基于自适应权重马尔科夫随机场的彩色纹理图像分割研究
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摘要
人眼对颜色的敏感度比对亮度的敏感度更强,彩色图像包含更大的信息量和更丰富的视觉感受。长期以来,在视觉研究领域的大部分研究都是针对灰度图像的。近年来,随着计算机硬件和图像采集设备性能提高以及它们的成本下降,使得对彩色图像处理的研究提供了条件。随着彩色图像设备越来越受到人们的青睐,广泛开展对彩色图像处理技术的研究也变得十分迫切。近年来基于图像内容、色彩以及纹理的图像检索技术成为数据库技术研究的一大热点,而基础的技术就是彩色图像分割。人类视觉对图像的分割是基于多方面知识的,其中两个重要的就是颜色和纹理。随着成像设备的发展,现在获得彩色图像并不是难事,这就给了我们通过与人类视觉一致的、自然的方法来分割图像的机会,彩色纹理图像的分割自然成为近年来研究的热点。
Markov随机场(Markov Random Field,即MRF)理论已经广泛应用于计算机视觉及图像处理领域中,它提供了方便而直接的方法以概率来描述图像像素所具有的一些空间相关的特性,MRF与Gibbs分布等价性的提出极大的推广了其在数字图像处理中的应用,MRF中联合分布的概念提出又为研究者提供了在贝叶斯体系下进行图像处理的MRF模型。
本文整合颜色和纹理两方面的信息,提出一个新的基于自适应权重马尔科夫场(MRF)的无监督分割模型,算法框架依赖于基于优化思想(模拟退火等)贝叶斯估计理论。不同的类有着不同的高斯分布,通过将像素归于不同的类就可以得到图像的分割结果。所以,这里唯一的假设是同一类的图像特征可以用唯一个高斯分布来描述。使用接近于人类感知颜色的HSV颜色空间得到颜色特征;使用Gabor滤波器得到图像的纹理特征。还提出了一个适用本算法的EM迭代算法进行高斯分布的参数估计。
本文提出的模型优点有三,其一:相比较于其他彩色纹理图像分割模型,这里的模型中只使用了一个单一的MRF场,这意味着算法的时间复杂度降低了;其二:将特征提取方式从MRF建模中独立出来,只使用MRF建模分割过程,使得很多经典的特征提取方法可直接用于此模型。例如,对于纹理特征提取来说,文献[52]中所有的滤波器方法等都可以在此模型直接使用。其三:使用新颖的自适应权重MRF模型,有效改善了分割结果,也减少了人工参数的主观臆断。
文中第五章设计了四个互相独立但又彼此关联的实验从各个角度证明此模型优于像素聚类算法、只利用彩色或颜色信息的MRF分割模型、传统的常量权重MRF分割模型。
Human eyes are more sensitive to colors than intensities and there exists more information in color images which can bring richer perception. For a long period, most researches in vision fields have focused on gray-level images. In recent years, the increasing performance of computer hardware and image capturing equipments and their decreased cost make color image processing possible. Furthermore, with the rapid development of multimedia techniques, more and more color images need to be processed(such as print images),and color image processing, especially color image segmentation, becomes an important topic in image processing area gradually. As color image devices are becoming more and more popular nowadays, it is really stringent to accelerate color image processing techniques. From two aspects of theoretical study and practical application, this paper pays more attention on several key issues in color image processing, i.e. color image feature extraction and color image segmentation. Image Segmentation is a process in which the image is segmented into different homogeneous regions. In other words, finding the edges among these regions can achieve this goal. Comparing with gray image, color image contains not only intensity information, but also other useful information such as tonality, saturation. In recent years, image retrieval based on image content, color and texture has been a focus in database technique, in which color image segmentation is the basic technique.
Markov Random Field has been widely applied to solve the problem fields of image processing and machine vision. MRF provides a straight way, which is based on decision- theory, to model the relationship between pixels. An equivalence relation between MRF and Gibbs distribution make MRF model be widely applied, and the joint distribution provides a model which researchers can used with Bayesian to solve the problems coming from image processing and machine vision.
We propose an adapting weight MRF image segmentation model, which aims at combining color and texture features. The theoretical framework relies on Bayesian estimation via combinatorial optimization (simulated annealing).The segmentation is obtained by classifying the pixels into different pixel classes. These classes are represented by multi-variate Gaussian distributions. Thus, the only hypotheses is about the nature of the features is that an additive Gaussian noise model is suitable to describe the feature distribution belonging to a given class. Here, we use the perceptually uniform HSV color values as color features and a set of Gabor filters as texture features. Gaussian parameters are either computed using a training data set or estimated from the input image. We also propose a parameter estimation method using the EM algorithm.
There are three advantages for our model; firstly, the time used for computer is reduced for we just use a simple single layer MRF model. Secondly, we use a combination of classical, gray-level based, texture features and color instead of direct modeling of color textures. Hence, most of the classical texture features can be used. Thirdly, we use a new adapting weight MRF model, which make the results better and artificial intervention reduced.
In chapter 5, we designed 4 experiments to illustrate the performance of our method on both synthetic and natural color image.
Markov随机场(Markov Random Field,即MRF)理论已经广泛应用于计算机视觉及图像处理领域中,它提供了方便而直接的方法以概率来描述图像像素所具有的一些空间相关的特性,MRF与Gibbs分布等价性的提出极大的推广了其在数字图像处理中的应用,MRF中联合分布的概念提出又为研究者提供了在贝叶斯体系下进行图像处理的MRF模型。
本文整合颜色和纹理两方面的信息,提出一个新的基于自适应权重马尔科夫场(MRF)的无监督分割模型,算法框架依赖于基于优化思想(模拟退火等)贝叶斯估计理论。不同的类有着不同的高斯分布,通过将像素归于不同的类就可以得到图像的分割结果。所以,这里唯一的假设是同一类的图像特征可以用唯一个高斯分布来描述。使用接近于人类感知颜色的HSV颜色空间得到颜色特征;使用Gabor滤波器得到图像的纹理特征。还提出了一个适用本算法的EM迭代算法进行高斯分布的参数估计。
本文提出的模型优点有三,其一:相比较于其他彩色纹理图像分割模型,这里的模型中只使用了一个单一的MRF场,这意味着算法的时间复杂度降低了;其二:将特征提取方式从MRF建模中独立出来,只使用MRF建模分割过程,使得很多经典的特征提取方法可直接用于此模型。例如,对于纹理特征提取来说,文献[52]中所有的滤波器方法等都可以在此模型直接使用。其三:使用新颖的自适应权重MRF模型,有效改善了分割结果,也减少了人工参数的主观臆断。
文中第五章设计了四个互相独立但又彼此关联的实验从各个角度证明此模型优于像素聚类算法、只利用彩色或颜色信息的MRF分割模型、传统的常量权重MRF分割模型。
Human eyes are more sensitive to colors than intensities and there exists more information in color images which can bring richer perception. For a long period, most researches in vision fields have focused on gray-level images. In recent years, the increasing performance of computer hardware and image capturing equipments and their decreased cost make color image processing possible. Furthermore, with the rapid development of multimedia techniques, more and more color images need to be processed(such as print images),and color image processing, especially color image segmentation, becomes an important topic in image processing area gradually. As color image devices are becoming more and more popular nowadays, it is really stringent to accelerate color image processing techniques. From two aspects of theoretical study and practical application, this paper pays more attention on several key issues in color image processing, i.e. color image feature extraction and color image segmentation. Image Segmentation is a process in which the image is segmented into different homogeneous regions. In other words, finding the edges among these regions can achieve this goal. Comparing with gray image, color image contains not only intensity information, but also other useful information such as tonality, saturation. In recent years, image retrieval based on image content, color and texture has been a focus in database technique, in which color image segmentation is the basic technique.
Markov Random Field has been widely applied to solve the problem fields of image processing and machine vision. MRF provides a straight way, which is based on decision- theory, to model the relationship between pixels. An equivalence relation between MRF and Gibbs distribution make MRF model be widely applied, and the joint distribution provides a model which researchers can used with Bayesian to solve the problems coming from image processing and machine vision.
We propose an adapting weight MRF image segmentation model, which aims at combining color and texture features. The theoretical framework relies on Bayesian estimation via combinatorial optimization (simulated annealing).The segmentation is obtained by classifying the pixels into different pixel classes. These classes are represented by multi-variate Gaussian distributions. Thus, the only hypotheses is about the nature of the features is that an additive Gaussian noise model is suitable to describe the feature distribution belonging to a given class. Here, we use the perceptually uniform HSV color values as color features and a set of Gabor filters as texture features. Gaussian parameters are either computed using a training data set or estimated from the input image. We also propose a parameter estimation method using the EM algorithm.
There are three advantages for our model; firstly, the time used for computer is reduced for we just use a simple single layer MRF model. Secondly, we use a combination of classical, gray-level based, texture features and color instead of direct modeling of color textures. Hence, most of the classical texture features can be used. Thirdly, we use a new adapting weight MRF model, which make the results better and artificial intervention reduced.
In chapter 5, we designed 4 experiments to illustrate the performance of our method on both synthetic and natural color image.
引文
[1]Stan Z.Li.Markov Random Field Modeling in Image Analysis 2~(nd)ed.2001,Springer-Verlag,Available at (http://www.cbsr.ia.ac.cn/users/szli/MRF_Book/book.html)
[2]A.Chaparro,C.I.Stromeyer,E.Huang,et al.,Colour is what the eye sees best,Nature,1993,361:348-350.
[3]F.A.A.Kingdom,Color brings relief to human vision,Nature Neuroscience,2003(6):641-644.
[4]R.Ramanath,W.E.Snyder,Y.Yoo,et al.,Color image processing pipeline,IEEE Signal Processing Magazine,2005(22):34-43.
[5]D.Tretter,C.A.Bouman,K.Khawaja,and A.Maciejewski.A multiscale stochastic image model for automated inspection.IEEE Trans.on Image Processing,1995.4(12):507-517
[6]S.Geman,D.Geman.Stochastic relaxation,Gibbs distributions and the Bayesian restoration of images,IEEE Transactions on Pattern Analysis and Machine Intelligence,1984(6):721-741
[7]A.Blake,A.Zisserman,Visual Reconstruction,MIT Press,Cambridge,MA,1987
[8]D.Mumford,J.Shah.Optimal approximations by piecewise smooth functions and associated variational problems,Communications on Pure and Applied Mathematics.1989(42):577-685
[9]Kenneth R.Castleman,Digital hnage Processing,Prince Hall,1996
[10]王萍,苏秀琴,刘雅轩.给予区域合并的动态阈值分割算法.光子学报,2004,33(3):378-381
[11]修春波,刘向东,张宇河.基于混沌优化的最佳熵阂值的图像分割.计算机工程与应用,2004,27:76-77
[12]Kim DY,Kim J H,Noh S M,et al.Pulmonary nodule detection using chest CT images.Acta Radiol,2003,44(3):252-257
[13]W.Skarbek and A.Koschan,Color image segmentation:A survey,Technical Report,Technical University of Berlin,1994
[14]L.Lucchese and S.K.Mitra,Color image segmentation:A state-of-the-art survey,Proc.of the Indian National Science Academy(INSA-A),New Delhi,India,2001:207-221
[15]H.D.Cheng,X.H.J iang,Y.Sun,et al.,Color image segmentation:advances and prospects Pattern Recognition,2001,34:2259-2281
[16]Y.Ohta,T.Kanade and T.Sakai,Color information for region segmentation,Computer Graphics and Image Processing,1980,13:222-241
[17]R.Ohlaner,K.Price and D.R.Reddy,Picture segmentation using a recursive region splitting method,Computer Graphics and Image Processing,1978,8:313-333
[18]A.Tremeau and N.Borel,A region growing and merging algorithm to color segmentation,Pattern Recognition,1997,30:867-881
[19]A.Koschan,A comparative study on color edge detection,Proc.of the 2nd Asia Conf.on Computer Vision ACCV'95,Singapore,1995:574-578
[20]T.Kanade,Image understanding research at CMU,Proc.Image understanding workshop,1978:574-578
[21]S.D.Zenzo,A note on the gradient of a multi-image,Comp.Vis.Graph.Image Proc.,1986:116-125
[22]A.Cumani,Edge detection in multispectral images,Comput.Vis.Graph.Image Process.:Graphical Models Image Processing,1991:40-51
[23]P.E.Trahanias and A.N.Venetsanopoulos,A color edge detection using vector order statistics,IEEE Trans.Image Processing,1993,2,:59-265
[24]J.Scharcanski and A.N.Venetsanopoulos,Edge detection of color images using directional operators,IEEE Trans.on Circuits and Systems for Video Technology,1997,7(7):397-401
[25]M.A.Ruzon and C.Tomasi,Edge,junction,and comer detection using color distribution,IEEE Trans.PAMI,2001,23:1281-1295
[26]D.R.Martin,C.C.Fowlkes and J.Malik,Learning to detect neural image boundaries using local brightness,color,and texture cues,IEEE Trans.PAMI,2004,26:530-549
[27]A.Koschan and M.Abidi,Detection and classification of edges in color images,IEEE Signal Processing Magazine,2005,22:64-73
[28]Y.N.Deng and B.S.Manjunath,Unsupervised segmentation of color-texture regions in images and video,IEEE Trans.on PAMI,2001,23:800-810
[29]F.Jing,M.Li,H.Zhang,et al.,Unsupervised image segmentation using local homogeneity analysis,Proc.IEEE International Symposium on Circuits and Systems 2003,2003:456-459
[30]Y.Zheng,J.Yang and Y.Zhou,Unsupervised segmentation on image with JSEG using soft class map,IDEAL'04,LNCS 3177,Springer,Berlin,2004:197-202
[31]Y.Wang,J.Yang and Y.Zhou,Unsupervised color-texture segmentation,ICIAR 2004,LNCS 3211,Springer,Berlin,2004:106-113
[32]李厚强,刘政凯,詹曙.一种彩色纹理图像的分割方法.计算机学报.2001,24(9):965-971.
[33]王志勇,邓达,余英林.分形技术在彩色纹理分割中的应用.华南理工大学学报,1998(10):64-70.
[34]Wang Xiao-Hui,Zhou Yue,Wang Yong-Gang,and Zhu WeiWei,Color Texture Segmentation Based on Quatemion-Gabor Features,CIARP 2006,2006(LNCS 4225):345-353.
[35]Z.Kato,T.C.Pong,G.Q,Song.Unsupervised segmentation of color textured images using a multi-layer MRF model.Proceedings of International Conference on Image Processing,vol.1,IEEE,Barcelona,Spain,2003,961-964
[36] Marroquin J, et al. Probabilistic solution of ill-posed problems in computational vision. 1987, J. Am.Statist, Assoc
[37] Bertero M, et al. Ill-posed problems in early vision. Proc. IEEE, 1988.76(8):869-889
[38] B. Hunt. Bayesian methods in nonlinear digital image restoration, IEEE Trans. on Comput, 1977.26(3):219-229
[39] T. J. Hebert and K. Lu. Expectation-maximization algorithms, null spaces, and MAP image restoration,IEEE Trans. on Image Processing, 1995.4(8): 1084-1095
[40] John Argyris. An Exploration of Chaos. North-Holland: Amsterdam, 1994.
[41] R. R. Schultz and R. L. Stevenson. Stochastic modeling and estimation of multi-spectral image data. IEEE Trans. on Image Processing, 1995.4(8): 1109-1119
[42] R. Chellappa and S. Chatterjee. Classication of textures using Gaussian Markov random fields. IEEE Trans. on Acoust. Speech and Signal Proc. ASSP1985.33(4): 959-963
[43] F. S. Cohen, Z. Fan, and M. A. Patel. Classification of rotated and scaled textured images using Gaussian Markov random field models. IEEE Trans.on Pattern Analysis and Machine Intelligence, 1991.13(2):192-202
[44] D. B .Cooper. Maximum likelihood estimation of Markov process blob boundariesin noisy images.IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI, 1979.1: 3723-3784
[45] D. B. Cooper, H. Elliott, F. Cohen, L. Reiss, and P. Symosek. Stochastic boundary estimation and object recognition. Comput. Vision Graphics and Image Process.1980.12: 326-356
[46] H. Elliott, D. B. Cooper, F. S. Cohen, and P. F. Symosek. Implementation, interpretation, and analysis of a suboptimal boundary finding algorithm. IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI 1982.4(2):167-182
[47] D. Geman, S. Geman, C. Gragne and P. Dong. Boundary detection by constrained optimization. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1990.12(7): 609-628
[48] H. Derin and W. Cole. Segmentation of textured images using Gibbs random fields. Comput. Vision Graphics and Image Process, 1986.35: 72-98
[49] H. Derin, H. Elliot, R. Cristi, and D. Geman. Bayes smoothing algorithms for segmentation of binary images modeled by Markov random fields. IEEE Trans. On Pattern Analysis and Machine Intelligence,PAMI,1984,6(6): 707-719
[50] H. Derin and H. Elliott. Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Trans. on Pattern Analysis and Machine Intelligence,PAMI,1987.9(1): 39-55
[51] S. Sista, C. A. Bouman, and J. P. Allebach. Fast image search using a multi-scale stochastic model. In Proc.of IEEE Int'l Conf. on Image Proc, 1994.1,225-228
[52]T.Randen,J.H.Husoy,Filtering for texture classification:A comparative study,IEEE Transactions on Pattern Analysis and Machine Intelligence,1999,21(4):291-310
[53]Besag,J.Spatial interaction and the statistical analysis of lattice systems(with discussions).Journal of the Royal Statistical Society,Series B,1974(36):192-236
[54]Hammersley,Clifford,Markov field on finite graphs and lattices.Unpublished.1971
[55]SGeman,D.Geman.Stochastic relaxation Gibbs distribution and Bayesian restoration of image.IEEE Trans.PatemAnal.Machine Intell,1984(6):721-741
[56]Smith,J.R.and Chang,S.F.Tools and techniques for color image retrieval,Storage & Retrieval for Image and Video Data bases Ⅳ,Vol.2670 of IS & T/SPIE Proceedings,San Jose,CA,USA,1996,2679,426-437
[57]Tuceryan.M.,Jain A.K.Texture analysis.In:Chert C.H,Pau L.F,Wang,P.S.P.The handbook of pattern recognition and computer vision,2nd.Singapore:World Scientific Publishing Company,1998,207-248
[58]Tamura H.,Mori S.,Yamawaki Y.Textural Features Corresponding to Visual Perception,IEEE Transactions on Systems,Man,and Cybernetics,1978.8:460-473
[59]Haralick R.M.Statistical and Structural Approaches to Texture.Proceedings of the IEEE 67,1979,786-804
[60]Richards W.,Polit A.Texture matching.Kybernetic,1974,16:155-162
[61]Hawkins J.K.Textural Properties for Pattern Recognition.In:Lipkin B.,Rosenfeld A.Picture Processing and Psychopictorics.Academic Press,New York,1969
[62]Bovik A.C.,Clark M.,Geisler W.S.Multichannel texture analysis using localized spatial filters.IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(1):55-73
[63]Chaudhuri B.,Sarkar N.Texture segmentation using fractal dimension.IEEE Transactions on Pattern Analysis and Machine Intelligence1995,17(1):72-77
[64]张建国.不变性纹理分析.中科院自动化所博士学位论文,北京,2002
[65]张毓晋.图像工程---图像分析与处理.北京:清华大学出版社,2001
[66]颜春梅,张友静,鲍颜松.基于灰度共生矩阵法的IKONOS影像中竹林信息提取.遥感信息.2004,2:31-34
[67]R.M.Haralick,K.Shanmugam.I.Dinstcin.Textural feature for image classification.IEEE Trans.On Systems.Man and Cybernetics.Vol.SMC-6,No.4,april 1976
[68]吴高洪.纹理分析的若干多尺度方法研究.清华大学论文.1999
[69]Fracos J.M.,Meiri A.Z.,Porat B,A Untitled Texture Model Based on a Wold Decomposition.IEEE Transactions on Signal Processing,1993,41(8):2665-2678
[70]Mao J.C.,Jain A.K.Texture classification and segmentation using multi-resolution auto regressive models,Pattern Recognition,1992,25(2):173-188
[71]Dunn D.,Higgins W.,Wakeley J.Texture segmentation using 2-D Gabor elementary functions.IEEE Transactions on Pattern Analysis and Machine Intelligence,1994,22:130-149
[72]Freeman W.T.,Adelson E.H.The design and use of steerable filters.IEEE Transactions on Pattern Analysis and Machine Intelligence,1991.13(9):891-906
[73]Chang T.H.and C.C Jay Kuo.Texture analysis and classification with tree-structured wavelet transform.IEEE transactions on Image Processing,1993,2(4):429-440
[74]CAMPBELL FW,ROBOSON J G.Application of Fourier Analysis to the Visibility of Gratings.J.Physiology,1977:551-566
[75]王文惠,周良柱,万建伟.基于内容的图象检索技术的研究和发展.计算机工程与应用,2001,5:54-56
[76]Jianguo Zhang,Tieniu Tan,Li Ma,Invariant texture segmentation via circular gabor filter.Proceedings of the 1.6~(th) IAPR International Conference on Pattern Recognition(ICPR),Vol Ⅱ,901-04
[77]Hammersley,J.M.and Clifford,P.Markov field on finite graphs and lattices.Unpublished.1971
[78]Deng,H.and Clausi,D.A.Unsupervised image segmentation using a simple MRF Model with a new implementation scheme,Pattern Recognition 2004.37:2323-335
[79]P.Felzenszwalb and D.Huttenlocher.Efficient Belief Propagation for Early Vision.International Journal of Computer Vision,2006.70(1):41-44
[80]Y.Boykov,O.Veksler,and R.Zabih.Fast approximate energy minhnization via graph-cuts.IEEE Transactions on Pattern Analysis and Machine Intelligence,2001.23(11):1222-239
[81]Kingsbury N G.The dual-tree complex wavelet transform:a new technique for shift invariance and directional fliers.Proceedings of 8th IEEE Digital Sign Processing Workshop,Bryce Can yon,Utah,
[2]A.Chaparro,C.I.Stromeyer,E.Huang,et al.,Colour is what the eye sees best,Nature,1993,361:348-350.
[3]F.A.A.Kingdom,Color brings relief to human vision,Nature Neuroscience,2003(6):641-644.
[4]R.Ramanath,W.E.Snyder,Y.Yoo,et al.,Color image processing pipeline,IEEE Signal Processing Magazine,2005(22):34-43.
[5]D.Tretter,C.A.Bouman,K.Khawaja,and A.Maciejewski.A multiscale stochastic image model for automated inspection.IEEE Trans.on Image Processing,1995.4(12):507-517
[6]S.Geman,D.Geman.Stochastic relaxation,Gibbs distributions and the Bayesian restoration of images,IEEE Transactions on Pattern Analysis and Machine Intelligence,1984(6):721-741
[7]A.Blake,A.Zisserman,Visual Reconstruction,MIT Press,Cambridge,MA,1987
[8]D.Mumford,J.Shah.Optimal approximations by piecewise smooth functions and associated variational problems,Communications on Pure and Applied Mathematics.1989(42):577-685
[9]Kenneth R.Castleman,Digital hnage Processing,Prince Hall,1996
[10]王萍,苏秀琴,刘雅轩.给予区域合并的动态阈值分割算法.光子学报,2004,33(3):378-381
[11]修春波,刘向东,张宇河.基于混沌优化的最佳熵阂值的图像分割.计算机工程与应用,2004,27:76-77
[12]Kim DY,Kim J H,Noh S M,et al.Pulmonary nodule detection using chest CT images.Acta Radiol,2003,44(3):252-257
[13]W.Skarbek and A.Koschan,Color image segmentation:A survey,Technical Report,Technical University of Berlin,1994
[14]L.Lucchese and S.K.Mitra,Color image segmentation:A state-of-the-art survey,Proc.of the Indian National Science Academy(INSA-A),New Delhi,India,2001:207-221
[15]H.D.Cheng,X.H.J iang,Y.Sun,et al.,Color image segmentation:advances and prospects Pattern Recognition,2001,34:2259-2281
[16]Y.Ohta,T.Kanade and T.Sakai,Color information for region segmentation,Computer Graphics and Image Processing,1980,13:222-241
[17]R.Ohlaner,K.Price and D.R.Reddy,Picture segmentation using a recursive region splitting method,Computer Graphics and Image Processing,1978,8:313-333
[18]A.Tremeau and N.Borel,A region growing and merging algorithm to color segmentation,Pattern Recognition,1997,30:867-881
[19]A.Koschan,A comparative study on color edge detection,Proc.of the 2nd Asia Conf.on Computer Vision ACCV'95,Singapore,1995:574-578
[20]T.Kanade,Image understanding research at CMU,Proc.Image understanding workshop,1978:574-578
[21]S.D.Zenzo,A note on the gradient of a multi-image,Comp.Vis.Graph.Image Proc.,1986:116-125
[22]A.Cumani,Edge detection in multispectral images,Comput.Vis.Graph.Image Process.:Graphical Models Image Processing,1991:40-51
[23]P.E.Trahanias and A.N.Venetsanopoulos,A color edge detection using vector order statistics,IEEE Trans.Image Processing,1993,2,:59-265
[24]J.Scharcanski and A.N.Venetsanopoulos,Edge detection of color images using directional operators,IEEE Trans.on Circuits and Systems for Video Technology,1997,7(7):397-401
[25]M.A.Ruzon and C.Tomasi,Edge,junction,and comer detection using color distribution,IEEE Trans.PAMI,2001,23:1281-1295
[26]D.R.Martin,C.C.Fowlkes and J.Malik,Learning to detect neural image boundaries using local brightness,color,and texture cues,IEEE Trans.PAMI,2004,26:530-549
[27]A.Koschan and M.Abidi,Detection and classification of edges in color images,IEEE Signal Processing Magazine,2005,22:64-73
[28]Y.N.Deng and B.S.Manjunath,Unsupervised segmentation of color-texture regions in images and video,IEEE Trans.on PAMI,2001,23:800-810
[29]F.Jing,M.Li,H.Zhang,et al.,Unsupervised image segmentation using local homogeneity analysis,Proc.IEEE International Symposium on Circuits and Systems 2003,2003:456-459
[30]Y.Zheng,J.Yang and Y.Zhou,Unsupervised segmentation on image with JSEG using soft class map,IDEAL'04,LNCS 3177,Springer,Berlin,2004:197-202
[31]Y.Wang,J.Yang and Y.Zhou,Unsupervised color-texture segmentation,ICIAR 2004,LNCS 3211,Springer,Berlin,2004:106-113
[32]李厚强,刘政凯,詹曙.一种彩色纹理图像的分割方法.计算机学报.2001,24(9):965-971.
[33]王志勇,邓达,余英林.分形技术在彩色纹理分割中的应用.华南理工大学学报,1998(10):64-70.
[34]Wang Xiao-Hui,Zhou Yue,Wang Yong-Gang,and Zhu WeiWei,Color Texture Segmentation Based on Quatemion-Gabor Features,CIARP 2006,2006(LNCS 4225):345-353.
[35]Z.Kato,T.C.Pong,G.Q,Song.Unsupervised segmentation of color textured images using a multi-layer MRF model.Proceedings of International Conference on Image Processing,vol.1,IEEE,Barcelona,Spain,2003,961-964
[36] Marroquin J, et al. Probabilistic solution of ill-posed problems in computational vision. 1987, J. Am.Statist, Assoc
[37] Bertero M, et al. Ill-posed problems in early vision. Proc. IEEE, 1988.76(8):869-889
[38] B. Hunt. Bayesian methods in nonlinear digital image restoration, IEEE Trans. on Comput, 1977.26(3):219-229
[39] T. J. Hebert and K. Lu. Expectation-maximization algorithms, null spaces, and MAP image restoration,IEEE Trans. on Image Processing, 1995.4(8): 1084-1095
[40] John Argyris. An Exploration of Chaos. North-Holland: Amsterdam, 1994.
[41] R. R. Schultz and R. L. Stevenson. Stochastic modeling and estimation of multi-spectral image data. IEEE Trans. on Image Processing, 1995.4(8): 1109-1119
[42] R. Chellappa and S. Chatterjee. Classication of textures using Gaussian Markov random fields. IEEE Trans. on Acoust. Speech and Signal Proc. ASSP1985.33(4): 959-963
[43] F. S. Cohen, Z. Fan, and M. A. Patel. Classification of rotated and scaled textured images using Gaussian Markov random field models. IEEE Trans.on Pattern Analysis and Machine Intelligence, 1991.13(2):192-202
[44] D. B .Cooper. Maximum likelihood estimation of Markov process blob boundariesin noisy images.IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI, 1979.1: 3723-3784
[45] D. B. Cooper, H. Elliott, F. Cohen, L. Reiss, and P. Symosek. Stochastic boundary estimation and object recognition. Comput. Vision Graphics and Image Process.1980.12: 326-356
[46] H. Elliott, D. B. Cooper, F. S. Cohen, and P. F. Symosek. Implementation, interpretation, and analysis of a suboptimal boundary finding algorithm. IEEE Trans. on Pattern Analysis and Machine Intelligence, PAMI 1982.4(2):167-182
[47] D. Geman, S. Geman, C. Gragne and P. Dong. Boundary detection by constrained optimization. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1990.12(7): 609-628
[48] H. Derin and W. Cole. Segmentation of textured images using Gibbs random fields. Comput. Vision Graphics and Image Process, 1986.35: 72-98
[49] H. Derin, H. Elliot, R. Cristi, and D. Geman. Bayes smoothing algorithms for segmentation of binary images modeled by Markov random fields. IEEE Trans. On Pattern Analysis and Machine Intelligence,PAMI,1984,6(6): 707-719
[50] H. Derin and H. Elliott. Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Trans. on Pattern Analysis and Machine Intelligence,PAMI,1987.9(1): 39-55
[51] S. Sista, C. A. Bouman, and J. P. Allebach. Fast image search using a multi-scale stochastic model. In Proc.of IEEE Int'l Conf. on Image Proc, 1994.1,225-228
[52]T.Randen,J.H.Husoy,Filtering for texture classification:A comparative study,IEEE Transactions on Pattern Analysis and Machine Intelligence,1999,21(4):291-310
[53]Besag,J.Spatial interaction and the statistical analysis of lattice systems(with discussions).Journal of the Royal Statistical Society,Series B,1974(36):192-236
[54]Hammersley,Clifford,Markov field on finite graphs and lattices.Unpublished.1971
[55]SGeman,D.Geman.Stochastic relaxation Gibbs distribution and Bayesian restoration of image.IEEE Trans.PatemAnal.Machine Intell,1984(6):721-741
[56]Smith,J.R.and Chang,S.F.Tools and techniques for color image retrieval,Storage & Retrieval for Image and Video Data bases Ⅳ,Vol.2670 of IS & T/SPIE Proceedings,San Jose,CA,USA,1996,2679,426-437
[57]Tuceryan.M.,Jain A.K.Texture analysis.In:Chert C.H,Pau L.F,Wang,P.S.P.The handbook of pattern recognition and computer vision,2nd.Singapore:World Scientific Publishing Company,1998,207-248
[58]Tamura H.,Mori S.,Yamawaki Y.Textural Features Corresponding to Visual Perception,IEEE Transactions on Systems,Man,and Cybernetics,1978.8:460-473
[59]Haralick R.M.Statistical and Structural Approaches to Texture.Proceedings of the IEEE 67,1979,786-804
[60]Richards W.,Polit A.Texture matching.Kybernetic,1974,16:155-162
[61]Hawkins J.K.Textural Properties for Pattern Recognition.In:Lipkin B.,Rosenfeld A.Picture Processing and Psychopictorics.Academic Press,New York,1969
[62]Bovik A.C.,Clark M.,Geisler W.S.Multichannel texture analysis using localized spatial filters.IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(1):55-73
[63]Chaudhuri B.,Sarkar N.Texture segmentation using fractal dimension.IEEE Transactions on Pattern Analysis and Machine Intelligence1995,17(1):72-77
[64]张建国.不变性纹理分析.中科院自动化所博士学位论文,北京,2002
[65]张毓晋.图像工程---图像分析与处理.北京:清华大学出版社,2001
[66]颜春梅,张友静,鲍颜松.基于灰度共生矩阵法的IKONOS影像中竹林信息提取.遥感信息.2004,2:31-34
[67]R.M.Haralick,K.Shanmugam.I.Dinstcin.Textural feature for image classification.IEEE Trans.On Systems.Man and Cybernetics.Vol.SMC-6,No.4,april 1976
[68]吴高洪.纹理分析的若干多尺度方法研究.清华大学论文.1999
[69]Fracos J.M.,Meiri A.Z.,Porat B,A Untitled Texture Model Based on a Wold Decomposition.IEEE Transactions on Signal Processing,1993,41(8):2665-2678
[70]Mao J.C.,Jain A.K.Texture classification and segmentation using multi-resolution auto regressive models,Pattern Recognition,1992,25(2):173-188
[71]Dunn D.,Higgins W.,Wakeley J.Texture segmentation using 2-D Gabor elementary functions.IEEE Transactions on Pattern Analysis and Machine Intelligence,1994,22:130-149
[72]Freeman W.T.,Adelson E.H.The design and use of steerable filters.IEEE Transactions on Pattern Analysis and Machine Intelligence,1991.13(9):891-906
[73]Chang T.H.and C.C Jay Kuo.Texture analysis and classification with tree-structured wavelet transform.IEEE transactions on Image Processing,1993,2(4):429-440
[74]CAMPBELL FW,ROBOSON J G.Application of Fourier Analysis to the Visibility of Gratings.J.Physiology,1977:551-566
[75]王文惠,周良柱,万建伟.基于内容的图象检索技术的研究和发展.计算机工程与应用,2001,5:54-56
[76]Jianguo Zhang,Tieniu Tan,Li Ma,Invariant texture segmentation via circular gabor filter.Proceedings of the 1.6~(th) IAPR International Conference on Pattern Recognition(ICPR),Vol Ⅱ,901-04
[77]Hammersley,J.M.and Clifford,P.Markov field on finite graphs and lattices.Unpublished.1971
[78]Deng,H.and Clausi,D.A.Unsupervised image segmentation using a simple MRF Model with a new implementation scheme,Pattern Recognition 2004.37:2323-335
[79]P.Felzenszwalb and D.Huttenlocher.Efficient Belief Propagation for Early Vision.International Journal of Computer Vision,2006.70(1):41-44
[80]Y.Boykov,O.Veksler,and R.Zabih.Fast approximate energy minhnization via graph-cuts.IEEE Transactions on Pattern Analysis and Machine Intelligence,2001.23(11):1222-239
[81]Kingsbury N G.The dual-tree complex wavelet transform:a new technique for shift invariance and directional fliers.Proceedings of 8th IEEE Digital Sign Processing Workshop,Bryce Can yon,Utah,