest path methods,"[J].Pattern Recognit.,vol.31,no.3,pp.231-234,1998.
[15]X.-D.Yang,Q.Xiao,and H.Raafat,"Direct mapping between histograms:An improved interactive image enhancement method,"[J].In Proc.1991 IEEE Int.Conf.Systems,Man,and Cybernetics,Decision Aiding for Complex Systems,vol.1,1991,pp.243-247.
[16]J.P.Rolland,V.Vo,B.Bloss,and C.K.Abbey,"Fast algorithm for histogram matching applications to texture synthesis,"[J].Electron.Imag.,vol.9,no.1,pp.39-45,2000.
[17]E.L.Hall,"Almost uniform distributions for computer image enhancement,"[J].IEEE Trans.Comput.,vol.23,no.2,pp.207-208,Feb.1974.
[18]D.Coltuc and Ph.Bolon,"Strict ordering on discrete images and applications,"[J].in Proc.ICIP'99,vol.Ⅲ,Tokyo,Japan,1999,pp.150-153.
[19]R.J.Wall,A.Klinger,and K.R.Castleman,Analysis of Image Histograms[M].Proc.Second Int.Gong.on.Pattenr Recogintion,Copenhagen,1974.
[20]Lian Guan Kamel M.,Histogram equalization utilizing spatial correlation for image enhancement[J].Proc SPIE.1989,1199:712-721.
[21]王洪兰,张若钢,浅谈图像增强的直方图处理及其MTALAB实现[J].人工智能及识别技术,2007,7.
[22]夏良正,数字图象处理[M].南京:东南大学出版社,1999,PP.105-124.
[23]阮秋琦,数字图像处理学[M].北京:电子工业出版社,2001,pp.198-235.
[24]张兆礼,赵春晖,梅晓丹,现代图像处理技术[M].北京:人民邮电出版社,2001.11,PP.126-132.
[25]李耀辉,刘保军,基于直方图均衡的图像增强[J].华北科技学院学报,2004,2.
[26]冯清枝,基于直方图修正的图像增强技术[J].广东公安科技,2003,5(2).
[27]汪志云,黄梦为等,基于直方图的图像增强及其MTALAB实现[J].计算机工程与科学,2006,28(2).
[28]冈萨雷斯(Gonzales,R.C.)等著,阮秋琦等译,数字图像处理(第二版)[M].北京:电子工业出版社,2003.3,pp.74.
[29]张娜,图像增强技术的研究[J].计算机仿真,2007,24(1).
[30]张毓晋编著,图像工程(上册)图像处理(第二版)[M].北京:清华大学出 版社,2006,pp.90-97.
[31]左长进,姜世恩,直方图规定化描述直观算法及其应用[J].铁路计算机应用,2003,12(5).
[32]李平,钱琳琳,利用单映射法改善图像直方图均衡化的精度[J].北京联合大学学报(自然科学版),2006,20(3).
[33]李平,钱琳琳,一种改善直方图均衡化精度的方法[J].微计算机信息,2006,22(8-3).
[34]费风长,方志军等,基于区间映射规则的数字直方图处理[J].计算机工程,2006(10),pp.217-220.
[35]韩殿元,陈子富,一种直方图规定化的组映射算法[J].潍坊学院学报,2005,5(6).
[36]D.T.Cobra,"Image histogram modification based on a new model of the visual system nonlinearity,"[J].Electron.Imag.,vol.7,no.4,pp.807-815,1998.
[37]J.Y.Kim,L.S.Kim,and S.H.Hwang,"An advanced contrast enhancement using partially overlapped sub-block histogram equalization"[J].IEEE Trans.Circuits Syst.Video Technol.,vol.11,no.4,pp.475-484,Apr.2001.
[38]J.A.Stark,"Adaptive image contrast enhancement using generalizations of histogram equalization,"[J].IEEE Trans.Image Process.,vol.9,no.5,pp.889-896,May 2000.
[39]V.Caselles,J.L.Lisani,J.M.Morel,and G.Sapiro,"Shape preserving local histogram modification,"[J].IEEE Trans.Image Process.,vol.8,no.2,pp.220-230,Feb.1999.
[40]A.R.Weeks,L.J.Sartor,and H.R.Myler,"Histogram specification of 24-bit color images in the color difference(C-Y) color space,"[J].Electron.Imag.,vol.8,no.3,pp.290-300,1999.
[41]J.Morovic and P.-L.Sun,"Accurate 3D image color histogram transformation,"[J].Pattern Recogn.Lett.,vol.24,pp.1725-1725,2003.
[42]D.Coltuc and Ph.Bolon,"Color image watermarking in HIS space,"[J].in Proc. ICIP'2000,vol.Ⅲ,Vancouver,BC,Canada,2000,pp.698-701.
[43]D.Coltuc,Ph.Bolon,and J.-M.Chassery,"Fragile and robust watermarking by histogram specification,"[J].in SPIE Proc.Conf.Security and Watermarking of Multimedia Contents Ⅳ,vol.4675,E.J.Delp and P.W.Wong,Eds.,2002,pp.701-710.
[2]魏世成,邓锋主编,口腔医学信息学[M].四川:四川大学出版社,2003.2,pp.42.
[3]胡学龙,许开宇著,数字图像处理[M].北京:电子工业出版社,2006.9,pp.4-5.
[4]http://blog.sina.com.cn/s/blog_4504388f0100060u.html
[5]高守传等编著,Visual C++实践与提高--数字图像处理与工程应用篇[M].北京:中国铁道出版社,2006.1,pp.2-4.
[6]王慧琴编著,数字图像处理[M].北京:北京邮电学院出版社,2006.11,pp.19-20.
[7]胡学龙,许开宇著,数字图像处理[M].北京:电子工业出版社,2006.9,PP.16-17.
[8]高守传等编著,Visual C-H-实践与提高--数字图像处理与工程应用篇[M].北京:中国铁道出版社,2006.1,pp.5.
[9]R.C.Gonzales and R.E.Woods,Digital Image Processing[M].Upper Saddle River,NJ:Prentice-Hall,2002.
[10]曹雪红,张宗橙,信息论与编码(第一版)[M].北京:北京邮电大学出版社,2002.
[11]A.Rosenfeld and A.Kak,Digital Picture Processing[M].Upper Saddle River,NJ:Prentice-Hall,1982.
[12]A.K.Jain,Fundamentals of Digital Image Processing[M].Upper Saddle River,NJ:Prentice-Hall,1989.
[13]Y.J.Zhang,"Improving the accuracy of direct histogram specification,"[J].Electron.Lett.,vol.28,no.3,pp.213-214,1992.
[14]S.Kundu,"A solution to histogram-equalization and other related problems by shortest path methods,"[J].Pattern Recognit.,vol.31,no.3,pp.231-234,1998.
[15]X.-D.Yang,Q.Xiao,and H.Raafat,"Direct mapping between histograms:An improved interactive image enhancement method,"[J].In Proc.1991 IEEE Int.Conf.Systems,Man,and Cybernetics,Decision Aiding for Complex Systems,vol.1,1991,pp.243-247.
[16]J.P.Rolland,V.Vo,B.Bloss,and C.K.Abbey,"Fast algorithm for histogram matching applications to texture synthesis,"[J].Electron.Imag.,vol.9,no.1,pp.39-45,2000.
[17]E.L.Hall,"Almost uniform distributions for computer image enhancement,"[J].IEEE Trans.Comput.,vol.23,no.2,pp.207-208,Feb.1974.
[18]D.Coltuc and Ph.Bolon,"Strict ordering on discrete images and applications,"[J].in Proc.ICIP'99,vol.Ⅲ,Tokyo,Japan,1999,pp.150-153.
[19]R.J.Wall,A.Klinger,and K.R.Castleman,Analysis of Image Histograms[M].Proc.Second Int.Gong.on.Pattenr Recogintion,Copenhagen,1974.
[20]Lian Guan Kamel M.,Histogram equalization utilizing spatial correlation for image enhancement[J].Proc SPIE.1989,1199:712-721.
[21]王洪兰,张若钢,浅谈图像增强的直方图处理及其MTALAB实现[J].人工智能及识别技术,2007,7.
[22]夏良正,数字图象处理[M].南京:东南大学出版社,1999,PP.105-124.
[23]阮秋琦,数字图像处理学[M].北京:电子工业出版社,2001,pp.198-235.
[24]张兆礼,赵春晖,梅晓丹,现代图像处理技术[M].北京:人民邮电出版社,2001.11,PP.126-132.
[25]李耀辉,刘保军,基于直方图均衡的图像增强[J].华北科技学院学报,2004,2.
[26]冯清枝,基于直方图修正的图像增强技术[J].广东公安科技,2003,5(2).
[27]汪志云,黄梦为等,基于直方图的图像增强及其MTALAB实现[J].计算机工程与科学,2006,28(2).
[28]冈萨雷斯(Gonzales,R.C.)等著,阮秋琦等译,数字图像处理(第二版)[M].北京:电子工业出版社,2003.3,pp.74.
[29]张娜,图像增强技术的研究[J].计算机仿真,2007,24(1).
[30]张毓晋编著,图像工程(上册)图像处理(第二版)[M].北京:清华大学出 版社,2006,pp.90-97.
[31]左长进,姜世恩,直方图规定化描述直观算法及其应用[J].铁路计算机应用,2003,12(5).
[32]李平,钱琳琳,利用单映射法改善图像直方图均衡化的精度[J].北京联合大学学报(自然科学版),2006,20(3).
[33]李平,钱琳琳,一种改善直方图均衡化精度的方法[J].微计算机信息,2006,22(8-3).
[34]费风长,方志军等,基于区间映射规则的数字直方图处理[J].计算机工程,2006(10),pp.217-220.
[35]韩殿元,陈子富,一种直方图规定化的组映射算法[J].潍坊学院学报,2005,5(6).
[36]D.T.Cobra,"Image histogram modification based on a new model of the visual system nonlinearity,"[J].Electron.Imag.,vol.7,no.4,pp.807-815,1998.
[37]J.Y.Kim,L.S.Kim,and S.H.Hwang,"An advanced contrast enhancement using partially overlapped sub-block histogram equalization"[J].IEEE Trans.Circuits Syst.Video Technol.,vol.11,no.4,pp.475-484,Apr.2001.
[38]J.A.Stark,"Adaptive image contrast enhancement using generalizations of histogram equalization,"[J].IEEE Trans.Image Process.,vol.9,no.5,pp.889-896,May 2000.
[39]V.Caselles,J.L.Lisani,J.M.Morel,and G.Sapiro,"Shape preserving local histogram modification,"[J].IEEE Trans.Image Process.,vol.8,no.2,pp.220-230,Feb.1999.
[40]A.R.Weeks,L.J.Sartor,and H.R.Myler,"Histogram specification of 24-bit color images in the color difference(C-Y) color space,"[J].Electron.Imag.,vol.8,no.3,pp.290-300,1999.
[41]J.Morovic and P.-L.Sun,"Accurate 3D image color histogram transformation,"[J].Pattern Recogn.Lett.,vol.24,pp.1725-1725,2003.
[42]D.Coltuc and Ph.Bolon,"Color image watermarking in HIS space,"[J].in Proc. ICIP'2000,vol.Ⅲ,Vancouver,BC,Canada,2000,pp.698-701.
[43]D.Coltuc,Ph.Bolon,and J.-M.Chassery,"Fragile and robust watermarking by histogram specification,"[J].in SPIE Proc.Conf.Security and Watermarking of Multimedia Contents Ⅳ,vol.4675,E.J.Delp and P.W.Wong,Eds.,2002,pp.701-710.