基于特征的纹理图像分割技术研究
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摘要
纹理图像分割是数字图像处理研究的一个重要分支，是众多图像分析和机器视觉应用的基础。但是，一方面由于自然纹理类型庞杂、形态各异且结构繁复，另一方面也因为对人类视觉系统感知纹理的机理认识不足，纹理图像分割一直是图像处理领域的一大难题。在过去的四十多年中，广大研究人员虽然提出了大量的纹理图像分割算法，似是这些算法都存在着一定的不足。迄今为止，纹理图像分割仍然是一个没有得到很好解决的富有挑战性的课题。
本文以灰度自然纹理图像的自动分割方法为研究内容，对目前广泛采用的一些纹理描述方法和纹理图像分割方法进行了认真的研究和总结，对各种方法的理论和实验结果进行了深入的分析和对比，选择了从基于特征的角度研究纹理图像分割问题。基于特征的纹理图像分割包括特征提取和图像分割这两个步骤。前者是描述图像的过程，旨在将图像中属于同一种纹理的像素映射为相似的矢量；后者进一步将矢量映射为类别标号，实现从特征集合到分割结果的转化。本文分别对这两个步骤进行了研究，完成了以下几个方面的工作：
1、对纹理图像分割的研究意义、研究现状，特别是各类纹理图像分割方法的基本思想、算法的提出和各种改进进行了比较全面的总结，旨在通过这些总结来说明本文对纹理图像分割研究的深刻认识。
2、研究了基于分形模型的纹理特征。提出了一种使用可变结构元的形态学分形维数估计算法。与四种传统的分形维数估计算法的对比实验显示，这种新算法不仅可以得到更加准确的分形纹理特征，而且算法的时间复杂度也更小。
3、研究了基于多重分形模型的纹理特征。率先提出了基于数学形态学的多重分形估计算法，得到了一种全新的纹理描述符——局部形态学多重分形指数谱。与两种基于盒计数的多重分形维数相比，这种新特征在纹理图像分割实验中得到的分割精度更高，时间复杂度更小。此外，还将形态学多重分形估计与分形签名的概念相结合，提出了另一种纹理描述符——局部形态学多重分形签名。纹理图像分割实验表明，该特征的纹理区分能力不仅优于分形签名和局部形态学多重分形指数谱，也明显优于基于马尔可夫随机场模型的特征。
4、研究了基于模糊聚类的图像分割技术。指出了图像的每一个纹理特征都可以被视为一个空间模式，提出了一种针对空间模式的模糊聚类算法实现了纹理图像分割。与经典的模糊聚类、空间模糊聚类和基于马尔可夫随机场模型的分割算法相比，新算法可以有效的提高纹理图像分割的精度。此外，还以该算法为核心，提出了一种基于图像四叉树的多级图像分割算法。对比实验显示，多级分割算法以牺牲少许分割精度为代价，将时间复杂度降低了一个数量级，从而使该算法可以被应用到数据量庞大且有一定实时性要求的场合。
5、提出了耦合马尔可夫随机场模型来建模特征提取与图像分割之间的相互依赖关系，基于该模型实现了一种自适应的纹理图像分割算法。与经典的基于马尔可夫随机场的分割算法相比，新算法可以更好的定位纹理区域的边缘，从而显著的提高了纹理图像分割的精度。
The segmentation of textured images aims to partition an image into severaldisjointed regions that are homogeneous with regards to some texture measures, sothat subsequent higher level computer vision processing can be performed. It has longbeen one of the most important branches of digital image processing and has drawnconsiderable attention of researchers from around the world. During the past threedecades, hundreds of segmentation algorithms have been proposed in the literature.However, due to the diversity of images, the complexity of natural textures and thelack of understanding of the human vision system (HVS), those algorithms usuallysuffer from less accuracy and narrow image specific orientation. Therefore, texturesegmentation is, up to now, still an open topic with great challenge in imageprocessing field.
This dissertation is devoted to the semi-supervised segmentation of textured graylevel images, where the number of texture patterns is known but the information abouttheir properties is not. After comprehensively reviewing the basic principles andexisted methods, the author chooses the feature-based approaches to solve thisproblem. Generally, feature-based texture segmentation algorithms can be viewed asconsisting of two successive processes: feature extraction and feature partition.Feature extraction tends to find an appropriate descriptor to characterize thehomogeneity of each texture in an image so that all pixels from the same texture canbe represented by vectors of similar value. Feature partition is a process of assigningeach feature a label to designate the region or class to which it belongs, and thussegmentation result can be obtained through the relationship between features andpixels. In this dissertation, the author investigates those two processes, respectively,and achieves highly effective, increasingly innovative and cutting-edge approaches oftexture segmentation, which can be summarized as follows.
1. An overview of segmentation of textured images, including the fundamentaldefinitions, the research background and the significance of this topic is presentedand the mainstream approaches and the state of art of algorithms in this field arereviewed in this dissertation.
2. Texture feature extraction is investigated by using the fractal model in this dissertation. Various fractal dimensions have been widely used as texturedescriptors. However, the popular box-counting based fractal dimension iscommonly criticized for its less accuracy,, which is mainly caused by the regularpartition and counting scheme. Through analyzing the disadvantages of thetraditional morphological method, the author proposes a modified morphologicalfractal estimation approach, which uses a series of structure elements withdifferent scales to take the place of the unit structure elements used by traditionalmethod so that the estimation accuracy has been further improved. Throughdelicately selecting the shape of structure elements and constructing an iterativedilation scheme, the proposed approach substantially reduces the computationaltime-cost. When applied to texture segmentation, the novel morphological fractaldimension demonstrates an improved ability to differentiate various textures.
3. Texture features based on the multifractal model is studied in this dissertation.Due to the limited bit depth and spatial resolution, most digital images are merelysemi-fractals and have anisotropic and inhomogeneous scaling properties.Therefore, fractal dimension alone is intrinsically not sufficient to representtexture patterns. To characterize the fractal reality of textured images, the authorgeneralizes the morphological fractal estimation algorithm to multifractalestimation, and thus proposes a novel texture descriptor called the localmorphological multifractal exponents (LMME). Furthermore, motivated by theidea of fractal signature, the author extends the LMME feature to themorphological multifractal signatures (MMFS). Those two multifractal texturefeatures has been compared with other commonly uses features in segmentation oftexture mosaics. The experimental results demonstrate that the novel features candifferentiate textured images more effectively and provide more robustsegmentations.
4. Feature partition based on fuzzy clustering is explored in this dissertation. Featurepartition in feature-based texture segmentation is different from traditional patternclassification problems in that texture features imply not only the position infeature space but the position on image surface. Therefore, a texture feature isindeed a spatial pattern so that a textured image can be modeled as a set of spatialpatterns. The author proposes an approach to perceptual segmentation of imagesthrough the means of fuzzy clustering of spatial patterns, where the distancebetween a spatial pattern and each cluster is defined as a combination of the Euclidean distance in the feature space and the spatial dissimilarity, which reflectshow much of the pattern's neighbourhood is occupied by other clusters. Theresults of comparative experiments demonstrate that the proposed approach cansubstantially improve the segmentation accuracy. Moreover, the author alsogeneralizes this approach to a multi-level feature partition algorithm, whichsignificantly decreases the computational complexity of texture segmentation.
5. In feature-based texture segmentation, feature estimation and feature partition arenot two independent processes. Regardless of this fact, traditional methods usuallysuffer from the less accuracy, which is intrinsically caused by the oversimplifiedassumption that each textured sub-image used to estimate a feature ishomogeneous. To solve this problem, the author proposes a coupled Markovrandom field (CMRF) model, which has two coupled components: one models theobserved image to estimate features, and the other models the labeling to achievefeature partition. When calculating the feature of each pixel, the homogeneity ofthe sub-image is ensured by using only the pixels currently labeled as the samepattern. With the acquired features, and the labeling is obtained through solving aMAP (maximum a posteriori) problem. In this adaptive segmentation approach,the features and the labeling are mutually dependent on each other, and thereforeare alternately optimized by a simulated annealing scheme. With the gradualimprovement of features' accuracy, the labeling is able to locate the exactboundary of each texture pattern. The proposed algorithm is compared with asimple MRF model based method in segmentation of both Brodatz texturemosaics and real scene images. The satisfying experimental results demonstratethat the proposed approach can differentiate textured images more accurately.
本文以灰度自然纹理图像的自动分割方法为研究内容，对目前广泛采用的一些纹理描述方法和纹理图像分割方法进行了认真的研究和总结，对各种方法的理论和实验结果进行了深入的分析和对比，选择了从基于特征的角度研究纹理图像分割问题。基于特征的纹理图像分割包括特征提取和图像分割这两个步骤。前者是描述图像的过程，旨在将图像中属于同一种纹理的像素映射为相似的矢量；后者进一步将矢量映射为类别标号，实现从特征集合到分割结果的转化。本文分别对这两个步骤进行了研究，完成了以下几个方面的工作：
1、对纹理图像分割的研究意义、研究现状，特别是各类纹理图像分割方法的基本思想、算法的提出和各种改进进行了比较全面的总结，旨在通过这些总结来说明本文对纹理图像分割研究的深刻认识。
2、研究了基于分形模型的纹理特征。提出了一种使用可变结构元的形态学分形维数估计算法。与四种传统的分形维数估计算法的对比实验显示，这种新算法不仅可以得到更加准确的分形纹理特征，而且算法的时间复杂度也更小。
3、研究了基于多重分形模型的纹理特征。率先提出了基于数学形态学的多重分形估计算法，得到了一种全新的纹理描述符——局部形态学多重分形指数谱。与两种基于盒计数的多重分形维数相比，这种新特征在纹理图像分割实验中得到的分割精度更高，时间复杂度更小。此外，还将形态学多重分形估计与分形签名的概念相结合，提出了另一种纹理描述符——局部形态学多重分形签名。纹理图像分割实验表明，该特征的纹理区分能力不仅优于分形签名和局部形态学多重分形指数谱，也明显优于基于马尔可夫随机场模型的特征。
4、研究了基于模糊聚类的图像分割技术。指出了图像的每一个纹理特征都可以被视为一个空间模式，提出了一种针对空间模式的模糊聚类算法实现了纹理图像分割。与经典的模糊聚类、空间模糊聚类和基于马尔可夫随机场模型的分割算法相比，新算法可以有效的提高纹理图像分割的精度。此外，还以该算法为核心，提出了一种基于图像四叉树的多级图像分割算法。对比实验显示，多级分割算法以牺牲少许分割精度为代价，将时间复杂度降低了一个数量级，从而使该算法可以被应用到数据量庞大且有一定实时性要求的场合。
5、提出了耦合马尔可夫随机场模型来建模特征提取与图像分割之间的相互依赖关系，基于该模型实现了一种自适应的纹理图像分割算法。与经典的基于马尔可夫随机场的分割算法相比，新算法可以更好的定位纹理区域的边缘，从而显著的提高了纹理图像分割的精度。
The segmentation of textured images aims to partition an image into severaldisjointed regions that are homogeneous with regards to some texture measures, sothat subsequent higher level computer vision processing can be performed. It has longbeen one of the most important branches of digital image processing and has drawnconsiderable attention of researchers from around the world. During the past threedecades, hundreds of segmentation algorithms have been proposed in the literature.However, due to the diversity of images, the complexity of natural textures and thelack of understanding of the human vision system (HVS), those algorithms usuallysuffer from less accuracy and narrow image specific orientation. Therefore, texturesegmentation is, up to now, still an open topic with great challenge in imageprocessing field.
This dissertation is devoted to the semi-supervised segmentation of textured graylevel images, where the number of texture patterns is known but the information abouttheir properties is not. After comprehensively reviewing the basic principles andexisted methods, the author chooses the feature-based approaches to solve thisproblem. Generally, feature-based texture segmentation algorithms can be viewed asconsisting of two successive processes: feature extraction and feature partition.Feature extraction tends to find an appropriate descriptor to characterize thehomogeneity of each texture in an image so that all pixels from the same texture canbe represented by vectors of similar value. Feature partition is a process of assigningeach feature a label to designate the region or class to which it belongs, and thussegmentation result can be obtained through the relationship between features andpixels. In this dissertation, the author investigates those two processes, respectively,and achieves highly effective, increasingly innovative and cutting-edge approaches oftexture segmentation, which can be summarized as follows.
1. An overview of segmentation of textured images, including the fundamentaldefinitions, the research background and the significance of this topic is presentedand the mainstream approaches and the state of art of algorithms in this field arereviewed in this dissertation.
2. Texture feature extraction is investigated by using the fractal model in this dissertation. Various fractal dimensions have been widely used as texturedescriptors. However, the popular box-counting based fractal dimension iscommonly criticized for its less accuracy,, which is mainly caused by the regularpartition and counting scheme. Through analyzing the disadvantages of thetraditional morphological method, the author proposes a modified morphologicalfractal estimation approach, which uses a series of structure elements withdifferent scales to take the place of the unit structure elements used by traditionalmethod so that the estimation accuracy has been further improved. Throughdelicately selecting the shape of structure elements and constructing an iterativedilation scheme, the proposed approach substantially reduces the computationaltime-cost. When applied to texture segmentation, the novel morphological fractaldimension demonstrates an improved ability to differentiate various textures.
3. Texture features based on the multifractal model is studied in this dissertation.Due to the limited bit depth and spatial resolution, most digital images are merelysemi-fractals and have anisotropic and inhomogeneous scaling properties.Therefore, fractal dimension alone is intrinsically not sufficient to representtexture patterns. To characterize the fractal reality of textured images, the authorgeneralizes the morphological fractal estimation algorithm to multifractalestimation, and thus proposes a novel texture descriptor called the localmorphological multifractal exponents (LMME). Furthermore, motivated by theidea of fractal signature, the author extends the LMME feature to themorphological multifractal signatures (MMFS). Those two multifractal texturefeatures has been compared with other commonly uses features in segmentation oftexture mosaics. The experimental results demonstrate that the novel features candifferentiate textured images more effectively and provide more robustsegmentations.
4. Feature partition based on fuzzy clustering is explored in this dissertation. Featurepartition in feature-based texture segmentation is different from traditional patternclassification problems in that texture features imply not only the position infeature space but the position on image surface. Therefore, a texture feature isindeed a spatial pattern so that a textured image can be modeled as a set of spatialpatterns. The author proposes an approach to perceptual segmentation of imagesthrough the means of fuzzy clustering of spatial patterns, where the distancebetween a spatial pattern and each cluster is defined as a combination of the Euclidean distance in the feature space and the spatial dissimilarity, which reflectshow much of the pattern's neighbourhood is occupied by other clusters. Theresults of comparative experiments demonstrate that the proposed approach cansubstantially improve the segmentation accuracy. Moreover, the author alsogeneralizes this approach to a multi-level feature partition algorithm, whichsignificantly decreases the computational complexity of texture segmentation.
5. In feature-based texture segmentation, feature estimation and feature partition arenot two independent processes. Regardless of this fact, traditional methods usuallysuffer from the less accuracy, which is intrinsically caused by the oversimplifiedassumption that each textured sub-image used to estimate a feature ishomogeneous. To solve this problem, the author proposes a coupled Markovrandom field (CMRF) model, which has two coupled components: one models theobserved image to estimate features, and the other models the labeling to achievefeature partition. When calculating the feature of each pixel, the homogeneity ofthe sub-image is ensured by using only the pixels currently labeled as the samepattern. With the acquired features, and the labeling is obtained through solving aMAP (maximum a posteriori) problem. In this adaptive segmentation approach,the features and the labeling are mutually dependent on each other, and thereforeare alternately optimized by a simulated annealing scheme. With the gradualimprovement of features' accuracy, the labeling is able to locate the exactboundary of each texture pattern. The proposed algorithm is compared with asimple MRF model based method in segmentation of both Brodatz texturemosaics and real scene images. The satisfying experimental results demonstratethat the proposed approach can differentiate textured images more accurately.
引文
[1] 赵荣椿(等)，数字图像处理导论[M]，西安：西北工业大学出版社，2000
[2] 王润生，图像理解[M]，长沙：国防科技大学出版社，1995
[3] K. Castleman, Digital Image Processing[M], NJ:Prentice-Hall, 1996
[4] 马颂德，张正友，计算机视觉[M]，北京：科学出版社，1998
[5] 贾云得，机器视觉[M]，北京：科学出版社，2000
[6] R.C.Gonzalez,R.E.Woods,Digital Image Process ing(2nd edition)[M]，北京：电子工业出版社，2002
[7] 章毓晋．图像工程上册—图象处理和分析[M]，北京：清华大学出版社，2003
[8] M．Sonka，V．Hlavac，R．Boyle，图像处理、分析与机器视觉(艾海舟、武勃等译)[M]，北京：人民邮电出版社，2003
[9] 阮秋琦，数字图像处理学[M]，北京：电子工业出版社，2004
[10] Wesley E．Snyder，Hairong Qi，机器视觉教程(林学訚，崔锦实，赵清杰等译)[M]，北京：机械工业出版社，2005
[11] 徐光佑，计算机视觉[M]，北京：科学出版社，1999
[12] J. K. Hawkins, Texture Properties for Pattern Recognition [A], in Picture Processing and Psychopictorics [C], B. S. Lipkin and A. Rosenfeld Eds, New York: Academic Press, 1980, pp 347-370
[13] L. Van Gool, P. Dewale, A. Oosterlinck, Survey Texture Analysis Anno 1983 [J], Computer Vision, Graphics, and Image Processing, 1985, 29(3):336-357
[14] R.M. Haralick, K. Shanmugam, I. Dinstein, Textural Features for Image Classification [J], IEEE Transactions on Systems, Man, and Cybernetics, 1973, SMC-3(6):610-621
[15] 章毓晋，图像图形科学丛书——图像分割[M]，北京：科学出版社，2001
[16] N.R. Pal, S.K. Pal, A review on image segmentation techniques [J], Pattern Recognition, 1993, 26(9):1227-1249
[17] K.S. Fu, J.K. Mui, A survey of image segmentation [J], Pattern Recognition, 1980, 13(1):3-16
[18] R.M. Haralick, L.G. Shapiro, Image segmentation techniques [J], Computer Vision, Graphics, and Image Processing, 1985, 29(1):100—132
[19] 赵荣椿，迟耀斌，朱重光，图像分割技术进展[J]，中国体视学与图像分析，1998，3(2)：121-128
[20] 罗希平(等)，图象分割方法综述[J]，模式识别与人工智能，1999，12(3)：300-312
[21] 王爱民，沈兰荪，图像分割研究综述[J]，测控技术，2000，19(5)：1-6
[22] Y.J. Zhang, J. J. Gerbrands, Objective and quantitative segmentation evaluation and comparison [J], Signal Processing, 1994, 39(1):43-54
[23] S. A. Barker, Image segmentation using Markov random field models (Ph.D. dissertation) [D], Cambridge University, 1998
[24] Y.Q. Chen, M.S. Nixon, D.W. Thomas, Statistical geometrical features for texture classification [J], Pattern Recognition, 1995, 28(4):537-552
[25] O. Pichler, A. Teuner, B. Hosticka, A comparison of texture feature extraction using adaptive Gabor filtering, pyramidal and tree—structured wavelet transforms [J], Pattern Rccognition, 1996, 29(5):733-742
[26] S.N. Jayaramamurthy, Texture discrimination using digital deconvolution filters [A], in Proceedings of the 5th International Conference on Pattern Recognition [C], Miami Beach, Florida, 1980:1184-1186
[27] T. Matsuyama, K. Saburi, M. Nagao, A structural analyzer for regularly arranged textures [J], Computer Graphics Image Processing, 1982, 18 (1): 259-278
[28] J. Toriwaki, Y. Yashima, S. Yokoi, Adjacency graphs on a digitized figure set and their applications to texture analysis [A], in Proceedings of the 7th International Conference on Pattern Recgonition [C], Canada. Montreal, 1984:1216-1218
[29] D. Chert, L. Wang, Texture features based on texture spectrum [J], Pattern Recognition, 1991, 24(5):391-399
[30] R.M. Haralick, Statistical and structural approaches to texture [J], Proceedings of IEEE, 1979, 67(5):786-804
[31] T.R. Reed, J.M.H. Buf, A review of recent texture segmentation and feature extraction techniques [J], Computer Vision, Graphics, and Image Processing, 1993, 57 (3):359-372
[32] T. N. Tan, Texture edge detection by modeling visual cortical channel s [J], Pattern Recognition, 1995, 28(9):1283-1298
[33] C.M. Chen, H.H. Lu, K.C. Han, A textural approach based on Gabor functions for texture edge detection in ultrasound images [J], Ultrasound in Medicine and Biology, 2001, 27(4):515-34
[34] V. Barranco Lopez, P. Luque Escamilla, J. Martinez Aroza, R. Roman Roldan, Entropic texture-edge detection for image segmentation [J], Electronic Letters, 1995, 31(11):867-869
[35] Sagiv Chen, N.A. Sochen, Y.Y. Zeevi, Integrated active contours for texture segmentation [J], IEEE Transactions on Image Processing, 2006, 15(6):1633-1646
[36] Nikos Paragios, Rachid Deriche, Geodesic active contours and level set methods for supervised texture segmentation [J], International Journal of Computer Vision, 2002, 46(3):223-247
[37] M. Kardan, JMH Du Buf, M. Span, Texture feature performance for image segmentation [J], Pattern Recognition, 1990, 23(3-4):291-309
[38] D. J. Marceau, P.J. Howarth, J.M.M. Dubois, D.J. Gration, Evaluation of grey level co-occurrence matrix method for land-cover classification using SPOT imagery [J], IEEE Transactions on Geoscience and Remote Sensing, 1990, GRS-28(4): 513-519
[39] L.K. Soh, C. Tsatsoulis, Texture analysis of SAR sea ice imagery using gray level co-occurrence matrices [J], IEEE Transactions on Geoscience and Remote Sensing, 1999, GR5-37(2):780-795
[40] Mari Partio, Bogdan Cramariuc, Moncef Gabbouj, Ari Visa, Rock texture retrieval using gray level co-occurrence matrix [J], in Proceedings of the 5th Nordic Signal Processing Symposium [C], Norway, 2002:4-7
[41] D.P. Panda, A. Rosenfeld, Image segmentation by pixel classification in (gray level, edge value) space [J], IEEE Transactions on Computers, 1978, 27(9):875-879
[42] M.M. Trivedi, C.A. Harlow, R.W. Conners, S. Goh, Object detection based on gray level co-occurrence [J], Computer Vision, Graphics, and Image Processing, 1984, 28(2): 199-219
[43] Q.A. Holmes, D.R. Neusch, R.A. Shuchman, Textural analysis and real-time classification of sea-ice types using digital SAR data [J], IEEE Transactions on Geoscience and Remote Sensing, 1984, GRS-22(2):113-120
[44] M. Unser, Sum and difference histograms for texture classification [J], IEEE Transactions Pattern Analysis and Machine Intelligence, 1986, PAMI-8(1):118-125
[45] S.H. Peckinpaugh, An improved method for computing gray level co-occurrence matrix based texture measures [J], Computer Vision, Graphics and Image Processing, 1991, 53(6):574-580
[46] M. Galloway, Texture analysis using gray-level run length [J], Computer Graphics Image Processing, 1974, 4:172—199
[47] D.B.C. Shu, Y.N. Sun, C.C. Li, J.F. Mancuso, Run lengthbased image segmentation schemes[A], in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition[C], USA Washington D.C., 1983:154-156
[48] J. Weszka, C. Dyer, A. Rosenfeld, A comparative study of texture measures for terrain classifications [J], IEEE Transactions on Systems, Man, and Cybernetics, 1976, SMC-6(4):269-285
[49] D. Harwood, T. Ojala, N. Pietikinen, S. Kelman, L. Davis, Texture Classification by Center-Symmetric Auto-Correlation, Using Kullback Discrimination of Distributions [J], Pattern Recognition Letters, 1995, 16(1):1-10
[50] R.N. Sutton, F.L. Hall, Texture Measures for Automatic Classification of Pulmonary Disease [J], IEEE Transactions on Computers, 1972, 21:667-676
[51] E. Triendl, T. Henderson, A model for texture edges [A], in Proceedings of the 5~(th) IEEE International Conference on Pattern Recognition [C], FL, Miami Beach,1980:1100-1102
[52]H. Taraura, S. Mori, T. Yamawaki, Texture features corresponding to visual perception [J], IEEE Transactions on Systems, Man, and Cybernetics, 1978,SMC-8(6):460-473
[53]M. Flickner, H. Sawhney, W. Niblack, J, Ashley, Q. Huang, B. Dom, M. Gorkani,J. Hafner, D. Lee, D. Petkovic, D. Steele, P. Yanker, Query by image and video content: The QBIC system [J], IEEE Transactions on Computers, 1995, 28(9):23-32
[54]Pentland A, PicardRW, SclaroffS. Photobook, Content-based manipulation of image databases [J], International Journal of Computer Vision, 1996, 18(3): 322-330
[55]P. A. Dondes, A. Rosenfeld, Pixel classification based on gray level and local "business" [J], IEEE Transactions on Pattern Analysis and Machine Intelligence,1982, PAMI-4(1):79-84
[56]G. E. Lowitz, Can a local histogram really map texture information? [J], Pattern Recognition, 1983, 16(2):141-147
[57]H. Wechsler, Taxonomy and segmentation of textured images [A], in Proceedings of the 5th International Conference on Pattern Recognition[C], USA, Florida, Miami Beach, 1980:532-534
[58]D. Barba, J. Ronsin, New method in texture analysis in the context of image segmentation [A], in Proceedings of the 2~(nd) European Signal Processing Conference[C], West Germany, Erlangen, 1983:283-286
[59]B. Ashjari, Computer detection and identification of a visually indiscernible texture mixture [A], in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition [C], USA, CA, San Francisco, 1985:172-174
[60]K. Laws, Textured Image Segmentation (Ph.D. Dissertation) [D], University of Southern California, 1980
[61]M. Unser, Local linear transforms for texture measurements [J], Signal Processing,1986, 11(1): 61-79
[62]R. Wang, A. R. Hanson, E. M. Riseman, Texture analysis based on local standard deviation of intensity [A], in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition [C], USA, Florida, Miami Beach, 1986:482-488
[63]G. H. Granlund, Description of texture using the general operator approach [A],in Proceedings of the 5~(th) International Conference on Pattern Recognition [C], USA,Florida, Miami Beach, 1980:776-779
[64]D. Wermser, N. Lissel, Comparison of algorithms for unsupervised segmentation of images by the use of texture information [A], in Proceedings of the 2nd European Signal Processing Conference [C], West Germany, Erlangen, 1983:287-290
[65]L. W. Abele, Feature selection by space invariant comparison with applications to the segmentation of textured pictures [A], in Proceedings of the 5~(th) International Conference on Pattern Recognition [C], USA, Florida, Miami Beach,1980:535-539
[66]P.C. Chen and T. Pavlidis, Segmentation of texture using a co-occurance matrix and a split-and-merge algorithm [J], Computer Graphics Image Processing, 1979,10(1):172-182
[67]H. Knutsson, G. H. Granlund, Texture analysis using two-dimensional quadrature filters [A], in IEEE Workshop CAPAIDM [C], CA, Pasadena, 1983:206-213
[68]J. Bigun, Frequency and orientation selective texture measures using linear symmetry and Laplacian pyramid [A], in Proceedings of Visual Communications and Image Processing [C], Switzerland, Lausanne, 1990:1319-1331
[69]M. Tuceryan, Moment based texture segmentation [J], Pattern Recognition Letters,1994, 15(7): 659-668
[70]M. E. Jernigan, F. D. Astous, Entropy-based texture analysis in the spatial frequency domain [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(2): 237-243
[71]F. D. Astous, M. E. Jernigan, Texture discrimination based on detailed measures of the power spectrum [A], in Proceedings of the 7th International Conference on Pattern Recognition [C], Canada, Montreal, 1984:83-86
[72]J.G. Daugman, Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters [J], Journal of the Optical Society of America A, 1985, 2(7):1160 - 1169
[73]A. C. Bovik, M. Clark, W. S. Geisler, Multichannel Texture Analysis Using Localized Spatial Filters [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, PAMI-12(1):55-73
[74]J. Fogel, D. Sagi, Gabor filters as texture discriminator [J], Biological Cybernetics, 1989, 61(1):103-113
[75]MR Turner, TexLure discrimination by Gabor functions [J], Biological Cybernetics, 1986, 55(2-3):71-82
[76]A. Jain, F. Farrokhnia, Unsupevised texture segmentation using Gabor filters [J],Pattern Recognition, 1991, 24(12):1167-1186
[77]D. Dunn, Designing Gabor filters for texture segmentation (Ph.D. dissertation)[D], The Pennsylvania State University, 1992
[78]D. Dunn, Higgins, Optimal Gabor Filters for Texture Segmentation [J], IEEE Transactions on Image Processing, 1995, 4(7) :947-964
[79]M. Clark, A. C. Bovik, W. S. Geisler, Texture segmentation using Gabor modulation/demodulation [J], Pattern Recognition Letters, 1987, 6(4):261 - 267
[80]A.C. Bovik, N. Gopal, T. Emmoth, A. Restrepo, Localized measurement of emergent image frequencies by Gabor wavelets [J], IEEE Transactions Information Theory,1992, 38(3): 691-712
[81]J. Bigun, J. M.H. du Buf, N-folded symmetries by complex moments in Gabor space [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994,PAMI-16(1):80-87
[82]S.E. Grigorescu, N. Petkov, P. Kruizinga, Comparison of texture features based on Gabor filters [J], IEEE Transactions on Image Processing, 2002, 11(10):1160-1167
[83] P. Kruizinga, N. Petkov, Non-linear operator for oriented texture [J], IEEE Transactions on Image Processing, 1999, 8(10):1395-1407
[84] I. Daubechies, The wavelet transform, time-frequency localization and signal analysis [J], IEEE Transactions on Information Theory, 1990, 36(5):961—1005
[85] S. Mallat, A Theory for Multiscale Signal Decomposition [J], The Wavelet Representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989, PAMI-11(7):674-693
[86] T. Chang, C.J. Kuo, Texture analysis and classification with tree-structured wavelet transform [J], IEEE Transactions on Image Processing, 1993, 2(4):429-441
[87] A. Laine, J. Fan, Texture classification by wavelet packet signatures [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, PAMI-15(11):1186-1191
[88] C.S. Lu, P.C. Chung, C.F. Chen, Unsupervised texture segmentation via wavelet transform [J], Pattern Recognition, 1997, 30(5):729-742
[89] M. Unser, Texture classification and segmentation using wavelet frames [J], IEEE Transactions on Image Processing, 1995, 4(11)1549-1560
[90] K.K. Simhadri, S.S. Iyengar, R.J. Holyer, Wavelet-based feature extraction from oceanographic images [J], IEEE Transactions on Geoscience and Remote Sensing, 1998, GRS-36(3):767—778
[91] D. Charalampidis, T. Kasparis, Wavelet-based rotational invariant roughness features for texture classification and segmentation [J], IEEE Transactions on Image Processing, 2002, 11(8):825-837
[92] Jean-Francois Aujol, Gilles Aubert, Laure Blanc-Feraud, Wavelet-based level set evolution for classification of textured images [J], IEEE Transactions on Image Processing, 2003, 12(12):1634-1641
[93] M.K. Bashar, T. Matsumoto, N. Ohnishi, Wavelet transform-based locally orderless images for texture segmentation [J], Pattern Recognition Letters, 2003, 24(15):2633-2650
[94] W. Y. Ms, B.S. Manjunath, A comparison of wavelet features for texture annotation [A], in Proceedings of IEER International Conference on Image Processing [C], USA, Washington PC, 1995:256-259
[95] J. Besag, Spatial interaction and the statistical analysis of lattice systems (with discussion) [J], Journal of the Royal Statistical Society, Series B, 36(2):192-236
[96] R. Kashyap, R. Chellappa, Estimation and choice of neighbors in spatial interaction models of images [J], IEEE Transactions on Information Theory, 1983, 29(1):60-72
[97] A. Speis, G. Healey, Feature extraction for texture discrimination via random field models with random spatial interaction [J], IEEE Transactions on Image Processing, 1996, 5(4):635-645
[98] X. Descombes, M. Sigelle, F. Preteux, Estimating Gaussian Markov random field parameters in a nonstationary framework: Application to remote sensing imaging [J]., IEEE Transactions on Image Processing, 1999, 8(4):490-503
[99] H.W. Deng, D. A. Clausi, Gaussian MRF Rotation-Invariant Features for Image Classification [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, PAMI-26(7):951-955
[100] D. Panjwani, G. Healey, Markov random field models for unsupervised segmentation of textured color images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, PAMI-17(10):939-954
[101] J. Bennett, A. Khotanzad, Maximum.Likelihood Estimation Methods for Multispectral Random Field Image Models [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, PAMI-21(6):537-543
[102] G.G. Hazel, Multivariate Gaussian MRF for multispectral scene segmentation and anomaly detection [J], IEEE Transactions on Geoscience and Remote Sensing, 2000, GRS-38(3):1199-1211
[103] G. Rellier, Texture Feature Analysis Using a Gauss-Markov Model in Hyperspectral Image Classification [J], IEEE Transactions on Geoscience and Remote Sensing, 2004, GRS-42(7):1543-1551
[104] 谢和平(等)，分形几何：数学基础与应用[M]，重庆：重庆大学出版社，1991
[105] B.B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractal dimension [J], Science, 1967, 156:636-638
[106] B.B. Mandelbrot, The Fractal Geometry of Nature [M], New York: W. H. Freeman, 1983
[107] A.P. Pentland, Fractal Based Description of Natural Scenes [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(6):661-674
[108] G.G. Medioni, Y. Yasumoto, A note on using the fractaI dimension for segmentation [A], in IEEE Computer Vision Workshop [C], MD Annapolis, 1984:25-30
[109] S. Peleg, J. Naor, R. Hartley, D. Avnir, MUltiple resolution texture analysis and classification [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(4):518-523
[110] P.T. Nguyen, J. Quinqueton, Space filling curves and texture analysis [A], in Proceedings of the 6th International Conference on Pattern Recognition [C], Germany; Munich, 1982:282-285
[111] N. Sarkar, B.B. Chaudhuri, An efficient differential box-counting approach to compute fractal dimension of image [J], IEEE Transactions on System, Man, and Cybernetics, 1994, SMC-24(1):115-120
[112] X.C. Jin, S.H. Ong, Jayasooriah, A practical method for estimation fractal dimension [J], Pattern Recognition Letters, 1995, 16(5):457-464
[113] F.W. Campbell, J.G. Robson, Application of Fourier analysis to the visibility of gratings [J], Journal of Physiology, 1968, 197:551-556
[1] 王润生，图像理解[M]，长沙：国防科技大学出版社，1995
[2] A.P. Pentland, Fractal Based Description of Natural Scenes [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(4):661-674
[3] B.B. Mandelbrot, The Fractal Geometry of Nature [M], New York: W.H. Freeman, 1983
[4] 谢和平(等)，分形几何：数学基础与应用[M]，重庆：重庆大学出版社，1991
[5] B. B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractal dimension [J], Science, 1967, 156:636-638
[6] B. Wohberg, and G. D. Jager, A review of the fractal image coding literature [J], IEEE Transactions on Image Processing, 1999, 8(12):1716-1729
[7] K. Belloulata, and J. Konrad, Fractal image compression with region-based functionality [J], IEEE Transactions on Image Processing, 2002, 11(4):351-362
[8] Y. Zhang, and L.M. Po, Variable tree size fractal compression for wavelet pyramid image coding [J], Signal Processing: Image Communication, 1999, 14:195-208
[9] N. Dodd, Multispectral texture synthesis using fractal concepts [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987, PAMI-9(5):703-707
[10] M. A. Stoksik, R.G. Lane, and D.T. Nguyen, Practical synthesis of accurate fractal images [J], CVGIP: Graphical Model and Image Processing, 1995, 57(3):206-219
[11] L. T. Bruton, and N.R. Bartley, Simulation of fractal multidimensional images using multidimensional recursive filters [J], IEEE Transactions on Circuits and Systems, 1994, 41(3):181-188
[12] B. B. Chaudhuri, arid N. Sarkar, Texture segmentation using fractal dimension [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, PAMI-17 (1): 72-77
[13] G. Du, and T.S. Yeo, A Novel Multifractal Estimation Method and Its Application to Remote Image Segmentation [J], IEEE Transactions on Geoscience Remote Sensing, 2002, GRS-40 (4):980-982
[14] L.M. Kaplan, Extended fractal analysis for texture classification and segmentation [J], IEEE Transactions on Image Processing, 1999, 8(11):1572-1585
[15] T. Kasparis, D. Charalampidis, M. Georgiopoulos, and J. Rolland, Segmentation of textured images based on fractals and image filtering [J], Pat tern Recognition, 2001, 34(10):1963-1973
[16] Y. Xia, (David) D.G. Feng, andR. C. Zhao, Morphological. Multifractal Estimation for Image Segmentation [J], IEEE Transactions on Image Processing, 2006, 15 (3):614-623
[17] Y. Liu, and Y. Li, Image Feature Extraction and Segmentation using Fractal Dimension [A], in Proceedings of ICSP' 97 [C], pp. 975-979, 1997.
[18] Voss, RF Fractals in nature: From characterization to simulation [A], In H. Peitgen, and D. Saupe, eds., The Science of Fractal Images [C], pp. 21—70, Springer-Verlag, New York, 1988
[19] B. J. Super, and A. C. Bovik, Localized Measurement of Image Fractal Dimension using Gabor Filters [J], Journal of Visual Communication and Image Representation, 1991, 2 (2): 114-28
[20] G. W. Wornell, and A.V. Oppenheim, Estimation of Fractal Signals from Noisy Measurements using Wavelets [J], IEEE Transactions on Signal Processing, 1992, 40(3):611-623
[21] S. Peleg, J. Naor, R. Hartley, and D. Avnir, Multiple resolution texture analysis and classification [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAOI-6(4):518-523
[22] S. Novianto, Y. Suzuki, and J. Maeda, Near optimum estimation of local fractal dimension for image segmentation [J], Pattern Recognition Letters, 2003, 24(1): 365-374
[23] J. Gangepain, and R. Carmes, Fractal approach to two dimensional and three dimensional surface roughness [J], Wear, 1986, 109:119-126
[24] R. ross, Random fractals: Characterization and measurement [A], In Scaling Phenomena in Disordered Systems [C], R. Pynn and A. Skjeltorp, eds., Plenum, New York, 1986
[25] J. M. Keller, and S. Chen, Texture description and segmentation through fractal geometry [J], Computer Vision, Graphics and Image Processing, 1989, 45 (2): 150-166
[26] N. Sarkar, and B.B. Chaudhuri, An efficient approach to estimation fractal dimension of textural images [J], Pattern Recognition, 1992, 25(9):1035-1041
[27] N. Sarkar, and B.B. Chaudhuri, An efficient differential box-counting approach to compute fractal dimension of image [J], IEEE Transactions on System, Man, and Cybernetics, 1994, SMC-24(1):115-120
[28] X.C. Jin, S.H. Ong, and Jayasooriah, A practical method for estimation fractal dimension, Pattern Recognition Letters, 1995, 16(5):457-464
[29] S.S. Chen, J.M. Keller, and R.M. Crownover, On the Calculation of Fractal Features from Images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, PAMI-15(10):1087-1090
[30] A.K. Bisoi, and J. Mishra, On calculation of fractal dimension of images [J], Pattern. Recognition Letters, 2001, 22(6):631-637
[31] J. Samarabandu, R. Acharya, E. Hausmann, and K. Allen, Analysis of Bone X-Rays Using Morphological fractals [J], IEEE Transactions on Medical Imaging, 1993, 12(2):466-470
[32] 郑南宁，数字信号处理[M]，西安：西安交通大学出版社，1991
[33] J. Feng, W.C. Lin, and C.T. Chen, Fractal Box-Counting Approach to Fractal Dimension Estimation [A], in Proceedings of IEEE International Conference on Pattern Recognition, ICPR' 96 [C], Vienna, 1996, 854-858.
[34] J. Serra, Image Analysis and Mathematical Morphology (vol. 1) [M], Academic Press, 1982
[35] 崔屹，图像处理与分析数学形态学方法及应用[M]，北京：科学出版社，2000
[36] 夏勇，赵荣椿，江泽涛，一种基于数学形态学的分形维数估计方法[J]，中国图像图形学报，2004，9A(6)：760-762
[37] P. Brodatz, Texture: A Photographic Album for Artists and Designers [M], New York: Dover, 1966
[38] Viterbi School of Engineering, University of Southern California, The USC-SIPI Image Database, Available: http://sipi.usc.edu/database
[39] J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms [M], New York: Plenum Press, 1981
[40] 李厚强，刘政，凯林峰，基于分形理论和Kohonen神经网络的纹理图像分割方法[J]，计算机工程与应用，2001，37(7)：44-46
[41] T. Kohonen, Self-Organization Maps [M], Berlin Heidelberg: Springer-Verlag, 1995
[1] B.B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractal dimension [J], Science, 1967, 156:636-638
[2] B.B. Mandelbrot, The Fractal Geometry of Nature [M], New York: W. H. Freeman, 1983
[3] A.P. Pentland, Fractal Based Description of Natural Scenes [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(4):661-674
[4] R. ross, Random fractals: characterization and measurement [M], In: Pynn R, Skjeltop A (eds.), Scaling Phenomena in Disordered Systems, New York: Plenum, 1986
[5] 谢和平(等)，分形几何：数学基础与应用[M]，重庆：重庆大学出版社，1991
[6] L. Pietronero, and E. Tosatti, eds., Fractals in Physics [M], North-Holland: Amsterdam, 1986
[7] B.B. Mandelbrot, Self-affine fractals and fractal dimension [J], Physical Scripts, 1985, 32:257-260
[8] F. Arduini, S. Fioravanti, and D.D. Giusto, A multifractal-based approach to natural scene analysis [J], IEEE Transactions on Acoustics Speech and Signal Processing, 1991, ASSP-4(6):2681-2684
[9] J.L. rebel, P. Mignot, and J. P. Berroir, Multifractals, texture, and image analysis [A]. in Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition, CVPR' 92 [C], Champaign, IL, June 15-18, 1992, pp. 661-664
[10] K. Uma, K.R. Ramakrishnan, and G. Ananthakrishna, Image analysis using multifractals [A], in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, ASSP' 96 [C]. May 7-10, 1996, pp. 2188-2190
[11] P. Martinez, D. Schertzer, and K.K. Pham, Texture modelisation by multifractal processes for SAR image segmentation [A], in Proceedings of Radar' 97 [C], Oct. 14-16, 1997, pp. 135-139
[12] H. Chert, and W. Kinsner, Texture segmentation using multifractal measures [A], in Proceedings of WESCANEX' 97 [CI, May. 22-23, 1997, pp. 222-227
[13] A. Conci, and L.H. Monteiro, Multifractal characterization of texture-based segmentation [A], in Proceedings of IEEE International Conference on Image Processing, ICIP'2000 [C], Vancouver, Sep. 10-13, pp. 792-795
[14] L. Kam, and J. Blanc-Talon, Are multifractal multipermuted multinomial measures good enough for unsupervised image segmentation? [A], in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, CVPR' 2000 [C], Hilton Head Island, June 13-15, 2000, pp. 58-63
[15] Reljin, B. Reljin, I. Pavlovic, and I. Rakoc evic, Multifractal analysis of gray-scale images [A], in Proceedings of IEEE 10th Mediterranean Electrotechnical Conference, MELECON-2000 [C], Vol. Ⅱ, Lemesos, Cyprus, May 29-31, 2000, pp. 490-493
[16] S. Blacher, F. Brouers, and G. Ananthakrishna, Multifractal analysis of real heterogeneous materials [J], Acta Stereologica, 1992, 11(1):327-330.
[17] S. Kanmani, C. Babu Rao, D.K. Bhattacharya and Baldev Raj, Multifractal analysis of stress corrosion cracks [J], Acta Stereologica, 1992, 11(1):349-354
[18] T. Lo, H. Leung, J. Litva, and S. Haykin, Fractal characterization of sea. scattered signals and detection of sea-surface targets [J], Proceedings of the IEEE, 1993, F140:243-250
[19] D. Gan, and Z. S. hong, Detection of sea-surface radar targets based on multifractal analysis [J], Electronics Letters, 2000, 36(13):1144-1145
[20] N. Sarkar, and B.B. Chaudhuri, Multifractal and generalized dimensions of gray-tone digital images [J], Signal Processing, 1995, 42(2):181-190
[21] B.B. Chaudhuri, and N. Sarkar, Texture segmentation using fractal dimension [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, PAMI-17(1):72-77
[22] G. Du, and T.S. Yeo, A Novel Multifractal Estimation Method and Its Application to Remote Image Segmentation [J], IEEE Transactions on Geoscience and Remote Sensing, 2002, 40 (4):980-982
[23] Q. Cheng, The gliding box method for multifractal modeling [J], Computers and Geosciences, 1999, 25 (9):1073-1079
[24] L.V. Meisel, and M.A. Johnson, Convergence of numerical box-counting and correlation integral multifractal analysis techniques [J], Pattern Recognition, 1997, 30(9):1565-1570
[25] 李厚强，刘政，凯林峰，基丁分形理论和Kohonen神经网络的纹理图像分割方法[J]，计算机工程与应用，2001，37(7)：44-46
[26] T. Kohonen, Self-Organization Maps [M], Berlin Heidelberg: Springer-Verlag, 1995
[27] X.C. Jin, S.H. Ong, and Jayasooriah, A practical method for estimation fractal dimension [J], Pattern Recognition Letters, 1995, 16(5):457-464
[28] N. Sarkar, and B.B. Chaudhuri, An efficient differential box-counting approach to compute fractal dimension of image [J], IEEE Transactions on System, Man, and Cybernetics, 1994, SMC-24(1):115-120
[29] 夏勇，赵荣椿，江泽涛，一种基于数学形态学的分形维数估计方法[J]，中国图像图形学报，2006，9A(6)：760-766
[30] Y. Xia, (David) D.G. Feng, and R.C. Zhao, Texture Segmentation using Local Morphological Multifractal Exponents [A], in Proceedings of International Symposium on Intelligent Multimedia, Video & Speech Processing, ISIMP'04 [C], Hong Kong, 2004, pp. 438-441
[31] Yong Xia, (David) D. G. Peng, and R. C. Zhao, Morphological Multifractal Estimation for Image Segmentation [J], IEEE Transactions on Image Processing, 2006, 15(3):614-623
[32] P. Brodatz, Texture: A Photographic Album for Artists and Designers[M], New York: Dover, 1966
[33] J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms [M], New York: Plenum Press, 1981
[34] Viterbi School of Engineering, University of Southern California, The USC-SIPI Image Database, Available: http://sipi.usc.edu/database
[35] A.F.L. Serafim, Fractal Signatures for complex natural textures recognition [A], in Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society [C], 1998:1252-1257.
[36] Y. Y. Tang, H. Ma, D.h. Xi, X.G. Mao, and C. Y. Suen, Modified Fractal Signature (MFS): A New Approach to Document Analysis for Automatic Knowledge Acquisition [J], IEEE Transactions on Knowledge and Data Engineering, 1997, 9(5):747-762
[37] G. Dougherty, and G.M. Henebry, Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images [J], Medical Engineering and Physics, 2001, 23(6):369-380
[38] Q. Wang, D.D. Feng, and Z. Chi, B-Spline Over-complete Wavelet Based Fractal Signature Analysis for Texture image Retrieval [A], International Symposium on Intelligent Multimedia, Video & Speech Processing (ISIMP2004) [C], Hong Kong, 2004, pp. 462-466
[39] S. Peleg, J. Naor, R. Hartley, and D. Avnir, Multiple resolution texture anatysis and classification [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(6):518-523
[40] R. Kashyap, and R. Chellappa, Estimation and choice of neighbors in spatial interaction models of images [J], IEEE Transactions on Information Theory, 1983, 29(1):60-72
[41] B.S. Manjunath, T. Simchony, and R. Chellappa, Stochastic and deterministic networks for texture segmentation [J], IEEE Transactions on Acoustics Speech and Signal Processing, 1990, ASSP-38(6):1039-1049.
[42] B. S. Man junath, and R. Chellappa, Unsupervised texture segmentation using Markov random fields [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, PAMI-13(5):478-482
[1] 赵荣椿(等)，数字图像处理导论[M]，西安：西北工业大学出版社，2000
[2] 贾云得，机器视觉[M]．北京：科学出版社，2000
[3] R. C. Gonzalez, and R. E. Woods, Digital Image Processing (2nd Edition) [M], NJ:Upper Saddle River, Prentice Hall, 2002
[4] 章毓晋(等)，图像图形科学丛书——图像分割[M]，北京：科学出版社，2001
[5] G.B. Coleman, and H.C. Andrews, Image segmentation by clusterin [J], Proceedings of IEEE, 1979, 67:773-785.
[6] M. Celenk, A colour clustering technique for image segmentation [J], Computer Vision, Graphic, and Image Processing, Nov. 1990, 52:145-170.
[7] 边肇祺，张学工(等)，模式识别[M]，北京：清华大学出版社，2000
[8] R.O. Duda, P.E. Hart, and D.G. Stork, Pattern Classification (2nd Edition) [M], New York: John Wiley, 2001
[9] A.K. Jain, M.N. Nutty, and P.J. Flynn, Data Clustering: A Review [J], ACM Computing Surveys, 1999, 31:264-323
[10] A. Baraldi, and P. Blonda, A Survey of Fuzzy Clustering Algorithms for Pattern Recognition—Part Ⅰ [J], IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 1999, SMC-29(6):778-785
[11] A. Baraldi, and P. Blonda, A Survey of Fuzzy Clustering Algorithms for Pattern Recognition—Part Ⅱ [J], IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 1999, SMC-29(6):786-801
[12] A.K. Jain, R.P.W. Duin, and J. Mao, Statistical pattern recognition: A review [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, PAMI-22(1): 4-37
[13] T．M．Mitchell，机器学习(曾华军等译)[M]，北京：机械工业出版社，2003
[14] B. King, Step-wise clustering procedures [J], Journal of the American Statistical Association, 1957, 69:86-101
[15] F. Murtagh, A survey of recent advances in hierarchical clustering algorithms which use cluster centres [J], The Computer Journal, 1984, 26(4):354-359
[16] J. MacQueen, Some methods for classification and analysis of multivariate observations [A], in Proceedings of the 5th Symposium on Mathematical Statistics and Probability [C], USA, Berkeley, 1967:281-297
[17] G.H. Ball, and D.J. Hall, ISODATA, A novel method of data analysis and classification [M], Technical report, Stanford University, Stanford, CA, USA, 1965
[18] C.T. Zahn, Graph-theoretical methods for detecting and describing gestalt clusters [J], IEEE Transactions on Computers, 1971, C-20:68-86
[19] A.P. Dempster, N.M. Laird, and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm [J], Journal of the Royal Statistical Society, Series B (Methodological), 39(1):1-38
[20] A.K. Jain, and R.C. Dubes, Algorithms for Clustering Data [M], NJ: Upper Saddle River, Prentice Hall, 1988
[21] S.Y. LU, and K.S. FU, A sentence-tosentence clustering procedure for pattern analysis [J], IEEE Transactions on Systems, Man, and Cybernetics, 1978, 8:381-389
[22] E.H. Ruspini, A new approach to clustering [J], Information and control, 1969, 15:22-32
[23] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms [M], New York: Plenum Press, 1981
[24] R.N. Dave, Generalized fuzzy C-shells clustering and detection of circular and elliptic boundaries [J], Pattern Recognition, 1992, 25:713-722
[25] A.K. Jain, and J. MAO, Artificial neural networks: A tutorial [J], IEEE Computer, Mar. 1996, 29:31-44
[26] T. Kohonen, The self-organizing map [J], Proceedings of IEEE, 1990, 78:1464-1480
[27] G. Carpenter, and S. Grossberg, ART3: Hierarchical search using chemical transmitters in self-organizing pattern recognition architectures [J], Neural Networks, 1990, 129-152
[28] S. Mitra, andS. K. Pal, Self-organizing neural networkas a fuzzy classifier [J], IEEE Transactions on Systems, Man, and Cybernetics, 1994, SMC-24:385-399
[29] R. Michalski, R.E. STEPP, and E. Diday, Automated construction of classifications: conceptual clustering versus numerical taxonomy [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1983, PAMI-5(5):396-409
[30] G.P. Babu, and M.N. Murty, Clustering with evolution strategies [J], Pattern Recognition, 1994, 27:321-329
[31] D.B. Fogel, and P.K. Simpson, Evolving fuzzy clusters [A], In Proceedings of the International Conference on Neural Networks [C], CA, San Francisco, 1993: 1829-1834
[32] R.W. Klein, and R. C. Dubes, Experiments in projection and clustering by simulated annealing [J], Pattern Recognition, 1989, 22:213-220
[33] K.S. Alsultan, and M.M. Khan, Computational experience on four algorithms for the hard clustering problem [J], Pattern Recognition Letters, 1996, 17(3):295-308
[34] K. Rose, E. Gurewitz, and G.C. Fox, Deterministic annealing approach to constrained clustering [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, PAMI-15:785-794
[35]L.A. Zadeh, Fuzzy sets [J], Information and control, 1965, 8:338-353
[36]R. Krishnapuram, and J.M. Keller, A possibilistic approach to clustering [J], IEEE Transactions on Fuzzy Systems, 1993, 1(2):98-110.
[37]K. L. Wu, and M. S. Yang, Alternative c-means clustering algorithms [J], Pattern Recognition, 2002, 35:2267-2278
[38] J. Fan, W. Zhen, and W. Xie, Suppressed fuzzy c-means clustering algorithm [J], Pattern Recognition Letters, 2003, 24:1607-1612
[39]J. C. Bezdek, and N. R. Pal, Two soft relative of learning vector quantization [J],Neural Networks, 1995, 8(5):729-743
[40]B. Fritzke, A growing neural gas network learns topologies in Advances[A], in Neural Information Processing Systems [C], G. Tesauro, D. S. Touretzky, T. K. Leen. Eds., Cambridge, MA: MIT Press, 1995:625-632.
[41]G. Carpenter, S. Grossberg, and D. B. Rosen, Fuzzy ART: Fast stable learning and categorization of analog patterns by an adaptive resonance system [J], Neural Networks, 1991, 4:759-771
[42]G. Carpenter, S. Grossberg, N. Maukuzon, j. Reynolds, and D. B. Rosen, Fuzzy ARTMAP:A neural network architecture for incremental supervised learning of analog multidimensional maps [J], IEEE Transactions on Neural Networks, 1992,3(5):698 - 713
[43]A. Baraldi, and E. Alpaydn, Simplified ART: A new class of ART algorithms (R),Technique Report of international computer science institute , Berkeley.California. 1998
[44]A. Baraldi, and F. Parmiggiani, Novel neural network model combining radial basis function, competitive Hebbian learning rule, and fuzzy simplified adaptive resonance theory [A], in Proceedings of SPIE Optical Science, Engineering Instrumentation' 97: Applications Fuzzy Logic Technology IV [C] CA, San Diego,1997, 3165:98-112
[45]R. Krishnapuram, and C. P. Freg, Fitting an unknown number of lines and planes to image data through compatible cluster merging [J], Pattern Recognition, 1992,25:385-400
[46]J. C. Tilton, Image segmentation by region growing and spectral clustering with a natural convergence criterion [A], in Proceedings of the International Geoscience and Remote Sensing Symposium [Cj, USA, WA, Seattle, 1998:1766-1768
[47]M. A. Kupinski, and M. L. Giger, Automated Seeded Lesion Segmentation on Digital Mammograms [J], IEEE Transactions on Medical Imaging, 1998, 17:510-517
[48]P. W. Verbeek, and D. J. de Jong, Edge preserving texture analysis [A], in Proceedings of the 7th International Joint Conference on Pattern Recognition [C],Montreal, IEEE Computer Society Press, 1984:179-182
[49]L.S. Davis, and A. Mitiche, A model driven iterative texture segmentation algorithm, Computer Graphics and Image Processing, 19(2):95-110
[50]A. W. C. Liew, S. H. Leung, and W. H. Lau, Segmentation of Color Lip Images by Spatial Fuzzy Clustering [J], IEEE Transactions on Fuzzy Systems, 2003, 11:542-549
[51]A. W.C. Liew, S.H. Leung, and W. H. Lau, Fuzzy image clustering incorporating spatial continuity [J], Proceedings of IEE—Vision, Image, Signal Processing, 2000,147:185-192
[52]S. Geman, and D. Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6:721-741
[53] J. Besag, On the statistical analysis of dirty pictures [J], Journal of the Royal Statistical Society, Series B (Methodological)., 48:259-302
[54] S.A. Barker, Image segmentation using Markov random field models (Ph.D. dissertation) [D], Depterment of Engineering, Cambridge University, 1998
[55] S.Z. Li, Modeling image analysis problems using Markov random fields [A], in C. R.. Rao and D.N. Shanbhag (Eds.), Stochastic Processes: Modeling and simulation, vol. 20 of Handbook of Statistics, Elsevier Science, 2000, pp. 1-43
[56] Y. Xia, R.C. Zhao, Y.N. Xhang, J. Sun, and D.G. Feng, Texture Segmentation by Fuzzy Clustering of Spatial Patterns [C]. in L. Wang et al. (Eds.), Fuzzy Systems and Knowledge Discovery, Proceedings of the 3rd International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2006, Lecture Notes of Computer Science, Vol. 4223, Springer, 2006, pp. 894-897
[57] H. Deng, and D.A. Clausi, Unsupervised image segmentation using a simple MRF model with a new implementation scheme[J], Pattern Recognition, 2004, 37:2323-2335
[58] H. Deng, and D.A. Clausi, Unsupervised segmentation of synthetic aperture radar sea ice imagery using a novel Markov random field model [J], IEEE Transactions on Geoscience and Remote Sensing, 2005, GRS-43:528-538
[59] P. Brodatz, Texture: A Photographic Album for Artists and Designers [M], New York, Dover: 1966
[60] Y. Xia, R.C. Zhao, P.G. Feng, Y.N. Zhang, and J. Sun, Texture Discrimination by Local Morphological Multifractal Signatures [C], in Proceedings of 2006 IEEE Region 10 Conference, TENCON' 06, Hong Kong, Nov. 14-17, 2006
[61] Y. Xia, (David) D.G. Feng, and R.C. Zhao, Morphological Multifractal Estimation for Image Segmentation [J], IEEE Transactions on Image Processing, 2006, 15(3):614-623
[62] University of Southern California, The USC-SIPI Image Database [Online], Available: http://sipi.usc.edu/database/
[63] B.S. Manjunath, T. Simchony, and R. Chellappa, Stochastic and deterministic networks for texture segmentation [J], IEEE Transactions on Acoustic, Speech, and Signal Processing, 1990, 38:1039-1049
[64] B.S. Manjunath, and R. Chellappa, Unsupervised texture segmentation using Markov random fields [J], IEEE Transact:ions on Pattern Analysis and Machine Intelligence, 1991, PAMI-13:478-482
[65] F.W. Campbell, and J.G. Robson, Application of Fourier analysis to the visibility of gratings [J], Journal of Physiology, 1968, 197:551-556
[66] 夏勇，赵荣椿，基于局部形态学多重分形指数的遥感图像粗分割[J]，计算机应用，2006，26(9)：2083-2085
[1] R. Chellappa, and A.K. Jain, Markov Random Fields: Theory and Applications [M], Academic Press, 1993
[2] J. Besag, Spatial interaction and the statistical analysis of lattice systems (with discussion) [J], Journal of the Royal Statistical Society, Series B (Methodological); 1974, 36:192-236
[3] J. Besag, On the statistical analysis of dirty pictures [J], Journal of the Royal Statistical Society, Series B (Methodological), 1986, 48(3):259-302.
[4] R.C. Dubes, and A.K. Jain, Random field models in image analysis [J], Journal of Applied Statistics, 1989, 16(2):131-164
[5] S.Z. Li, Modeling image analysis problems using Markov random fields [A], in C. R. Rao and D. N. Shanbhag (Eds.), Stochastic Processes: Modeling and simulation, vol. 20 of Handbook of Statistics. Elsevier Science, 2000, pp. 1-43
[6] Z. Kato, Multi-scale Markovian Modelisation in Computer Vision withApplication to SPOT Image Segmentation (Ph.D. Dissertation) [D], Nice: Universtity of Nice, 1994
[7] J.M. Hammersley, and P. Clifford, Markov field on finite graphs and lattices [M], unpublished, 1971
[8] R. Chellappa, and R.L. Kashyap, Digital Image Restoration Using Spatial Interaction Models [J], IEEE Transactions on Acoustics, Speech, and Signal Processing, 1982, 30(3):461-471
[9] S. Geman, and D. Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, MPAI-6:721-741
[10] S. Z. Li, MAP Lmage Restoration and Segmentation by Constrained Optimization [J], IEEE Transactions on Image Processing, 1998, 7(12):1730-1735
[11] M. Snyder, On the mathematical foundations of smoothness constraints for the determination of optical flow and for surface reconstruction [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(11):1105-1113
[12] D. Geiger, and F. Girosi, Parallel and deterministic algorithms from MRF's: Surface reconstruction [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(5):401-412
[13] L.S. Davis, Shape matching using relaxation techniques [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1979, 1(1):60-72
[14] N.S. Friedland, and A. Rosenfeld, Compact Object Recognition Using Energy-Function-based Optimization [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, PAMI-14(7):770-777
[15] R.D. Morris, Image Sequence Restoration using Gibbs Distributions (Ph.D. Dissertation) [D], U.K.: University of Cambridge, 1995
[16] F. Luthon, A. Caplier, and M. Lievin, Spatiotemporal MRF approach to video segmentation: application to motion detection and lip segmentation [J], Signal Processing, 1999, 76(1):61-80
[17] J.W. Modestino, and J. Zhang, A Markov Random Field Model-Based Approach to Image Interpretation [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, PAMI-14(6):606-615
[18] G.H. Geoffrey, Multivariate Gaussian MRF for multispectral Scene segmentation and anomaly detection [J], IEEE Transactions on Geoscience and Remote Sensing, 2000, 38(3):1199-1211
[19] D. Geman, S. 6eman, C. Graffigne, and P. Dong, Boundary detection by constrained optimization [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, PAMI-12(7):609-628
[20] J. Zerubia, and R. Chellappa, Mean field annealing using compound Gauss-Markov random fields for edge detection and image estimation [J], IEEE Transactions on Neural Networks, 1993, 4:703-709
[21] G. Storvik, A Bayesian approach to dynamic contours through stochastic sampling and simulated annealing [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994, PAMI-16(10):976-986
[22]G. R. Cross, and A. K. Jain, Markov Random Field Texture Models [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1983, PAMI-5:25-39
[23]F. S. Cohen, Z. Fan, and M. A. Patel, Classification of rotated and scaled textured images using Gaussian Markov Random Field models [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, PAMI-13(2):192-202
[24]R. Kashyap, and R. Chellappa, Estimation and choice of neighbors in spatial interaction models of images [J], IEEE Transactions on Information Theory, 1983,29:60-72
[25]R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (2nd Edit) [M], John Wiley, New York, 2001
[26]H. Derin, and H. Elliott, Modeling and segmentation of noisy and textured images using Gibbs random fields [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987, MPAI-9:39-55
[27]F.S. Cohen, and D.B. Cooper, Simple Parallel Hierarchical and Relaxation Algorithms for Segmenting Noncausal Markovian Random Fields [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987, PAMI-9:195-219
[28]S. Kirkpatrick, CD. Gelatt Jr, and M. P. Vecchi, Optimization by simulated annealing [J], Science, 1983, 220(4598):671-680
[29]R. Neal, Probabilistic Inference Using Markov Chain Monte Carlo Methods,Technical Report CRG-TR-93-1, Department of Computer science, University of Toronto, Canada, 1993
[30]H. Szu, and R. Hartley, Fast Simulated Annealing [J], Physics Letters A., 1987,122:157-162
[31]B. S. Manjunath, and R. Chellappa, Unsupervised texture segmentation using Markov random fields [J], IEEE Transactions on Pattern Analysis and Machine Intelligence,1991, PAMI-13:478-482
[32]N. Balram, and J.M. F. Moura, Noncausal Gauss Markov Random Fields: Parameter Structure and Estimation [J], IEEE Transactions on Information Theory, 1993,39:1333-1355
[33]A. Speis, and G. Healey, Feature Extraction for Texture Discrimination via Random Field Models with Random Spatial Interaction [J], IEEE Transactions on Image Processing, 1996, 5(4):635-645
[34]J. Bennett, and A. Khotanzad, Maximum Likelihood Estimation Methods for Multispectral Random Field Image Models [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, PAMI-21(6):537-543
[35]H. W. Deng, and D. A. Clausi, Gaussian MRF Rotation-Invariant Features for Image Classification [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(7):951-955
[36]I.M. Elfadel, and R.W. Picard, Gibbs random fields, co-occurrences, and texture modeling [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994,16(1):24-37
[37]H. Deng, and D. A. Clausi, Unsupervised image segmentation using a simple MRF model with a new implementation scheme [J], Pattern Recognition, 2004, 37(12) :2323-2335
[38]H. Deng, and D. A. Clausi, Unsupervised segmentation of synthetic aperture radar sea ice imagery using a novel Markov random field model [J], IEEE Transactions on Geoscience and Remote Sensing, 2005, GRS-43:528-538
[39] D.E. Melas, and S.P. Wilson, Double Markov random fields and Bayesian image segmentation [J], IEEE Transactions on Signal Processing, 2002, SP-50:357-365
[40] F.C. Jeng, and J.W. Woods,.Compound Gauss-Markov random fields for image segmentation [J], IEEE Transactions on Signal Processing, 1991, SP-39:683-697
[41] A. Sarkar, M.K. Biswas, and K.M.S. Sharma, A Simple unsupervised MRF model based image segmentation approach [J], IEEE Transactions on Image Processing, 2000, IP-9:801-812
[42] S.A. Barker and P.J.W. Rayner, Unsupervised image segmentation using Markov random field models [J], Pattern Recognition, 2000, 33:587-602
[43] S.A. Barker, Image segmentation using Markov random field models (Ph.D. Dissertation) [D], U.K.: Department of Engineering, Cambridge University, 1998
[44] J. Zhang, The mean field theory in EM procedures for Markov random fields [J], IEEE Transactions on Signal Processing, 1992, 40:2570-2583
[45] B.S. Manjunath, T. Simchony, and R. Chellappa, Stochastic and deterministic networks for texture segmentation [J], IEEE Transactions on Acoustics, Speech, and Signal Processing, 1990, ASSP-38:1039-1049
[46] C.H. Wu, and P.C. Doerschuk, Tree approximations to Markov random fields [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, 17:391-343
[47] I.Y. Kim, and H.S. Yang, A systematic way for region-based image segmentation based on Markov random field model [J], Pattern Recognition Letters, 1994, 15:969-976
[48] A. Sarkar, M.K. Biswas, B. Kartikeyan, V. Kumar, K.L. Majumdar, and D.K. Pal, A MRF model based segmentation approach to classification for multispectral imagery [J], IEEE Transactions on Geoscience and Remote Sensing, 2002, 40(4):1102-1113
[49] R.K. Pina, and R.C. Pueter, Bayesian image reconstruction: The pixonand optimal image modeling [J], Publ istron Soc Pac, 1993, 105:630-637
[50] X. Descombes, and F. Kruggel, A Markov pixon information approach for low-level image description [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21:482-494
[51] F. Yang, and T. Jiang, Pixon-based image segmentation with Markov random fields [J], IEEE Transactions on Image Processing, 2003, IP-12:1552-1559
[52] D. Terzopoulos, Image analysis using multigrid relaxation methods [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1986, 8:129-139
[53] P.C. Chen, and T. Pavlidis, Imace segmentation as an estimation problem [J], Computer Vision, Graphics, and Image Processing, 1980, 12:153-173
[54] C. Bouman, and B. Liu, Multiple resolution segmentation of textured images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, PAMI-13:99-113
[55] P. Perez, and F. Heitz, Multiscale Markov random fields and constrained relaxation in low level image analysis [A], in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing [C], 1992, 3:61-64
[56] J. Mao, and A.K. Jain, Texture classification and segmentation using multiresolution simultaneous autoregressive models [J], Pattern Recognition, 1992, 25(2):173-188
[57] F.C. Jeng, Subsampling of Markov random fields [J], Journal of Visual Communication and Image Representation, 1992, 3(3):225-229
[58] S. Lakshmanan, and H. Derin, Gaussian Markov random fieldsat multiple resolutions [A], in R. Chellappa, Eds. Markov Random Fields: Theory and Applications, New York:Academic, 1993:131-157
[59]S. Krishnamachari, and R. Chellappa, Multiresolution Gauss-Markov random field models for texture segmentation [J], IEEE Transactions on Image Processing, 1997,IP-6:251-267
[60]D. Panjwani, and G. Healey, Markov random field models for unsupervised segmentation of textured color images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, PAMI-17(10):939-954
[61]P.C. Smits, and S. G. Dellepiane, Synthetic aperture radar image segmentation by a detail preserving Markov Random Field approach [J], IEEE Transactions on Geoscience and Remote Sensing, 1997, GRS-35(4):844-857
[62]G. Rellier, Texture Feature Analysis Using a Gauss-Markov Model in Hyperspectral Image Classification[J], IEEE Transactions on Geoscience and Remote Sensing, 2004,GRS-42(7):1543-1551
[63]M. Mignotle, C. Collet, P. Perez, and P. Bouthemy, Sonar Image Segmentation Using an Unsupervised Hierarchical MRF Model [J], IEEE Transactions on Image Processing,2000, 9(7):1216-1231
[64]Y. Xia, (David) D. G. Feng, and R. C. Zhao, Adaptive Segmentation of Textured Images by Using the Coupled Markov Random Field Model [J], IEEE Transactions on Image Processing, 2006, 15(11): 3559-3566
[65]P. Brodatz, Texture: A Photographic Album for Artists and Designers [M], NewYork:Dover, 1966
[66]Viterbi School of Engineering, University of Southern California, The USC-SIPI Image Database. Available: http://sipi.usc.edu/database
[67]J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms [M],New York: Plenum Press, 1981
[2] 王润生，图像理解[M]，长沙：国防科技大学出版社，1995
[3] K. Castleman, Digital Image Processing[M], NJ:Prentice-Hall, 1996
[4] 马颂德，张正友，计算机视觉[M]，北京：科学出版社，1998
[5] 贾云得，机器视觉[M]，北京：科学出版社，2000
[6] R.C.Gonzalez,R.E.Woods,Digital Image Process ing(2nd edition)[M]，北京：电子工业出版社，2002
[7] 章毓晋．图像工程上册—图象处理和分析[M]，北京：清华大学出版社，2003
[8] M．Sonka，V．Hlavac，R．Boyle，图像处理、分析与机器视觉(艾海舟、武勃等译)[M]，北京：人民邮电出版社，2003
[9] 阮秋琦，数字图像处理学[M]，北京：电子工业出版社，2004
[10] Wesley E．Snyder，Hairong Qi，机器视觉教程(林学訚，崔锦实，赵清杰等译)[M]，北京：机械工业出版社，2005
[11] 徐光佑，计算机视觉[M]，北京：科学出版社，1999
[12] J. K. Hawkins, Texture Properties for Pattern Recognition [A], in Picture Processing and Psychopictorics [C], B. S. Lipkin and A. Rosenfeld Eds, New York: Academic Press, 1980, pp 347-370
[13] L. Van Gool, P. Dewale, A. Oosterlinck, Survey Texture Analysis Anno 1983 [J], Computer Vision, Graphics, and Image Processing, 1985, 29(3):336-357
[14] R.M. Haralick, K. Shanmugam, I. Dinstein, Textural Features for Image Classification [J], IEEE Transactions on Systems, Man, and Cybernetics, 1973, SMC-3(6):610-621
[15] 章毓晋，图像图形科学丛书——图像分割[M]，北京：科学出版社，2001
[16] N.R. Pal, S.K. Pal, A review on image segmentation techniques [J], Pattern Recognition, 1993, 26(9):1227-1249
[17] K.S. Fu, J.K. Mui, A survey of image segmentation [J], Pattern Recognition, 1980, 13(1):3-16
[18] R.M. Haralick, L.G. Shapiro, Image segmentation techniques [J], Computer Vision, Graphics, and Image Processing, 1985, 29(1):100—132
[19] 赵荣椿，迟耀斌，朱重光，图像分割技术进展[J]，中国体视学与图像分析，1998，3(2)：121-128
[20] 罗希平(等)，图象分割方法综述[J]，模式识别与人工智能，1999，12(3)：300-312
[21] 王爱民，沈兰荪，图像分割研究综述[J]，测控技术，2000，19(5)：1-6
[22] Y.J. Zhang, J. J. Gerbrands, Objective and quantitative segmentation evaluation and comparison [J], Signal Processing, 1994, 39(1):43-54
[23] S. A. Barker, Image segmentation using Markov random field models (Ph.D. dissertation) [D], Cambridge University, 1998
[24] Y.Q. Chen, M.S. Nixon, D.W. Thomas, Statistical geometrical features for texture classification [J], Pattern Recognition, 1995, 28(4):537-552
[25] O. Pichler, A. Teuner, B. Hosticka, A comparison of texture feature extraction using adaptive Gabor filtering, pyramidal and tree—structured wavelet transforms [J], Pattern Rccognition, 1996, 29(5):733-742
[26] S.N. Jayaramamurthy, Texture discrimination using digital deconvolution filters [A], in Proceedings of the 5th International Conference on Pattern Recognition [C], Miami Beach, Florida, 1980:1184-1186
[27] T. Matsuyama, K. Saburi, M. Nagao, A structural analyzer for regularly arranged textures [J], Computer Graphics Image Processing, 1982, 18 (1): 259-278
[28] J. Toriwaki, Y. Yashima, S. Yokoi, Adjacency graphs on a digitized figure set and their applications to texture analysis [A], in Proceedings of the 7th International Conference on Pattern Recgonition [C], Canada. Montreal, 1984:1216-1218
[29] D. Chert, L. Wang, Texture features based on texture spectrum [J], Pattern Recognition, 1991, 24(5):391-399
[30] R.M. Haralick, Statistical and structural approaches to texture [J], Proceedings of IEEE, 1979, 67(5):786-804
[31] T.R. Reed, J.M.H. Buf, A review of recent texture segmentation and feature extraction techniques [J], Computer Vision, Graphics, and Image Processing, 1993, 57 (3):359-372
[32] T. N. Tan, Texture edge detection by modeling visual cortical channel s [J], Pattern Recognition, 1995, 28(9):1283-1298
[33] C.M. Chen, H.H. Lu, K.C. Han, A textural approach based on Gabor functions for texture edge detection in ultrasound images [J], Ultrasound in Medicine and Biology, 2001, 27(4):515-34
[34] V. Barranco Lopez, P. Luque Escamilla, J. Martinez Aroza, R. Roman Roldan, Entropic texture-edge detection for image segmentation [J], Electronic Letters, 1995, 31(11):867-869
[35] Sagiv Chen, N.A. Sochen, Y.Y. Zeevi, Integrated active contours for texture segmentation [J], IEEE Transactions on Image Processing, 2006, 15(6):1633-1646
[36] Nikos Paragios, Rachid Deriche, Geodesic active contours and level set methods for supervised texture segmentation [J], International Journal of Computer Vision, 2002, 46(3):223-247
[37] M. Kardan, JMH Du Buf, M. Span, Texture feature performance for image segmentation [J], Pattern Recognition, 1990, 23(3-4):291-309
[38] D. J. Marceau, P.J. Howarth, J.M.M. Dubois, D.J. Gration, Evaluation of grey level co-occurrence matrix method for land-cover classification using SPOT imagery [J], IEEE Transactions on Geoscience and Remote Sensing, 1990, GRS-28(4): 513-519
[39] L.K. Soh, C. Tsatsoulis, Texture analysis of SAR sea ice imagery using gray level co-occurrence matrices [J], IEEE Transactions on Geoscience and Remote Sensing, 1999, GR5-37(2):780-795
[40] Mari Partio, Bogdan Cramariuc, Moncef Gabbouj, Ari Visa, Rock texture retrieval using gray level co-occurrence matrix [J], in Proceedings of the 5th Nordic Signal Processing Symposium [C], Norway, 2002:4-7
[41] D.P. Panda, A. Rosenfeld, Image segmentation by pixel classification in (gray level, edge value) space [J], IEEE Transactions on Computers, 1978, 27(9):875-879
[42] M.M. Trivedi, C.A. Harlow, R.W. Conners, S. Goh, Object detection based on gray level co-occurrence [J], Computer Vision, Graphics, and Image Processing, 1984, 28(2): 199-219
[43] Q.A. Holmes, D.R. Neusch, R.A. Shuchman, Textural analysis and real-time classification of sea-ice types using digital SAR data [J], IEEE Transactions on Geoscience and Remote Sensing, 1984, GRS-22(2):113-120
[44] M. Unser, Sum and difference histograms for texture classification [J], IEEE Transactions Pattern Analysis and Machine Intelligence, 1986, PAMI-8(1):118-125
[45] S.H. Peckinpaugh, An improved method for computing gray level co-occurrence matrix based texture measures [J], Computer Vision, Graphics and Image Processing, 1991, 53(6):574-580
[46] M. Galloway, Texture analysis using gray-level run length [J], Computer Graphics Image Processing, 1974, 4:172—199
[47] D.B.C. Shu, Y.N. Sun, C.C. Li, J.F. Mancuso, Run lengthbased image segmentation schemes[A], in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition[C], USA Washington D.C., 1983:154-156
[48] J. Weszka, C. Dyer, A. Rosenfeld, A comparative study of texture measures for terrain classifications [J], IEEE Transactions on Systems, Man, and Cybernetics, 1976, SMC-6(4):269-285
[49] D. Harwood, T. Ojala, N. Pietikinen, S. Kelman, L. Davis, Texture Classification by Center-Symmetric Auto-Correlation, Using Kullback Discrimination of Distributions [J], Pattern Recognition Letters, 1995, 16(1):1-10
[50] R.N. Sutton, F.L. Hall, Texture Measures for Automatic Classification of Pulmonary Disease [J], IEEE Transactions on Computers, 1972, 21:667-676
[51] E. Triendl, T. Henderson, A model for texture edges [A], in Proceedings of the 5~(th) IEEE International Conference on Pattern Recognition [C], FL, Miami Beach,1980:1100-1102
[52]H. Taraura, S. Mori, T. Yamawaki, Texture features corresponding to visual perception [J], IEEE Transactions on Systems, Man, and Cybernetics, 1978,SMC-8(6):460-473
[53]M. Flickner, H. Sawhney, W. Niblack, J, Ashley, Q. Huang, B. Dom, M. Gorkani,J. Hafner, D. Lee, D. Petkovic, D. Steele, P. Yanker, Query by image and video content: The QBIC system [J], IEEE Transactions on Computers, 1995, 28(9):23-32
[54]Pentland A, PicardRW, SclaroffS. Photobook, Content-based manipulation of image databases [J], International Journal of Computer Vision, 1996, 18(3): 322-330
[55]P. A. Dondes, A. Rosenfeld, Pixel classification based on gray level and local "business" [J], IEEE Transactions on Pattern Analysis and Machine Intelligence,1982, PAMI-4(1):79-84
[56]G. E. Lowitz, Can a local histogram really map texture information? [J], Pattern Recognition, 1983, 16(2):141-147
[57]H. Wechsler, Taxonomy and segmentation of textured images [A], in Proceedings of the 5th International Conference on Pattern Recognition[C], USA, Florida, Miami Beach, 1980:532-534
[58]D. Barba, J. Ronsin, New method in texture analysis in the context of image segmentation [A], in Proceedings of the 2~(nd) European Signal Processing Conference[C], West Germany, Erlangen, 1983:283-286
[59]B. Ashjari, Computer detection and identification of a visually indiscernible texture mixture [A], in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition [C], USA, CA, San Francisco, 1985:172-174
[60]K. Laws, Textured Image Segmentation (Ph.D. Dissertation) [D], University of Southern California, 1980
[61]M. Unser, Local linear transforms for texture measurements [J], Signal Processing,1986, 11(1): 61-79
[62]R. Wang, A. R. Hanson, E. M. Riseman, Texture analysis based on local standard deviation of intensity [A], in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition [C], USA, Florida, Miami Beach, 1986:482-488
[63]G. H. Granlund, Description of texture using the general operator approach [A],in Proceedings of the 5~(th) International Conference on Pattern Recognition [C], USA,Florida, Miami Beach, 1980:776-779
[64]D. Wermser, N. Lissel, Comparison of algorithms for unsupervised segmentation of images by the use of texture information [A], in Proceedings of the 2nd European Signal Processing Conference [C], West Germany, Erlangen, 1983:287-290
[65]L. W. Abele, Feature selection by space invariant comparison with applications to the segmentation of textured pictures [A], in Proceedings of the 5~(th) International Conference on Pattern Recognition [C], USA, Florida, Miami Beach,1980:535-539
[66]P.C. Chen and T. Pavlidis, Segmentation of texture using a co-occurance matrix and a split-and-merge algorithm [J], Computer Graphics Image Processing, 1979,10(1):172-182
[67]H. Knutsson, G. H. Granlund, Texture analysis using two-dimensional quadrature filters [A], in IEEE Workshop CAPAIDM [C], CA, Pasadena, 1983:206-213
[68]J. Bigun, Frequency and orientation selective texture measures using linear symmetry and Laplacian pyramid [A], in Proceedings of Visual Communications and Image Processing [C], Switzerland, Lausanne, 1990:1319-1331
[69]M. Tuceryan, Moment based texture segmentation [J], Pattern Recognition Letters,1994, 15(7): 659-668
[70]M. E. Jernigan, F. D. Astous, Entropy-based texture analysis in the spatial frequency domain [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(2): 237-243
[71]F. D. Astous, M. E. Jernigan, Texture discrimination based on detailed measures of the power spectrum [A], in Proceedings of the 7th International Conference on Pattern Recognition [C], Canada, Montreal, 1984:83-86
[72]J.G. Daugman, Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters [J], Journal of the Optical Society of America A, 1985, 2(7):1160 - 1169
[73]A. C. Bovik, M. Clark, W. S. Geisler, Multichannel Texture Analysis Using Localized Spatial Filters [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, PAMI-12(1):55-73
[74]J. Fogel, D. Sagi, Gabor filters as texture discriminator [J], Biological Cybernetics, 1989, 61(1):103-113
[75]MR Turner, TexLure discrimination by Gabor functions [J], Biological Cybernetics, 1986, 55(2-3):71-82
[76]A. Jain, F. Farrokhnia, Unsupevised texture segmentation using Gabor filters [J],Pattern Recognition, 1991, 24(12):1167-1186
[77]D. Dunn, Designing Gabor filters for texture segmentation (Ph.D. dissertation)[D], The Pennsylvania State University, 1992
[78]D. Dunn, Higgins, Optimal Gabor Filters for Texture Segmentation [J], IEEE Transactions on Image Processing, 1995, 4(7) :947-964
[79]M. Clark, A. C. Bovik, W. S. Geisler, Texture segmentation using Gabor modulation/demodulation [J], Pattern Recognition Letters, 1987, 6(4):261 - 267
[80]A.C. Bovik, N. Gopal, T. Emmoth, A. Restrepo, Localized measurement of emergent image frequencies by Gabor wavelets [J], IEEE Transactions Information Theory,1992, 38(3): 691-712
[81]J. Bigun, J. M.H. du Buf, N-folded symmetries by complex moments in Gabor space [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994,PAMI-16(1):80-87
[82]S.E. Grigorescu, N. Petkov, P. Kruizinga, Comparison of texture features based on Gabor filters [J], IEEE Transactions on Image Processing, 2002, 11(10):1160-1167
[83] P. Kruizinga, N. Petkov, Non-linear operator for oriented texture [J], IEEE Transactions on Image Processing, 1999, 8(10):1395-1407
[84] I. Daubechies, The wavelet transform, time-frequency localization and signal analysis [J], IEEE Transactions on Information Theory, 1990, 36(5):961—1005
[85] S. Mallat, A Theory for Multiscale Signal Decomposition [J], The Wavelet Representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989, PAMI-11(7):674-693
[86] T. Chang, C.J. Kuo, Texture analysis and classification with tree-structured wavelet transform [J], IEEE Transactions on Image Processing, 1993, 2(4):429-441
[87] A. Laine, J. Fan, Texture classification by wavelet packet signatures [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, PAMI-15(11):1186-1191
[88] C.S. Lu, P.C. Chung, C.F. Chen, Unsupervised texture segmentation via wavelet transform [J], Pattern Recognition, 1997, 30(5):729-742
[89] M. Unser, Texture classification and segmentation using wavelet frames [J], IEEE Transactions on Image Processing, 1995, 4(11)1549-1560
[90] K.K. Simhadri, S.S. Iyengar, R.J. Holyer, Wavelet-based feature extraction from oceanographic images [J], IEEE Transactions on Geoscience and Remote Sensing, 1998, GRS-36(3):767—778
[91] D. Charalampidis, T. Kasparis, Wavelet-based rotational invariant roughness features for texture classification and segmentation [J], IEEE Transactions on Image Processing, 2002, 11(8):825-837
[92] Jean-Francois Aujol, Gilles Aubert, Laure Blanc-Feraud, Wavelet-based level set evolution for classification of textured images [J], IEEE Transactions on Image Processing, 2003, 12(12):1634-1641
[93] M.K. Bashar, T. Matsumoto, N. Ohnishi, Wavelet transform-based locally orderless images for texture segmentation [J], Pattern Recognition Letters, 2003, 24(15):2633-2650
[94] W. Y. Ms, B.S. Manjunath, A comparison of wavelet features for texture annotation [A], in Proceedings of IEER International Conference on Image Processing [C], USA, Washington PC, 1995:256-259
[95] J. Besag, Spatial interaction and the statistical analysis of lattice systems (with discussion) [J], Journal of the Royal Statistical Society, Series B, 36(2):192-236
[96] R. Kashyap, R. Chellappa, Estimation and choice of neighbors in spatial interaction models of images [J], IEEE Transactions on Information Theory, 1983, 29(1):60-72
[97] A. Speis, G. Healey, Feature extraction for texture discrimination via random field models with random spatial interaction [J], IEEE Transactions on Image Processing, 1996, 5(4):635-645
[98] X. Descombes, M. Sigelle, F. Preteux, Estimating Gaussian Markov random field parameters in a nonstationary framework: Application to remote sensing imaging [J]., IEEE Transactions on Image Processing, 1999, 8(4):490-503
[99] H.W. Deng, D. A. Clausi, Gaussian MRF Rotation-Invariant Features for Image Classification [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, PAMI-26(7):951-955
[100] D. Panjwani, G. Healey, Markov random field models for unsupervised segmentation of textured color images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, PAMI-17(10):939-954
[101] J. Bennett, A. Khotanzad, Maximum.Likelihood Estimation Methods for Multispectral Random Field Image Models [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, PAMI-21(6):537-543
[102] G.G. Hazel, Multivariate Gaussian MRF for multispectral scene segmentation and anomaly detection [J], IEEE Transactions on Geoscience and Remote Sensing, 2000, GRS-38(3):1199-1211
[103] G. Rellier, Texture Feature Analysis Using a Gauss-Markov Model in Hyperspectral Image Classification [J], IEEE Transactions on Geoscience and Remote Sensing, 2004, GRS-42(7):1543-1551
[104] 谢和平(等)，分形几何：数学基础与应用[M]，重庆：重庆大学出版社，1991
[105] B.B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractal dimension [J], Science, 1967, 156:636-638
[106] B.B. Mandelbrot, The Fractal Geometry of Nature [M], New York: W. H. Freeman, 1983
[107] A.P. Pentland, Fractal Based Description of Natural Scenes [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(6):661-674
[108] G.G. Medioni, Y. Yasumoto, A note on using the fractaI dimension for segmentation [A], in IEEE Computer Vision Workshop [C], MD Annapolis, 1984:25-30
[109] S. Peleg, J. Naor, R. Hartley, D. Avnir, MUltiple resolution texture analysis and classification [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(4):518-523
[110] P.T. Nguyen, J. Quinqueton, Space filling curves and texture analysis [A], in Proceedings of the 6th International Conference on Pattern Recognition [C], Germany; Munich, 1982:282-285
[111] N. Sarkar, B.B. Chaudhuri, An efficient differential box-counting approach to compute fractal dimension of image [J], IEEE Transactions on System, Man, and Cybernetics, 1994, SMC-24(1):115-120
[112] X.C. Jin, S.H. Ong, Jayasooriah, A practical method for estimation fractal dimension [J], Pattern Recognition Letters, 1995, 16(5):457-464
[113] F.W. Campbell, J.G. Robson, Application of Fourier analysis to the visibility of gratings [J], Journal of Physiology, 1968, 197:551-556
[1] 王润生，图像理解[M]，长沙：国防科技大学出版社，1995
[2] A.P. Pentland, Fractal Based Description of Natural Scenes [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(4):661-674
[3] B.B. Mandelbrot, The Fractal Geometry of Nature [M], New York: W.H. Freeman, 1983
[4] 谢和平(等)，分形几何：数学基础与应用[M]，重庆：重庆大学出版社，1991
[5] B. B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractal dimension [J], Science, 1967, 156:636-638
[6] B. Wohberg, and G. D. Jager, A review of the fractal image coding literature [J], IEEE Transactions on Image Processing, 1999, 8(12):1716-1729
[7] K. Belloulata, and J. Konrad, Fractal image compression with region-based functionality [J], IEEE Transactions on Image Processing, 2002, 11(4):351-362
[8] Y. Zhang, and L.M. Po, Variable tree size fractal compression for wavelet pyramid image coding [J], Signal Processing: Image Communication, 1999, 14:195-208
[9] N. Dodd, Multispectral texture synthesis using fractal concepts [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987, PAMI-9(5):703-707
[10] M. A. Stoksik, R.G. Lane, and D.T. Nguyen, Practical synthesis of accurate fractal images [J], CVGIP: Graphical Model and Image Processing, 1995, 57(3):206-219
[11] L. T. Bruton, and N.R. Bartley, Simulation of fractal multidimensional images using multidimensional recursive filters [J], IEEE Transactions on Circuits and Systems, 1994, 41(3):181-188
[12] B. B. Chaudhuri, arid N. Sarkar, Texture segmentation using fractal dimension [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, PAMI-17 (1): 72-77
[13] G. Du, and T.S. Yeo, A Novel Multifractal Estimation Method and Its Application to Remote Image Segmentation [J], IEEE Transactions on Geoscience Remote Sensing, 2002, GRS-40 (4):980-982
[14] L.M. Kaplan, Extended fractal analysis for texture classification and segmentation [J], IEEE Transactions on Image Processing, 1999, 8(11):1572-1585
[15] T. Kasparis, D. Charalampidis, M. Georgiopoulos, and J. Rolland, Segmentation of textured images based on fractals and image filtering [J], Pat tern Recognition, 2001, 34(10):1963-1973
[16] Y. Xia, (David) D.G. Feng, andR. C. Zhao, Morphological. Multifractal Estimation for Image Segmentation [J], IEEE Transactions on Image Processing, 2006, 15 (3):614-623
[17] Y. Liu, and Y. Li, Image Feature Extraction and Segmentation using Fractal Dimension [A], in Proceedings of ICSP' 97 [C], pp. 975-979, 1997.
[18] Voss, RF Fractals in nature: From characterization to simulation [A], In H. Peitgen, and D. Saupe, eds., The Science of Fractal Images [C], pp. 21—70, Springer-Verlag, New York, 1988
[19] B. J. Super, and A. C. Bovik, Localized Measurement of Image Fractal Dimension using Gabor Filters [J], Journal of Visual Communication and Image Representation, 1991, 2 (2): 114-28
[20] G. W. Wornell, and A.V. Oppenheim, Estimation of Fractal Signals from Noisy Measurements using Wavelets [J], IEEE Transactions on Signal Processing, 1992, 40(3):611-623
[21] S. Peleg, J. Naor, R. Hartley, and D. Avnir, Multiple resolution texture analysis and classification [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAOI-6(4):518-523
[22] S. Novianto, Y. Suzuki, and J. Maeda, Near optimum estimation of local fractal dimension for image segmentation [J], Pattern Recognition Letters, 2003, 24(1): 365-374
[23] J. Gangepain, and R. Carmes, Fractal approach to two dimensional and three dimensional surface roughness [J], Wear, 1986, 109:119-126
[24] R. ross, Random fractals: Characterization and measurement [A], In Scaling Phenomena in Disordered Systems [C], R. Pynn and A. Skjeltorp, eds., Plenum, New York, 1986
[25] J. M. Keller, and S. Chen, Texture description and segmentation through fractal geometry [J], Computer Vision, Graphics and Image Processing, 1989, 45 (2): 150-166
[26] N. Sarkar, and B.B. Chaudhuri, An efficient approach to estimation fractal dimension of textural images [J], Pattern Recognition, 1992, 25(9):1035-1041
[27] N. Sarkar, and B.B. Chaudhuri, An efficient differential box-counting approach to compute fractal dimension of image [J], IEEE Transactions on System, Man, and Cybernetics, 1994, SMC-24(1):115-120
[28] X.C. Jin, S.H. Ong, and Jayasooriah, A practical method for estimation fractal dimension, Pattern Recognition Letters, 1995, 16(5):457-464
[29] S.S. Chen, J.M. Keller, and R.M. Crownover, On the Calculation of Fractal Features from Images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, PAMI-15(10):1087-1090
[30] A.K. Bisoi, and J. Mishra, On calculation of fractal dimension of images [J], Pattern. Recognition Letters, 2001, 22(6):631-637
[31] J. Samarabandu, R. Acharya, E. Hausmann, and K. Allen, Analysis of Bone X-Rays Using Morphological fractals [J], IEEE Transactions on Medical Imaging, 1993, 12(2):466-470
[32] 郑南宁，数字信号处理[M]，西安：西安交通大学出版社，1991
[33] J. Feng, W.C. Lin, and C.T. Chen, Fractal Box-Counting Approach to Fractal Dimension Estimation [A], in Proceedings of IEEE International Conference on Pattern Recognition, ICPR' 96 [C], Vienna, 1996, 854-858.
[34] J. Serra, Image Analysis and Mathematical Morphology (vol. 1) [M], Academic Press, 1982
[35] 崔屹，图像处理与分析数学形态学方法及应用[M]，北京：科学出版社，2000
[36] 夏勇，赵荣椿，江泽涛，一种基于数学形态学的分形维数估计方法[J]，中国图像图形学报，2004，9A(6)：760-762
[37] P. Brodatz, Texture: A Photographic Album for Artists and Designers [M], New York: Dover, 1966
[38] Viterbi School of Engineering, University of Southern California, The USC-SIPI Image Database, Available: http://sipi.usc.edu/database
[39] J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms [M], New York: Plenum Press, 1981
[40] 李厚强，刘政，凯林峰，基于分形理论和Kohonen神经网络的纹理图像分割方法[J]，计算机工程与应用，2001，37(7)：44-46
[41] T. Kohonen, Self-Organization Maps [M], Berlin Heidelberg: Springer-Verlag, 1995
[1] B.B. Mandelbrot, How long is the coast of Britain? Statistical self-similarity and fractal dimension [J], Science, 1967, 156:636-638
[2] B.B. Mandelbrot, The Fractal Geometry of Nature [M], New York: W. H. Freeman, 1983
[3] A.P. Pentland, Fractal Based Description of Natural Scenes [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(4):661-674
[4] R. ross, Random fractals: characterization and measurement [M], In: Pynn R, Skjeltop A (eds.), Scaling Phenomena in Disordered Systems, New York: Plenum, 1986
[5] 谢和平(等)，分形几何：数学基础与应用[M]，重庆：重庆大学出版社，1991
[6] L. Pietronero, and E. Tosatti, eds., Fractals in Physics [M], North-Holland: Amsterdam, 1986
[7] B.B. Mandelbrot, Self-affine fractals and fractal dimension [J], Physical Scripts, 1985, 32:257-260
[8] F. Arduini, S. Fioravanti, and D.D. Giusto, A multifractal-based approach to natural scene analysis [J], IEEE Transactions on Acoustics Speech and Signal Processing, 1991, ASSP-4(6):2681-2684
[9] J.L. rebel, P. Mignot, and J. P. Berroir, Multifractals, texture, and image analysis [A]. in Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition, CVPR' 92 [C], Champaign, IL, June 15-18, 1992, pp. 661-664
[10] K. Uma, K.R. Ramakrishnan, and G. Ananthakrishna, Image analysis using multifractals [A], in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, ASSP' 96 [C]. May 7-10, 1996, pp. 2188-2190
[11] P. Martinez, D. Schertzer, and K.K. Pham, Texture modelisation by multifractal processes for SAR image segmentation [A], in Proceedings of Radar' 97 [C], Oct. 14-16, 1997, pp. 135-139
[12] H. Chert, and W. Kinsner, Texture segmentation using multifractal measures [A], in Proceedings of WESCANEX' 97 [CI, May. 22-23, 1997, pp. 222-227
[13] A. Conci, and L.H. Monteiro, Multifractal characterization of texture-based segmentation [A], in Proceedings of IEEE International Conference on Image Processing, ICIP'2000 [C], Vancouver, Sep. 10-13, pp. 792-795
[14] L. Kam, and J. Blanc-Talon, Are multifractal multipermuted multinomial measures good enough for unsupervised image segmentation? [A], in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, CVPR' 2000 [C], Hilton Head Island, June 13-15, 2000, pp. 58-63
[15] Reljin, B. Reljin, I. Pavlovic, and I. Rakoc evic, Multifractal analysis of gray-scale images [A], in Proceedings of IEEE 10th Mediterranean Electrotechnical Conference, MELECON-2000 [C], Vol. Ⅱ, Lemesos, Cyprus, May 29-31, 2000, pp. 490-493
[16] S. Blacher, F. Brouers, and G. Ananthakrishna, Multifractal analysis of real heterogeneous materials [J], Acta Stereologica, 1992, 11(1):327-330.
[17] S. Kanmani, C. Babu Rao, D.K. Bhattacharya and Baldev Raj, Multifractal analysis of stress corrosion cracks [J], Acta Stereologica, 1992, 11(1):349-354
[18] T. Lo, H. Leung, J. Litva, and S. Haykin, Fractal characterization of sea. scattered signals and detection of sea-surface targets [J], Proceedings of the IEEE, 1993, F140:243-250
[19] D. Gan, and Z. S. hong, Detection of sea-surface radar targets based on multifractal analysis [J], Electronics Letters, 2000, 36(13):1144-1145
[20] N. Sarkar, and B.B. Chaudhuri, Multifractal and generalized dimensions of gray-tone digital images [J], Signal Processing, 1995, 42(2):181-190
[21] B.B. Chaudhuri, and N. Sarkar, Texture segmentation using fractal dimension [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, PAMI-17(1):72-77
[22] G. Du, and T.S. Yeo, A Novel Multifractal Estimation Method and Its Application to Remote Image Segmentation [J], IEEE Transactions on Geoscience and Remote Sensing, 2002, 40 (4):980-982
[23] Q. Cheng, The gliding box method for multifractal modeling [J], Computers and Geosciences, 1999, 25 (9):1073-1079
[24] L.V. Meisel, and M.A. Johnson, Convergence of numerical box-counting and correlation integral multifractal analysis techniques [J], Pattern Recognition, 1997, 30(9):1565-1570
[25] 李厚强，刘政，凯林峰，基丁分形理论和Kohonen神经网络的纹理图像分割方法[J]，计算机工程与应用，2001，37(7)：44-46
[26] T. Kohonen, Self-Organization Maps [M], Berlin Heidelberg: Springer-Verlag, 1995
[27] X.C. Jin, S.H. Ong, and Jayasooriah, A practical method for estimation fractal dimension [J], Pattern Recognition Letters, 1995, 16(5):457-464
[28] N. Sarkar, and B.B. Chaudhuri, An efficient differential box-counting approach to compute fractal dimension of image [J], IEEE Transactions on System, Man, and Cybernetics, 1994, SMC-24(1):115-120
[29] 夏勇，赵荣椿，江泽涛，一种基于数学形态学的分形维数估计方法[J]，中国图像图形学报，2006，9A(6)：760-766
[30] Y. Xia, (David) D.G. Feng, and R.C. Zhao, Texture Segmentation using Local Morphological Multifractal Exponents [A], in Proceedings of International Symposium on Intelligent Multimedia, Video & Speech Processing, ISIMP'04 [C], Hong Kong, 2004, pp. 438-441
[31] Yong Xia, (David) D. G. Peng, and R. C. Zhao, Morphological Multifractal Estimation for Image Segmentation [J], IEEE Transactions on Image Processing, 2006, 15(3):614-623
[32] P. Brodatz, Texture: A Photographic Album for Artists and Designers[M], New York: Dover, 1966
[33] J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms [M], New York: Plenum Press, 1981
[34] Viterbi School of Engineering, University of Southern California, The USC-SIPI Image Database, Available: http://sipi.usc.edu/database
[35] A.F.L. Serafim, Fractal Signatures for complex natural textures recognition [A], in Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society [C], 1998:1252-1257.
[36] Y. Y. Tang, H. Ma, D.h. Xi, X.G. Mao, and C. Y. Suen, Modified Fractal Signature (MFS): A New Approach to Document Analysis for Automatic Knowledge Acquisition [J], IEEE Transactions on Knowledge and Data Engineering, 1997, 9(5):747-762
[37] G. Dougherty, and G.M. Henebry, Fractal signature and lacunarity in the measurement of the texture of trabecular bone in clinical CT images [J], Medical Engineering and Physics, 2001, 23(6):369-380
[38] Q. Wang, D.D. Feng, and Z. Chi, B-Spline Over-complete Wavelet Based Fractal Signature Analysis for Texture image Retrieval [A], International Symposium on Intelligent Multimedia, Video & Speech Processing (ISIMP2004) [C], Hong Kong, 2004, pp. 462-466
[39] S. Peleg, J. Naor, R. Hartley, and D. Avnir, Multiple resolution texture anatysis and classification [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6(6):518-523
[40] R. Kashyap, and R. Chellappa, Estimation and choice of neighbors in spatial interaction models of images [J], IEEE Transactions on Information Theory, 1983, 29(1):60-72
[41] B.S. Manjunath, T. Simchony, and R. Chellappa, Stochastic and deterministic networks for texture segmentation [J], IEEE Transactions on Acoustics Speech and Signal Processing, 1990, ASSP-38(6):1039-1049.
[42] B. S. Man junath, and R. Chellappa, Unsupervised texture segmentation using Markov random fields [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, PAMI-13(5):478-482
[1] 赵荣椿(等)，数字图像处理导论[M]，西安：西北工业大学出版社，2000
[2] 贾云得，机器视觉[M]．北京：科学出版社，2000
[3] R. C. Gonzalez, and R. E. Woods, Digital Image Processing (2nd Edition) [M], NJ:Upper Saddle River, Prentice Hall, 2002
[4] 章毓晋(等)，图像图形科学丛书——图像分割[M]，北京：科学出版社，2001
[5] G.B. Coleman, and H.C. Andrews, Image segmentation by clusterin [J], Proceedings of IEEE, 1979, 67:773-785.
[6] M. Celenk, A colour clustering technique for image segmentation [J], Computer Vision, Graphic, and Image Processing, Nov. 1990, 52:145-170.
[7] 边肇祺，张学工(等)，模式识别[M]，北京：清华大学出版社，2000
[8] R.O. Duda, P.E. Hart, and D.G. Stork, Pattern Classification (2nd Edition) [M], New York: John Wiley, 2001
[9] A.K. Jain, M.N. Nutty, and P.J. Flynn, Data Clustering: A Review [J], ACM Computing Surveys, 1999, 31:264-323
[10] A. Baraldi, and P. Blonda, A Survey of Fuzzy Clustering Algorithms for Pattern Recognition—Part Ⅰ [J], IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 1999, SMC-29(6):778-785
[11] A. Baraldi, and P. Blonda, A Survey of Fuzzy Clustering Algorithms for Pattern Recognition—Part Ⅱ [J], IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 1999, SMC-29(6):786-801
[12] A.K. Jain, R.P.W. Duin, and J. Mao, Statistical pattern recognition: A review [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, PAMI-22(1): 4-37
[13] T．M．Mitchell，机器学习(曾华军等译)[M]，北京：机械工业出版社，2003
[14] B. King, Step-wise clustering procedures [J], Journal of the American Statistical Association, 1957, 69:86-101
[15] F. Murtagh, A survey of recent advances in hierarchical clustering algorithms which use cluster centres [J], The Computer Journal, 1984, 26(4):354-359
[16] J. MacQueen, Some methods for classification and analysis of multivariate observations [A], in Proceedings of the 5th Symposium on Mathematical Statistics and Probability [C], USA, Berkeley, 1967:281-297
[17] G.H. Ball, and D.J. Hall, ISODATA, A novel method of data analysis and classification [M], Technical report, Stanford University, Stanford, CA, USA, 1965
[18] C.T. Zahn, Graph-theoretical methods for detecting and describing gestalt clusters [J], IEEE Transactions on Computers, 1971, C-20:68-86
[19] A.P. Dempster, N.M. Laird, and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm [J], Journal of the Royal Statistical Society, Series B (Methodological), 39(1):1-38
[20] A.K. Jain, and R.C. Dubes, Algorithms for Clustering Data [M], NJ: Upper Saddle River, Prentice Hall, 1988
[21] S.Y. LU, and K.S. FU, A sentence-tosentence clustering procedure for pattern analysis [J], IEEE Transactions on Systems, Man, and Cybernetics, 1978, 8:381-389
[22] E.H. Ruspini, A new approach to clustering [J], Information and control, 1969, 15:22-32
[23] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms [M], New York: Plenum Press, 1981
[24] R.N. Dave, Generalized fuzzy C-shells clustering and detection of circular and elliptic boundaries [J], Pattern Recognition, 1992, 25:713-722
[25] A.K. Jain, and J. MAO, Artificial neural networks: A tutorial [J], IEEE Computer, Mar. 1996, 29:31-44
[26] T. Kohonen, The self-organizing map [J], Proceedings of IEEE, 1990, 78:1464-1480
[27] G. Carpenter, and S. Grossberg, ART3: Hierarchical search using chemical transmitters in self-organizing pattern recognition architectures [J], Neural Networks, 1990, 129-152
[28] S. Mitra, andS. K. Pal, Self-organizing neural networkas a fuzzy classifier [J], IEEE Transactions on Systems, Man, and Cybernetics, 1994, SMC-24:385-399
[29] R. Michalski, R.E. STEPP, and E. Diday, Automated construction of classifications: conceptual clustering versus numerical taxonomy [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1983, PAMI-5(5):396-409
[30] G.P. Babu, and M.N. Murty, Clustering with evolution strategies [J], Pattern Recognition, 1994, 27:321-329
[31] D.B. Fogel, and P.K. Simpson, Evolving fuzzy clusters [A], In Proceedings of the International Conference on Neural Networks [C], CA, San Francisco, 1993: 1829-1834
[32] R.W. Klein, and R. C. Dubes, Experiments in projection and clustering by simulated annealing [J], Pattern Recognition, 1989, 22:213-220
[33] K.S. Alsultan, and M.M. Khan, Computational experience on four algorithms for the hard clustering problem [J], Pattern Recognition Letters, 1996, 17(3):295-308
[34] K. Rose, E. Gurewitz, and G.C. Fox, Deterministic annealing approach to constrained clustering [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993, PAMI-15:785-794
[35]L.A. Zadeh, Fuzzy sets [J], Information and control, 1965, 8:338-353
[36]R. Krishnapuram, and J.M. Keller, A possibilistic approach to clustering [J], IEEE Transactions on Fuzzy Systems, 1993, 1(2):98-110.
[37]K. L. Wu, and M. S. Yang, Alternative c-means clustering algorithms [J], Pattern Recognition, 2002, 35:2267-2278
[38] J. Fan, W. Zhen, and W. Xie, Suppressed fuzzy c-means clustering algorithm [J], Pattern Recognition Letters, 2003, 24:1607-1612
[39]J. C. Bezdek, and N. R. Pal, Two soft relative of learning vector quantization [J],Neural Networks, 1995, 8(5):729-743
[40]B. Fritzke, A growing neural gas network learns topologies in Advances[A], in Neural Information Processing Systems [C], G. Tesauro, D. S. Touretzky, T. K. Leen. Eds., Cambridge, MA: MIT Press, 1995:625-632.
[41]G. Carpenter, S. Grossberg, and D. B. Rosen, Fuzzy ART: Fast stable learning and categorization of analog patterns by an adaptive resonance system [J], Neural Networks, 1991, 4:759-771
[42]G. Carpenter, S. Grossberg, N. Maukuzon, j. Reynolds, and D. B. Rosen, Fuzzy ARTMAP:A neural network architecture for incremental supervised learning of analog multidimensional maps [J], IEEE Transactions on Neural Networks, 1992,3(5):698 - 713
[43]A. Baraldi, and E. Alpaydn, Simplified ART: A new class of ART algorithms (R),Technique Report of international computer science institute , Berkeley.California. 1998
[44]A. Baraldi, and F. Parmiggiani, Novel neural network model combining radial basis function, competitive Hebbian learning rule, and fuzzy simplified adaptive resonance theory [A], in Proceedings of SPIE Optical Science, Engineering Instrumentation' 97: Applications Fuzzy Logic Technology IV [C] CA, San Diego,1997, 3165:98-112
[45]R. Krishnapuram, and C. P. Freg, Fitting an unknown number of lines and planes to image data through compatible cluster merging [J], Pattern Recognition, 1992,25:385-400
[46]J. C. Tilton, Image segmentation by region growing and spectral clustering with a natural convergence criterion [A], in Proceedings of the International Geoscience and Remote Sensing Symposium [Cj, USA, WA, Seattle, 1998:1766-1768
[47]M. A. Kupinski, and M. L. Giger, Automated Seeded Lesion Segmentation on Digital Mammograms [J], IEEE Transactions on Medical Imaging, 1998, 17:510-517
[48]P. W. Verbeek, and D. J. de Jong, Edge preserving texture analysis [A], in Proceedings of the 7th International Joint Conference on Pattern Recognition [C],Montreal, IEEE Computer Society Press, 1984:179-182
[49]L.S. Davis, and A. Mitiche, A model driven iterative texture segmentation algorithm, Computer Graphics and Image Processing, 19(2):95-110
[50]A. W. C. Liew, S. H. Leung, and W. H. Lau, Segmentation of Color Lip Images by Spatial Fuzzy Clustering [J], IEEE Transactions on Fuzzy Systems, 2003, 11:542-549
[51]A. W.C. Liew, S.H. Leung, and W. H. Lau, Fuzzy image clustering incorporating spatial continuity [J], Proceedings of IEE—Vision, Image, Signal Processing, 2000,147:185-192
[52]S. Geman, and D. Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, PAMI-6:721-741
[53] J. Besag, On the statistical analysis of dirty pictures [J], Journal of the Royal Statistical Society, Series B (Methodological)., 48:259-302
[54] S.A. Barker, Image segmentation using Markov random field models (Ph.D. dissertation) [D], Depterment of Engineering, Cambridge University, 1998
[55] S.Z. Li, Modeling image analysis problems using Markov random fields [A], in C. R.. Rao and D.N. Shanbhag (Eds.), Stochastic Processes: Modeling and simulation, vol. 20 of Handbook of Statistics, Elsevier Science, 2000, pp. 1-43
[56] Y. Xia, R.C. Zhao, Y.N. Xhang, J. Sun, and D.G. Feng, Texture Segmentation by Fuzzy Clustering of Spatial Patterns [C]. in L. Wang et al. (Eds.), Fuzzy Systems and Knowledge Discovery, Proceedings of the 3rd International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2006, Lecture Notes of Computer Science, Vol. 4223, Springer, 2006, pp. 894-897
[57] H. Deng, and D.A. Clausi, Unsupervised image segmentation using a simple MRF model with a new implementation scheme[J], Pattern Recognition, 2004, 37:2323-2335
[58] H. Deng, and D.A. Clausi, Unsupervised segmentation of synthetic aperture radar sea ice imagery using a novel Markov random field model [J], IEEE Transactions on Geoscience and Remote Sensing, 2005, GRS-43:528-538
[59] P. Brodatz, Texture: A Photographic Album for Artists and Designers [M], New York, Dover: 1966
[60] Y. Xia, R.C. Zhao, P.G. Feng, Y.N. Zhang, and J. Sun, Texture Discrimination by Local Morphological Multifractal Signatures [C], in Proceedings of 2006 IEEE Region 10 Conference, TENCON' 06, Hong Kong, Nov. 14-17, 2006
[61] Y. Xia, (David) D.G. Feng, and R.C. Zhao, Morphological Multifractal Estimation for Image Segmentation [J], IEEE Transactions on Image Processing, 2006, 15(3):614-623
[62] University of Southern California, The USC-SIPI Image Database [Online], Available: http://sipi.usc.edu/database/
[63] B.S. Manjunath, T. Simchony, and R. Chellappa, Stochastic and deterministic networks for texture segmentation [J], IEEE Transactions on Acoustic, Speech, and Signal Processing, 1990, 38:1039-1049
[64] B.S. Manjunath, and R. Chellappa, Unsupervised texture segmentation using Markov random fields [J], IEEE Transact:ions on Pattern Analysis and Machine Intelligence, 1991, PAMI-13:478-482
[65] F.W. Campbell, and J.G. Robson, Application of Fourier analysis to the visibility of gratings [J], Journal of Physiology, 1968, 197:551-556
[66] 夏勇，赵荣椿，基于局部形态学多重分形指数的遥感图像粗分割[J]，计算机应用，2006，26(9)：2083-2085
[1] R. Chellappa, and A.K. Jain, Markov Random Fields: Theory and Applications [M], Academic Press, 1993
[2] J. Besag, Spatial interaction and the statistical analysis of lattice systems (with discussion) [J], Journal of the Royal Statistical Society, Series B (Methodological); 1974, 36:192-236
[3] J. Besag, On the statistical analysis of dirty pictures [J], Journal of the Royal Statistical Society, Series B (Methodological), 1986, 48(3):259-302.
[4] R.C. Dubes, and A.K. Jain, Random field models in image analysis [J], Journal of Applied Statistics, 1989, 16(2):131-164
[5] S.Z. Li, Modeling image analysis problems using Markov random fields [A], in C. R. Rao and D. N. Shanbhag (Eds.), Stochastic Processes: Modeling and simulation, vol. 20 of Handbook of Statistics. Elsevier Science, 2000, pp. 1-43
[6] Z. Kato, Multi-scale Markovian Modelisation in Computer Vision withApplication to SPOT Image Segmentation (Ph.D. Dissertation) [D], Nice: Universtity of Nice, 1994
[7] J.M. Hammersley, and P. Clifford, Markov field on finite graphs and lattices [M], unpublished, 1971
[8] R. Chellappa, and R.L. Kashyap, Digital Image Restoration Using Spatial Interaction Models [J], IEEE Transactions on Acoustics, Speech, and Signal Processing, 1982, 30(3):461-471
[9] S. Geman, and D. Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, MPAI-6:721-741
[10] S. Z. Li, MAP Lmage Restoration and Segmentation by Constrained Optimization [J], IEEE Transactions on Image Processing, 1998, 7(12):1730-1735
[11] M. Snyder, On the mathematical foundations of smoothness constraints for the determination of optical flow and for surface reconstruction [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(11):1105-1113
[12] D. Geiger, and F. Girosi, Parallel and deterministic algorithms from MRF's: Surface reconstruction [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(5):401-412
[13] L.S. Davis, Shape matching using relaxation techniques [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1979, 1(1):60-72
[14] N.S. Friedland, and A. Rosenfeld, Compact Object Recognition Using Energy-Function-based Optimization [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, PAMI-14(7):770-777
[15] R.D. Morris, Image Sequence Restoration using Gibbs Distributions (Ph.D. Dissertation) [D], U.K.: University of Cambridge, 1995
[16] F. Luthon, A. Caplier, and M. Lievin, Spatiotemporal MRF approach to video segmentation: application to motion detection and lip segmentation [J], Signal Processing, 1999, 76(1):61-80
[17] J.W. Modestino, and J. Zhang, A Markov Random Field Model-Based Approach to Image Interpretation [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1992, PAMI-14(6):606-615
[18] G.H. Geoffrey, Multivariate Gaussian MRF for multispectral Scene segmentation and anomaly detection [J], IEEE Transactions on Geoscience and Remote Sensing, 2000, 38(3):1199-1211
[19] D. Geman, S. 6eman, C. Graffigne, and P. Dong, Boundary detection by constrained optimization [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, PAMI-12(7):609-628
[20] J. Zerubia, and R. Chellappa, Mean field annealing using compound Gauss-Markov random fields for edge detection and image estimation [J], IEEE Transactions on Neural Networks, 1993, 4:703-709
[21] G. Storvik, A Bayesian approach to dynamic contours through stochastic sampling and simulated annealing [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994, PAMI-16(10):976-986
[22]G. R. Cross, and A. K. Jain, Markov Random Field Texture Models [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1983, PAMI-5:25-39
[23]F. S. Cohen, Z. Fan, and M. A. Patel, Classification of rotated and scaled textured images using Gaussian Markov Random Field models [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, PAMI-13(2):192-202
[24]R. Kashyap, and R. Chellappa, Estimation and choice of neighbors in spatial interaction models of images [J], IEEE Transactions on Information Theory, 1983,29:60-72
[25]R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (2nd Edit) [M], John Wiley, New York, 2001
[26]H. Derin, and H. Elliott, Modeling and segmentation of noisy and textured images using Gibbs random fields [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987, MPAI-9:39-55
[27]F.S. Cohen, and D.B. Cooper, Simple Parallel Hierarchical and Relaxation Algorithms for Segmenting Noncausal Markovian Random Fields [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1987, PAMI-9:195-219
[28]S. Kirkpatrick, CD. Gelatt Jr, and M. P. Vecchi, Optimization by simulated annealing [J], Science, 1983, 220(4598):671-680
[29]R. Neal, Probabilistic Inference Using Markov Chain Monte Carlo Methods,Technical Report CRG-TR-93-1, Department of Computer science, University of Toronto, Canada, 1993
[30]H. Szu, and R. Hartley, Fast Simulated Annealing [J], Physics Letters A., 1987,122:157-162
[31]B. S. Manjunath, and R. Chellappa, Unsupervised texture segmentation using Markov random fields [J], IEEE Transactions on Pattern Analysis and Machine Intelligence,1991, PAMI-13:478-482
[32]N. Balram, and J.M. F. Moura, Noncausal Gauss Markov Random Fields: Parameter Structure and Estimation [J], IEEE Transactions on Information Theory, 1993,39:1333-1355
[33]A. Speis, and G. Healey, Feature Extraction for Texture Discrimination via Random Field Models with Random Spatial Interaction [J], IEEE Transactions on Image Processing, 1996, 5(4):635-645
[34]J. Bennett, and A. Khotanzad, Maximum Likelihood Estimation Methods for Multispectral Random Field Image Models [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, PAMI-21(6):537-543
[35]H. W. Deng, and D. A. Clausi, Gaussian MRF Rotation-Invariant Features for Image Classification [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(7):951-955
[36]I.M. Elfadel, and R.W. Picard, Gibbs random fields, co-occurrences, and texture modeling [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994,16(1):24-37
[37]H. Deng, and D. A. Clausi, Unsupervised image segmentation using a simple MRF model with a new implementation scheme [J], Pattern Recognition, 2004, 37(12) :2323-2335
[38]H. Deng, and D. A. Clausi, Unsupervised segmentation of synthetic aperture radar sea ice imagery using a novel Markov random field model [J], IEEE Transactions on Geoscience and Remote Sensing, 2005, GRS-43:528-538
[39] D.E. Melas, and S.P. Wilson, Double Markov random fields and Bayesian image segmentation [J], IEEE Transactions on Signal Processing, 2002, SP-50:357-365
[40] F.C. Jeng, and J.W. Woods,.Compound Gauss-Markov random fields for image segmentation [J], IEEE Transactions on Signal Processing, 1991, SP-39:683-697
[41] A. Sarkar, M.K. Biswas, and K.M.S. Sharma, A Simple unsupervised MRF model based image segmentation approach [J], IEEE Transactions on Image Processing, 2000, IP-9:801-812
[42] S.A. Barker and P.J.W. Rayner, Unsupervised image segmentation using Markov random field models [J], Pattern Recognition, 2000, 33:587-602
[43] S.A. Barker, Image segmentation using Markov random field models (Ph.D. Dissertation) [D], U.K.: Department of Engineering, Cambridge University, 1998
[44] J. Zhang, The mean field theory in EM procedures for Markov random fields [J], IEEE Transactions on Signal Processing, 1992, 40:2570-2583
[45] B.S. Manjunath, T. Simchony, and R. Chellappa, Stochastic and deterministic networks for texture segmentation [J], IEEE Transactions on Acoustics, Speech, and Signal Processing, 1990, ASSP-38:1039-1049
[46] C.H. Wu, and P.C. Doerschuk, Tree approximations to Markov random fields [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, 17:391-343
[47] I.Y. Kim, and H.S. Yang, A systematic way for region-based image segmentation based on Markov random field model [J], Pattern Recognition Letters, 1994, 15:969-976
[48] A. Sarkar, M.K. Biswas, B. Kartikeyan, V. Kumar, K.L. Majumdar, and D.K. Pal, A MRF model based segmentation approach to classification for multispectral imagery [J], IEEE Transactions on Geoscience and Remote Sensing, 2002, 40(4):1102-1113
[49] R.K. Pina, and R.C. Pueter, Bayesian image reconstruction: The pixonand optimal image modeling [J], Publ istron Soc Pac, 1993, 105:630-637
[50] X. Descombes, and F. Kruggel, A Markov pixon information approach for low-level image description [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21:482-494
[51] F. Yang, and T. Jiang, Pixon-based image segmentation with Markov random fields [J], IEEE Transactions on Image Processing, 2003, IP-12:1552-1559
[52] D. Terzopoulos, Image analysis using multigrid relaxation methods [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1986, 8:129-139
[53] P.C. Chen, and T. Pavlidis, Imace segmentation as an estimation problem [J], Computer Vision, Graphics, and Image Processing, 1980, 12:153-173
[54] C. Bouman, and B. Liu, Multiple resolution segmentation of textured images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, PAMI-13:99-113
[55] P. Perez, and F. Heitz, Multiscale Markov random fields and constrained relaxation in low level image analysis [A], in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing [C], 1992, 3:61-64
[56] J. Mao, and A.K. Jain, Texture classification and segmentation using multiresolution simultaneous autoregressive models [J], Pattern Recognition, 1992, 25(2):173-188
[57] F.C. Jeng, Subsampling of Markov random fields [J], Journal of Visual Communication and Image Representation, 1992, 3(3):225-229
[58] S. Lakshmanan, and H. Derin, Gaussian Markov random fieldsat multiple resolutions [A], in R. Chellappa, Eds. Markov Random Fields: Theory and Applications, New York:Academic, 1993:131-157
[59]S. Krishnamachari, and R. Chellappa, Multiresolution Gauss-Markov random field models for texture segmentation [J], IEEE Transactions on Image Processing, 1997,IP-6:251-267
[60]D. Panjwani, and G. Healey, Markov random field models for unsupervised segmentation of textured color images [J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, PAMI-17(10):939-954
[61]P.C. Smits, and S. G. Dellepiane, Synthetic aperture radar image segmentation by a detail preserving Markov Random Field approach [J], IEEE Transactions on Geoscience and Remote Sensing, 1997, GRS-35(4):844-857
[62]G. Rellier, Texture Feature Analysis Using a Gauss-Markov Model in Hyperspectral Image Classification[J], IEEE Transactions on Geoscience and Remote Sensing, 2004,GRS-42(7):1543-1551
[63]M. Mignotle, C. Collet, P. Perez, and P. Bouthemy, Sonar Image Segmentation Using an Unsupervised Hierarchical MRF Model [J], IEEE Transactions on Image Processing,2000, 9(7):1216-1231
[64]Y. Xia, (David) D. G. Feng, and R. C. Zhao, Adaptive Segmentation of Textured Images by Using the Coupled Markov Random Field Model [J], IEEE Transactions on Image Processing, 2006, 15(11): 3559-3566
[65]P. Brodatz, Texture: A Photographic Album for Artists and Designers [M], NewYork:Dover, 1966
[66]Viterbi School of Engineering, University of Southern California, The USC-SIPI Image Database. Available: http://sipi.usc.edu/database
[67]J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms [M],New York: Plenum Press, 1981