基于边缘惩罚TMF的无监督SAR图像多类分割算法
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摘要
合成孔径雷达(Synthetic Aperture Rader, SAR)图像分割是图像目标识别与解译技术的重要环节,一直是雷达信号处理领域的热点。但是SAR侧视成像和相干成像的特点,决定了SAR图像中包含大量相干斑乘性噪声,信噪比低,这使得传统的图像处理技术很难应用。
本文针对SAR图像非高斯、非平稳的统计特性,提出了一种基于边缘惩罚三重马尔可夫场(Triplet Markov fields, TMF)的SAR图像多类分割新算法。该算法依据边缘惩罚准则将基于局部边缘强度信息的惩罚函数引入到TMF势能函数中,在对SAR图像的非平稳性很好地建模的同时解决了TMF算法在分割时出现的边界定位不准确的问题,然后对新势能函数下的目标函数进行优化,导出多重区域迭代合并的贝叶斯最大后验模型(Bayesian maximum posteriori model, MPM)分割公式。本文对测试图和实测SAR图像进行了仿真,仿真结果和分析表明:与经典的马尔可夫随机场(Markov Random Field, MRF)模型和近年来的TMF分割算法相比,本文算法在抑制斑点噪声的同时,有效地提高了SAR图像的分割精度,尤其是在弱边缘处的分割定位更加准确。
Synthetic Aperture Rader(SAR) image segmentation is an important stage for SAR images’recognition and understanding, and the research for the SAR image segmentation algorithm has been a hot spot. However, according to the characteristics of SAR side-view imaging and coherent imaging, the image contains a large number of multiplicative speckle noise, signal to noise ratio is low. These present problems for standard image processing techniques.
In this dissertation, we propose a new unsupervised multi-class segmentation of SAR images using the triplet Markov fields(TMF)models based on edge penalty, the new algorithm fuse the traditional energy function of TMF model with the principle of edge penalty, which could prevent segment from smoothing across boundaries while modeling the non-stationary SAR image better. Then we optimize the objective function that stems from the new energy function to obtain an iterative multi-region combined Bayesian maximum posteriori model (MPM) segmentation equation for the new segmentation algorithm. Simulated data and real SAR images are applied to evaluate the performance of the proposed algorithm in segmentation. Experimental results and analysis indicate that compared with the classical Markov random field (MRF) and the recent TMF segmentation algorithm, the proposed algorithm effectively improves the segmentation accuracy of the SAR image while reducing the influence of multiplicative speckle noise, with the weak edge location being more accurate especially.
本文针对SAR图像非高斯、非平稳的统计特性,提出了一种基于边缘惩罚三重马尔可夫场(Triplet Markov fields, TMF)的SAR图像多类分割新算法。该算法依据边缘惩罚准则将基于局部边缘强度信息的惩罚函数引入到TMF势能函数中,在对SAR图像的非平稳性很好地建模的同时解决了TMF算法在分割时出现的边界定位不准确的问题,然后对新势能函数下的目标函数进行优化,导出多重区域迭代合并的贝叶斯最大后验模型(Bayesian maximum posteriori model, MPM)分割公式。本文对测试图和实测SAR图像进行了仿真,仿真结果和分析表明:与经典的马尔可夫随机场(Markov Random Field, MRF)模型和近年来的TMF分割算法相比,本文算法在抑制斑点噪声的同时,有效地提高了SAR图像的分割精度,尤其是在弱边缘处的分割定位更加准确。
Synthetic Aperture Rader(SAR) image segmentation is an important stage for SAR images’recognition and understanding, and the research for the SAR image segmentation algorithm has been a hot spot. However, according to the characteristics of SAR side-view imaging and coherent imaging, the image contains a large number of multiplicative speckle noise, signal to noise ratio is low. These present problems for standard image processing techniques.
In this dissertation, we propose a new unsupervised multi-class segmentation of SAR images using the triplet Markov fields(TMF)models based on edge penalty, the new algorithm fuse the traditional energy function of TMF model with the principle of edge penalty, which could prevent segment from smoothing across boundaries while modeling the non-stationary SAR image better. Then we optimize the objective function that stems from the new energy function to obtain an iterative multi-region combined Bayesian maximum posteriori model (MPM) segmentation equation for the new segmentation algorithm. Simulated data and real SAR images are applied to evaluate the performance of the proposed algorithm in segmentation. Experimental results and analysis indicate that compared with the classical Markov random field (MRF) and the recent TMF segmentation algorithm, the proposed algorithm effectively improves the segmentation accuracy of the SAR image while reducing the influence of multiplicative speckle noise, with the weak edge location being more accurate especially.
引文
[1] Brown W.M. Synthetic Aperture Radar. IEEE Trans. On AES. 1967, 3(2). 217-299.
[2]舒宁.雷达遥感原理.第一版.北京:测绘出版社,1997. 28-35.
[3]舒士畏.雷达图像及其应用.第一版.北京:中国铁道出版社,1988. 60-126.
[4] Stofan E.R. Overview of results of Spaceborne Imaging Radar-C, X-Band Synthetic Aperture Radar (SIR-C/X-SAR). IEEE Transaction on Geoscience and Remote Sensing. 1995, 3(4). 817-828.
[5] Cumming I.G.等著,洪文等译.合成孔径雷达成像-算法与实现.第一版.北京:北京工业出版社,2007. 3-4.
[6]梁家琳.合成孔径雷达的军事应用.军事淤会. 1994, Vol.2. 23-26.
[7]张直中.合成孔径雷达遥感技术及其应用.火控雷达技术. 2000, 29(1). 1-7.
[8]郑圣虎,程迎春.合成孔径雷达的民用与直升机机载应用.微计算机信息. 2009, 25(16). 165-167.
[9]吴一戎,朱敏慧.合成孔径雷达技术的发展现状与趋势.遥感技术与应用. 2000, 15(2). 121-122.
[10]周健,沈成忠.国外雷达卫星的发展概况及发展趋势.空间电子技术. 1999, Vol.4. 56-64.
[11]张直中.合成孔径雷达(SAR)的最新进展.现在雷达. 2003, 25(1). 1-8.
[12] Marc S., Gianfranco D. Analysis of Speckle Noise Contribution on Wavelet Decomposition of SAR Images. IEEE Trans. on Geoscience and Remote Sensing. 1998, 6(2). 1953-1962.
[13] Haralick R., Shapiro L. Image segmentation techniques. Comput. Vis., Grapg., Image Process. 1985, Vol.29. 100-132.
[14] Simard M., DeGrandi G., Thomson K.P.B., et al. Analysis of speckle noise contribution on wavelet decomposition of SAR images. IEEE Trans. on GRS. 1998, 36(6).1953-1962.
[15] Cao Lan-ying , Zhang Kun-hui , Xia Liang-zheng . SAR image segmentation by 2- D fussy entropy. IEEE Proceedings of Geoscience and Remote Sensing Symposium. 2004, Vol.6. 3798-3801.
[16] Xu Xin, Li Deren, Sun Hong. Multiscale SAR image segmentation using a double markov random field model. IEEE Proceedings of Seventh International Symposium on Signal Processing and Its Applications. 2003, Vol.1.349-352.
[17]薛景浩,章毓晋,林行刚. SAR图像基于Rayleigh分布假设的最小误差阈值化分割.电子科学学刊. 1999, Vol.2. 219-225.
[18] Fjortoft R., Lopes A., Marthon P., et al. An optimal multi-edge detector for SAR image segmentation. IGARSS’02. Vol.6. 3402-3404.
[19]刘振华,毛士艺,袁运能. SAR图像组合分割算法.电子学报. 2003, 31(6). 833-836.
[20] Vincent.L., Soille P. Watersheds in Digital Spaces: an efficient algorithm base immersion simulations. IEEE Trans on Pattern Analysis and Machine Intelligence. 1991, 13(6). 583-598.
[21]沈定刚,戚飞虎.基于神经网络的自适应图像分割.上海交通大学学报. 1994, 28(S1). 39-45.
[22]蒋剑,吴建华.在小波域进行图像的最大熵分割的一种方法.南昌大学(工科版). 2003, 25(2). 59-63.
[23] Benboudjema D., Pieczynski W. Unsupervised Statistical Segmentation of Nonstationary Images Using Triplet Markov Fields, IEEE Trans. PAMI. 2007, 29(8). 1367-1378.
[24]吴艳,王霞,廖桂生.基于小波域隐马尔可夫混合模型SAR图像降斑算法.电波科学学报. 2006, 22(2). 244-250.
[25] Kindermann R., Snell J. Markov random fields and their applications. Amer. Math. Soc. 1980
[26] Geman S., Geman D., Stochastic relaxation Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Analysis and Machine Intelligence. 1984, 6(6). 721-741.
[27] Panjwani D. K., Healey G. Markov Random Field Models for Unsupervised Segmentation of Textured Color Images. IEEE Trans. Pattern Anal. Machine Intell. 1995, 17(10). 939-954.
[28]郦苏丹,张翠,王正志.基于马尔可夫随机场的SAR图像目标分割.中国图象图形学报. 2002, 7(8). 794-799.
[29]夏桂松,何楚,孙洪.一种基于非参数密度估计和马尔可夫上下文的SAR图像分割算法.电子与信息学报. 2006, 28(12). 2209-2213.
[30] Giordana N., Pieczynski W. Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation. IEEE Trans. Pattern Analysis and Machine Intelligence. 1997, 19(5). 465-475.
[31] Poggi G., Scarpa G., Zerubia J.B. Supervised Segmentation of Remote Sensing Images Based on a Tree-Structured MRF Model. IEEE Trans. on Geoscience andRemote Sensing. 2005, 43(8). 1901-1911.
[32] Kumar S., Hebert M. Discriminative Random Fields. International Journal of Computer Vision. 2006, 68(2). 179-202.
[33] Derrode S., Pieczynski W. Signal and Image Segmentation Using Pairwise Markov Chains. IEEE Trans. Signal Processing. 2004, 52(9). 2477-2489.
[34] Pieczynski W., Tebbache A. N. Pairwise. Markov random Fields and Segmentation of Textured Images. Machine Graphics and Vision. 2000, 9(3). 705-718.
[35] Destrempes F., Mignotte M. A Statistical Model for Contours in Images. IEEE Trans. Pattern Analysis and Machine Intelligence. 2004, 26(5). 626-238.
[36] Benboudjema D., Pieczynski W. Unsupervised Image Segmentation Using Triplet Markov Fields. Computer Vision and Image Understanding. 2005, 99(3). 476-498.
[37] Pieczynski W., Benboudjema D. Multisensor Triplet Markov Fields and Theory of Evidence. Image and Vision Computing. 2006, 24(1). 61-69.
[38] Lanchantin P., Pieczynski W. Unsupervised NonStationary Image Segmentation Using Triplet Markov Chains. Proc. Advanced Concepts for Intelligent Vision Systems. 2004, 31(3). 1-6.
[39] Benboudjema D., Tupin F., Pieczynski W., et al. Unsupervised segmentation of SAR images using Triplet Markov fields and Fisher noise distributions. IEEE International Geoscience and Remote Sensing Symposium. 2007, 3891-3893.
[40] Lanchantin P., Pieczynski W. Unsupervised segmentation of triplet Markov chains hidden with long-memory noise. Advanced Concepts for Intelligent Vision Systems. 2008, 88(5). 1134-1151.
[41] Blanchet J., Forbes F. Triplet Markov Fields for the Classification of Complex Structure Data. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2008, 30(6). 1055-1067.
[42] Benboudjema D., Pieczynski W. Unsupervised Statistical Segmentation of Nonstationary Images Using Triplet Markov Fields. IEEE Transactions on Pattern analysis and Machine intelligence. 2007, 29(8). 1367-1378.
[43]张澄波.综合孔径雷达原理、系统分析与应用.第一版.北京:科学出版社,1989. 19-59.
[44] Cumming I.G.等著,洪文等译.合成孔径雷达成像-算法与实现.第一版.北京:北京工业出版社, 2007. 154-243.
[45]王超,张红,陈曦等.全极化合成孔径雷达图像处理.第一版.北京:科学出版社,2008. 55-57.
[46] Moreira A. Improved Multilook Techniques Applied to SAR and SCANSAR Imagery. IEEE Transaction on Geoscience and Remote Sensing. 1991, 29(4). 529-534.
[47] Goodman J.W. Some Fundamental Properties of Speckle. Journal of the Optical Society of America. 1976, 66(11). 1145-1150.
[48] Norvang Madsen S. Spectral Properties of Homogeneous and Non-homogeneous Radar Image. IEEE Transaction on Aerospace Electronic Systems. 1987, 23(58). 3-58.
[49] Oliver C., Quegan S. Understanding synthetic Aperture radar images. Artech House Eds, Norwood(MA). 1998.
[50] Verhoeye J., Wulf D. An Image Processing Chain for Land-Cover Classification Using Multitemporal ERS-1 Data. Photogrammetric Engineering and Remote Sensing. 1999, 65(10). 1179-1514.
[51] Gonzalez R. C., Wood R. E. Digital Image Processing. 3rd.ed. Addison-wesley. 1992.
[52]李禹.合成孔径雷达图像分割技术综述.宇航学报. 2008, 29(2). 407-412.
[53] Giordana N., Pieczynski W. Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation. IEEE Trans. Pattern Analysis and Machine Intelligence. 1997, 19(5). 65-475.
[54] Destrempes F., Mignotte M. A Statistical Model for Contours in Images. IEEE Trans. Pattern Analysis and Machine Intelligence. 2004, 26(5). 626-238.
[55]刘振华,毛士艺,袁运. SAR图像组合分割算法.电子学报. 2003, 31(6). 833-836.
[56] Vincent L., Soille P. Watersheds in digital spaces: An efficient algorithm based on immersion simulations. IEEE Trans. On PAMI. 1991, 13(6). 583-598.
[57] Lombardo P., Farina A. Coherent radar detection against K-distributed clutter with partially correlated texture . Signal Processing. 1996, 48(1). 1-15.
[58] Derin H., Elliot H. Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Trans. on PAMI. 1987, 9(1). 39-55.
[59] Descombes X., Morris R.D., Zerubia J., et al. Estimation of Markov Random Field Prior Parameters Using Markov Chain Monte Carlo Maximum Likelihood. IEEE Trans. Image Processing. 1999, 8(7). 954-963.
[60] Benboudjema D., Pieczynski W. Unsupervised Image Segmentation Using Triplet Markov Fields. Computer Vision and Image Understanding. 2005, 99(3). 476-498.
[61] Yu Qi-yao, Clausi D. A. Image Segmentation Using Edge Penalties and RegionGrowing. IEEE Transactions on Pattern analysis and Machine intelligence. 2008, 30(12). 2126-2139.
[62] Dzung L. P. Integrating Intensity and Boundary Information for Tissue Classification. Proceedings of the 17th IEEE Symposium on Computer-Based Medical Systems. 2004, 216-220.
[63] Yu Qi-yao, Clausi D. A. Combining Local and Global Features for Image Segmentation Using Iterative Classification and Region Merging. Proc. Second Canadian Conf. Computer and Robot Vision. 2005, 579-586.
[64] Yu Qi-yao, Clausi D. A. SAR Sea-Ice Image Analysis Based on Iterative Region Growing Using Semantics. IEEE Trans. Geoscience and Remote Sensing. 2007, 45(12). 3918-3931.
[65] Caves R., Quegna S., White R. Quantitative Comparison of the Perfomance of SAR Segmentation Algorithms. IEEE Trans. on Image Processing. 1998, 7(11). 1534-1546.
[2]舒宁.雷达遥感原理.第一版.北京:测绘出版社,1997. 28-35.
[3]舒士畏.雷达图像及其应用.第一版.北京:中国铁道出版社,1988. 60-126.
[4] Stofan E.R. Overview of results of Spaceborne Imaging Radar-C, X-Band Synthetic Aperture Radar (SIR-C/X-SAR). IEEE Transaction on Geoscience and Remote Sensing. 1995, 3(4). 817-828.
[5] Cumming I.G.等著,洪文等译.合成孔径雷达成像-算法与实现.第一版.北京:北京工业出版社,2007. 3-4.
[6]梁家琳.合成孔径雷达的军事应用.军事淤会. 1994, Vol.2. 23-26.
[7]张直中.合成孔径雷达遥感技术及其应用.火控雷达技术. 2000, 29(1). 1-7.
[8]郑圣虎,程迎春.合成孔径雷达的民用与直升机机载应用.微计算机信息. 2009, 25(16). 165-167.
[9]吴一戎,朱敏慧.合成孔径雷达技术的发展现状与趋势.遥感技术与应用. 2000, 15(2). 121-122.
[10]周健,沈成忠.国外雷达卫星的发展概况及发展趋势.空间电子技术. 1999, Vol.4. 56-64.
[11]张直中.合成孔径雷达(SAR)的最新进展.现在雷达. 2003, 25(1). 1-8.
[12] Marc S., Gianfranco D. Analysis of Speckle Noise Contribution on Wavelet Decomposition of SAR Images. IEEE Trans. on Geoscience and Remote Sensing. 1998, 6(2). 1953-1962.
[13] Haralick R., Shapiro L. Image segmentation techniques. Comput. Vis., Grapg., Image Process. 1985, Vol.29. 100-132.
[14] Simard M., DeGrandi G., Thomson K.P.B., et al. Analysis of speckle noise contribution on wavelet decomposition of SAR images. IEEE Trans. on GRS. 1998, 36(6).1953-1962.
[15] Cao Lan-ying , Zhang Kun-hui , Xia Liang-zheng . SAR image segmentation by 2- D fussy entropy. IEEE Proceedings of Geoscience and Remote Sensing Symposium. 2004, Vol.6. 3798-3801.
[16] Xu Xin, Li Deren, Sun Hong. Multiscale SAR image segmentation using a double markov random field model. IEEE Proceedings of Seventh International Symposium on Signal Processing and Its Applications. 2003, Vol.1.349-352.
[17]薛景浩,章毓晋,林行刚. SAR图像基于Rayleigh分布假设的最小误差阈值化分割.电子科学学刊. 1999, Vol.2. 219-225.
[18] Fjortoft R., Lopes A., Marthon P., et al. An optimal multi-edge detector for SAR image segmentation. IGARSS’02. Vol.6. 3402-3404.
[19]刘振华,毛士艺,袁运能. SAR图像组合分割算法.电子学报. 2003, 31(6). 833-836.
[20] Vincent.L., Soille P. Watersheds in Digital Spaces: an efficient algorithm base immersion simulations. IEEE Trans on Pattern Analysis and Machine Intelligence. 1991, 13(6). 583-598.
[21]沈定刚,戚飞虎.基于神经网络的自适应图像分割.上海交通大学学报. 1994, 28(S1). 39-45.
[22]蒋剑,吴建华.在小波域进行图像的最大熵分割的一种方法.南昌大学(工科版). 2003, 25(2). 59-63.
[23] Benboudjema D., Pieczynski W. Unsupervised Statistical Segmentation of Nonstationary Images Using Triplet Markov Fields, IEEE Trans. PAMI. 2007, 29(8). 1367-1378.
[24]吴艳,王霞,廖桂生.基于小波域隐马尔可夫混合模型SAR图像降斑算法.电波科学学报. 2006, 22(2). 244-250.
[25] Kindermann R., Snell J. Markov random fields and their applications. Amer. Math. Soc. 1980
[26] Geman S., Geman D., Stochastic relaxation Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Analysis and Machine Intelligence. 1984, 6(6). 721-741.
[27] Panjwani D. K., Healey G. Markov Random Field Models for Unsupervised Segmentation of Textured Color Images. IEEE Trans. Pattern Anal. Machine Intell. 1995, 17(10). 939-954.
[28]郦苏丹,张翠,王正志.基于马尔可夫随机场的SAR图像目标分割.中国图象图形学报. 2002, 7(8). 794-799.
[29]夏桂松,何楚,孙洪.一种基于非参数密度估计和马尔可夫上下文的SAR图像分割算法.电子与信息学报. 2006, 28(12). 2209-2213.
[30] Giordana N., Pieczynski W. Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation. IEEE Trans. Pattern Analysis and Machine Intelligence. 1997, 19(5). 465-475.
[31] Poggi G., Scarpa G., Zerubia J.B. Supervised Segmentation of Remote Sensing Images Based on a Tree-Structured MRF Model. IEEE Trans. on Geoscience andRemote Sensing. 2005, 43(8). 1901-1911.
[32] Kumar S., Hebert M. Discriminative Random Fields. International Journal of Computer Vision. 2006, 68(2). 179-202.
[33] Derrode S., Pieczynski W. Signal and Image Segmentation Using Pairwise Markov Chains. IEEE Trans. Signal Processing. 2004, 52(9). 2477-2489.
[34] Pieczynski W., Tebbache A. N. Pairwise. Markov random Fields and Segmentation of Textured Images. Machine Graphics and Vision. 2000, 9(3). 705-718.
[35] Destrempes F., Mignotte M. A Statistical Model for Contours in Images. IEEE Trans. Pattern Analysis and Machine Intelligence. 2004, 26(5). 626-238.
[36] Benboudjema D., Pieczynski W. Unsupervised Image Segmentation Using Triplet Markov Fields. Computer Vision and Image Understanding. 2005, 99(3). 476-498.
[37] Pieczynski W., Benboudjema D. Multisensor Triplet Markov Fields and Theory of Evidence. Image and Vision Computing. 2006, 24(1). 61-69.
[38] Lanchantin P., Pieczynski W. Unsupervised NonStationary Image Segmentation Using Triplet Markov Chains. Proc. Advanced Concepts for Intelligent Vision Systems. 2004, 31(3). 1-6.
[39] Benboudjema D., Tupin F., Pieczynski W., et al. Unsupervised segmentation of SAR images using Triplet Markov fields and Fisher noise distributions. IEEE International Geoscience and Remote Sensing Symposium. 2007, 3891-3893.
[40] Lanchantin P., Pieczynski W. Unsupervised segmentation of triplet Markov chains hidden with long-memory noise. Advanced Concepts for Intelligent Vision Systems. 2008, 88(5). 1134-1151.
[41] Blanchet J., Forbes F. Triplet Markov Fields for the Classification of Complex Structure Data. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2008, 30(6). 1055-1067.
[42] Benboudjema D., Pieczynski W. Unsupervised Statistical Segmentation of Nonstationary Images Using Triplet Markov Fields. IEEE Transactions on Pattern analysis and Machine intelligence. 2007, 29(8). 1367-1378.
[43]张澄波.综合孔径雷达原理、系统分析与应用.第一版.北京:科学出版社,1989. 19-59.
[44] Cumming I.G.等著,洪文等译.合成孔径雷达成像-算法与实现.第一版.北京:北京工业出版社, 2007. 154-243.
[45]王超,张红,陈曦等.全极化合成孔径雷达图像处理.第一版.北京:科学出版社,2008. 55-57.
[46] Moreira A. Improved Multilook Techniques Applied to SAR and SCANSAR Imagery. IEEE Transaction on Geoscience and Remote Sensing. 1991, 29(4). 529-534.
[47] Goodman J.W. Some Fundamental Properties of Speckle. Journal of the Optical Society of America. 1976, 66(11). 1145-1150.
[48] Norvang Madsen S. Spectral Properties of Homogeneous and Non-homogeneous Radar Image. IEEE Transaction on Aerospace Electronic Systems. 1987, 23(58). 3-58.
[49] Oliver C., Quegan S. Understanding synthetic Aperture radar images. Artech House Eds, Norwood(MA). 1998.
[50] Verhoeye J., Wulf D. An Image Processing Chain for Land-Cover Classification Using Multitemporal ERS-1 Data. Photogrammetric Engineering and Remote Sensing. 1999, 65(10). 1179-1514.
[51] Gonzalez R. C., Wood R. E. Digital Image Processing. 3rd.ed. Addison-wesley. 1992.
[52]李禹.合成孔径雷达图像分割技术综述.宇航学报. 2008, 29(2). 407-412.
[53] Giordana N., Pieczynski W. Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation. IEEE Trans. Pattern Analysis and Machine Intelligence. 1997, 19(5). 65-475.
[54] Destrempes F., Mignotte M. A Statistical Model for Contours in Images. IEEE Trans. Pattern Analysis and Machine Intelligence. 2004, 26(5). 626-238.
[55]刘振华,毛士艺,袁运. SAR图像组合分割算法.电子学报. 2003, 31(6). 833-836.
[56] Vincent L., Soille P. Watersheds in digital spaces: An efficient algorithm based on immersion simulations. IEEE Trans. On PAMI. 1991, 13(6). 583-598.
[57] Lombardo P., Farina A. Coherent radar detection against K-distributed clutter with partially correlated texture . Signal Processing. 1996, 48(1). 1-15.
[58] Derin H., Elliot H. Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Trans. on PAMI. 1987, 9(1). 39-55.
[59] Descombes X., Morris R.D., Zerubia J., et al. Estimation of Markov Random Field Prior Parameters Using Markov Chain Monte Carlo Maximum Likelihood. IEEE Trans. Image Processing. 1999, 8(7). 954-963.
[60] Benboudjema D., Pieczynski W. Unsupervised Image Segmentation Using Triplet Markov Fields. Computer Vision and Image Understanding. 2005, 99(3). 476-498.
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