顾及梯度的高斯混合模型在三维属性场空间聚类中的应用
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摘要
针对高斯混合模型(GMM)在空间聚类中由于忽视目标对象之间的空间关联性而导致的高误判率等问题,本文提出了一种顾及梯度的高斯混合模型:GMM-G,并将其应用在三维属性场的空间聚类中。GMM-G用反映标量场最大属性变化方向的梯度因子来定义邻域规则,设定梯度正交平面所通过的邻域体元更倾向于与中心体元归属于相同或相近的类别;并据此设计了符合归一性和空间连续性的空间邻域信息函数,来定义中心体元属于各类别的具有空间领域规则约束的后验概率。通过对由蒙特卡洛随机抽样构建的实验场的空间聚类结果进行对比表明,相对GMM方法,GMM-G具有更优的聚类精度及效率。最后,把GMM-G方法用于红透山铜矿区可控源音频大地电磁法(CSAMT)三维视电阻率场的空间聚类,得到了与已知岩性划分具有较高匹配度的分类结果,该方法可为物性属性场的岩性划分及地质推断提供相关的依据和参考。
To solve the problem of high rate of misjudgment due to ignoring the target objects' spatial correlation in the Gaussian mixture model(GMM)spatial clustering this paper proposes a new spatial clustering method,i.e.the gradient-based Gaussian mixture model(GMM-G)and it is applied to spatial clustering of three-dimensional attribute field.In this method the gradient factor,which reflects the biggest attribute changing direction of scalar field is selected to define the neighborhood rules and is assumed that the neighboring voxels,which is intersected by the gradient orthogonal plane,are more inclined to belonged to the same or similar class as the central voxel.Accordingly,the spatial neighborhood information function which make need of unitary and spatial continuity is designed to define the posteriori probability of central voxel belonging to various class with rules of the spatial constraints.The experimental results show that the GMM-G method has better clustering accuracy and efficiency than the GMM method in the spatial clustering of experimental filed which is created by the Monte Carlo random sampling technique.In the end,the GMM-G method is applied in spatial clustering of the controlled source audio-frequency magnetotelluric method(CSAMT)three-dimensional resistivity field in Hongtoushan copper mining area,NE China.The clustering result has the high matching ratio with the known lithology classification,therefore,this method can provide the lithology classification and geological inferences of geophysical attribute field with the basis and references.
To solve the problem of high rate of misjudgment due to ignoring the target objects' spatial correlation in the Gaussian mixture model(GMM)spatial clustering this paper proposes a new spatial clustering method,i.e.the gradient-based Gaussian mixture model(GMM-G)and it is applied to spatial clustering of three-dimensional attribute field.In this method the gradient factor,which reflects the biggest attribute changing direction of scalar field is selected to define the neighborhood rules and is assumed that the neighboring voxels,which is intersected by the gradient orthogonal plane,are more inclined to belonged to the same or similar class as the central voxel.Accordingly,the spatial neighborhood information function which make need of unitary and spatial continuity is designed to define the posteriori probability of central voxel belonging to various class with rules of the spatial constraints.The experimental results show that the GMM-G method has better clustering accuracy and efficiency than the GMM method in the spatial clustering of experimental filed which is created by the Monte Carlo random sampling technique.In the end,the GMM-G method is applied in spatial clustering of the controlled source audio-frequency magnetotelluric method(CSAMT)three-dimensional resistivity field in Hongtoushan copper mining area,NE China.The clustering result has the high matching ratio with the known lithology classification,therefore,this method can provide the lithology classification and geological inferences of geophysical attribute field with the basis and references.
引文
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[11]王丽芳，吴湘滨，张宝一，李小丽，杨莉．一种可存储路径的三维非均质空间最短距离场生成算法[J]．吉林大学学报：地球科学版，2015,45(4):1257-1268．
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[17]汪闽，周成虎，裴韬，骆剑承．MSCMO：基于数学形态学算子的尺度空间聚类方法[J]．遥感学报，2004,8(1):45-50．
[18]Bishop C M.Pattern Recognition and Machine Learning[M].New York:Springer,2006．
[19]艾廷华，郭仁忠．基于格式塔识别原则挖掘空间分布模式[J]．测绘学报，2007,36(3):302-308．
[20]Murphy K P.Machine learning:aprobabilistic perspective[M].Cambridge,MA,USA:The MIT Press,2012．
[21]Richards J A.Remote sensing digital image analysis:an introduction[M].Fifth Edition.Heidelberg:Springer,2013．
[22]李德仁，王树良，李德毅．空间数据挖掘理论与应用[M]．第2版．北京：科学出版社，2013．
[23]Dempster A P.Maximan likelihood estimation from incomplete data via the algorithm[J].J Roystatist Soc B,1977,39:1-38．
[24]Wells W M,Grimson W L,Kikinis R,Jolesz F A.Adaptive segmentation of MRI data[J].IEEE Transactions on Medical Imaging,1996,15(4):429-442．
[25]Guillemaud R,Brady M.Estimating the bias field of MR images[J].IEEE Transactions on Medical Imaging,1997,16(3):238-251．
[26]Stauffer C,Grimson W E L.Learning patterns of activity using real-time tracking[J].IEEE Transactions on Pattern A-nalysis and Machine Intelligence,2000,22(8):747-757．
[27]Xu R,Wunsch D.Survey of clustering algorithms[J].IEEETransactions on Neural Networks,2005,16(3):645-678．
[28]向晶，周绍光，陈超．基于改进高斯混合模型的遥感影像道路提取[J]．测绘工程，2014,23(3):42-45．
[29]Tso B,Mather P M.Classification methods for remotely sensed data[M].Second Edition.Boca Raton:CRC Press,2009．
[30]Sanjay-Gopal S,Hebert T J.Bayesian pixel classification using spatially variant finite mixtures and the generalized EMalgorithm[J].IEEE transactions on image processing,1998,7(7):1014-1028．
[31]Blekas K,Likas A,Galatsanos N P,Lagaris I E.A spatially constrained mixture model for image segmentation[J].IEEETransactions on Neural Networks,2005,16(2):494-498．
[32]Zhang Y Y,Brady M,Smith S.Segmentation of brain MRimages through a hidden Markov random field model and the expectation-maximization algorithm[J].IEEE transactions on medical imaging,2001,20(1):45-57．
[33]Greenspan H,Ruf A,Goldberger J.Constrained Gaussian mixture model framework for automatic segmentation of MRbrain images[J].IEEE transactions on medical imaging,2006,25(9):1233-1245．
[34]Alfo M,Nieddu L,Vicari D.A finite mixture model for image segmentation[J].Statistics and Computing,2008,18(2):137-150．
[35]Nikou C,Galatsanos N P,Likas A C.A class-adaptive spatially variant mixture model for image segmentation[J].IEEE transactions on image processing,2007,16(4):1121-1130．
[36]Zhang H,Wen T,Zheng Y,Xu D,Wang D,Nguyen T M,Wu Q M J.Two Fast and Robust Modified Gaussian Mixture Models Incorporating Local Spatial Information for Image Segmentation[J].Journal of Signal Processing Systems,2015,81(1):45-58．
[37]Xiong T,Zhang L,Yi Z.Double Gaussian mixture model for image segmentation with spatial relationships[J].Journal of Visual Communication and Image Representation,2016,34:135-145．
[38]Tang H,Dillenseger J L,Bao X D,Luo L M.A vectorial image soft segmentation method based on neighborhood weighted Gaussian mixture model[J].Computerized Medical Imaging and Graphics,2009,33(8):644-650．
[39]朱峰，罗立民，宋余庆，陈健美，左欣．基于自适应空间邻域信息高斯混合模型的图像分割[J]．计算机研究与发展，2011,48(11):2000-2007．
[40]Ari C,Aksoy S.Detection of Compound Structures Using a Gaussian Mixture Model With Spectral and Spatial Constraints[J].IEEE Transactions on Geoscience and Remote Sensing,2014,52(10):6627-6638．
[41]Dong F,Peng J.Brain MR image segmentation based on local Gaussian mixture model and nonlocal spatial regularization[J].Journal of Visual Communication and Image Representation,2014,25(5):827-839．
[42]Zhao B,Zhong Y,Ma A,Zhang L.A Spatial Gaussian Mixture Model for Optical Remote Sensing Image Clustering[J].IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2016,9(12):5748-5759．
[43]Meena Prakash R,Kumari R S S.Gaussian Mixture Model with the Inclusion of Spatial Factor and Pixel Re-labelling:Application to MR Brain Image Segmentation[J].Arabian Journal for Science and Engineering,2017,42(2):595-605．
[44]Metropolis N,Ulam S.The Monte Carlo method[J].Journal of the American Statistical Association,1949,44(247):335-341.
[2]安聪荣，刘展，黄荣刚，白永良．基于三维栅格模型的最短距离等值面提取[J]．计算机工程，2011,37(8):7-9．
[3]Carranza E J M,Hale M.Spatial association of mineral occurrences and curvilinear geological features[J].Mathematical Geology,2002,34(2):203-221．
[4]李芳玉，潘懋，朱雷．三维缓冲体生成栅格算法研究[J]．计算机辅助设计与图形学学报，2005,17(9):1928-1932．
[5]Payne C E,Cunningham F,Peters K J,Nielsen S,Puccioni E,Wildman C,Partington G A.From 2Dto 3D:Prospectivity modelling in the Taupo Volcanic Zone,New Zealand[J].Ore Geology Reviews,2015,71:558-577．
[6]Wang G W,Li R X,Carranza E J M,Zhang S T,Yan C H,Zhu Y Y,Qu J N,Hong D M,Song Y W,Han J W,Ma Z B,Zhang H,Yang F.3Dgeological modeling for prediction of subsurface Mo targets in the Luanchuan district,China[J].Ore Geology Reviews,2015,71:592-610．
[7]李楠，肖克炎，阴江宁，范建福，王琨．表面模型缓冲区分析方法[J]．计算机辅助设计与图形学学报，2015,27(9):1625-1636．
[8]Li N,Bagas L,Li X H,Xiao K Y,Li Y,Ying L J,Song XL.An improved buffer analysis technique for model-based 3Dmineral potential mapping and its application[J].Ore Geology Reviews,2016,76:94-107．
[9]毛先成，邹艳红，陈进，赖健清，彭省临．隐伏矿体三维可视化预测[M]．长沙：中南大学出版社，2011．
[10]Li X H,Yuan F,Zhang M M,Jia C,Jowitt S M,Ord A,Zheng T K,Hu X Y,Li Y.Three-dimensional mineral prospectivity modeling for targeting of concealed mineralization within the Zhonggu iron orefield,Ningwu Basin,China[J].Ore Geology Reviews,2015,71:633-654．
[11]王丽芳，吴湘滨，张宝一，李小丽，杨莉．一种可存储路径的三维非均质空间最短距离场生成算法[J]．吉林大学学报：地球科学版，2015,45(4):1257-1268．
[12]张宝一，代鹏遥，蒙菲，王丽芳，吴湘滨．基于距离场的三维矿体模型与地表化探数据的关联关系分析---以红透山铜矿田为例[J]．地质论评，2017,63(2):511-524．
[13]张宝一，吴湘滨，王丽芳，刘文玉，杜方．红透山铜矿外围隐伏矿体三维定量预测[J]．中国有色金属学报，2012,22(3):863-871．
[14]毛先成，唐艳华，邓浩．地质体的三维形态分析方法与应用[J]．中南大学学报：自然科学版，2012,43(2):588-595．
[15]Mao X,Zhang B,Deng H,Zou Y,Chen J.Three-dimensional morphological analysis method for geologic bodies and its parallel implementation[J].Computers&Geosciences,2016,96:11-22．
[16]McLachlan G J,Peel D.Finite mixture models[M].New York:Wiley,2000．
[17]汪闽，周成虎，裴韬，骆剑承．MSCMO：基于数学形态学算子的尺度空间聚类方法[J]．遥感学报，2004,8(1):45-50．
[18]Bishop C M.Pattern Recognition and Machine Learning[M].New York:Springer,2006．
[19]艾廷华，郭仁忠．基于格式塔识别原则挖掘空间分布模式[J]．测绘学报，2007,36(3):302-308．
[20]Murphy K P.Machine learning:aprobabilistic perspective[M].Cambridge,MA,USA:The MIT Press,2012．
[21]Richards J A.Remote sensing digital image analysis:an introduction[M].Fifth Edition.Heidelberg:Springer,2013．
[22]李德仁，王树良，李德毅．空间数据挖掘理论与应用[M]．第2版．北京：科学出版社，2013．
[23]Dempster A P.Maximan likelihood estimation from incomplete data via the algorithm[J].J Roystatist Soc B,1977,39:1-38．
[24]Wells W M,Grimson W L,Kikinis R,Jolesz F A.Adaptive segmentation of MRI data[J].IEEE Transactions on Medical Imaging,1996,15(4):429-442．
[25]Guillemaud R,Brady M.Estimating the bias field of MR images[J].IEEE Transactions on Medical Imaging,1997,16(3):238-251．
[26]Stauffer C,Grimson W E L.Learning patterns of activity using real-time tracking[J].IEEE Transactions on Pattern A-nalysis and Machine Intelligence,2000,22(8):747-757．
[27]Xu R,Wunsch D.Survey of clustering algorithms[J].IEEETransactions on Neural Networks,2005,16(3):645-678．
[28]向晶，周绍光，陈超．基于改进高斯混合模型的遥感影像道路提取[J]．测绘工程，2014,23(3):42-45．
[29]Tso B,Mather P M.Classification methods for remotely sensed data[M].Second Edition.Boca Raton:CRC Press,2009．
[30]Sanjay-Gopal S,Hebert T J.Bayesian pixel classification using spatially variant finite mixtures and the generalized EMalgorithm[J].IEEE transactions on image processing,1998,7(7):1014-1028．
[31]Blekas K,Likas A,Galatsanos N P,Lagaris I E.A spatially constrained mixture model for image segmentation[J].IEEETransactions on Neural Networks,2005,16(2):494-498．
[32]Zhang Y Y,Brady M,Smith S.Segmentation of brain MRimages through a hidden Markov random field model and the expectation-maximization algorithm[J].IEEE transactions on medical imaging,2001,20(1):45-57．
[33]Greenspan H,Ruf A,Goldberger J.Constrained Gaussian mixture model framework for automatic segmentation of MRbrain images[J].IEEE transactions on medical imaging,2006,25(9):1233-1245．
[34]Alfo M,Nieddu L,Vicari D.A finite mixture model for image segmentation[J].Statistics and Computing,2008,18(2):137-150．
[35]Nikou C,Galatsanos N P,Likas A C.A class-adaptive spatially variant mixture model for image segmentation[J].IEEE transactions on image processing,2007,16(4):1121-1130．
[36]Zhang H,Wen T,Zheng Y,Xu D,Wang D,Nguyen T M,Wu Q M J.Two Fast and Robust Modified Gaussian Mixture Models Incorporating Local Spatial Information for Image Segmentation[J].Journal of Signal Processing Systems,2015,81(1):45-58．
[37]Xiong T,Zhang L,Yi Z.Double Gaussian mixture model for image segmentation with spatial relationships[J].Journal of Visual Communication and Image Representation,2016,34:135-145．
[38]Tang H,Dillenseger J L,Bao X D,Luo L M.A vectorial image soft segmentation method based on neighborhood weighted Gaussian mixture model[J].Computerized Medical Imaging and Graphics,2009,33(8):644-650．
[39]朱峰，罗立民，宋余庆，陈健美，左欣．基于自适应空间邻域信息高斯混合模型的图像分割[J]．计算机研究与发展，2011,48(11):2000-2007．
[40]Ari C,Aksoy S.Detection of Compound Structures Using a Gaussian Mixture Model With Spectral and Spatial Constraints[J].IEEE Transactions on Geoscience and Remote Sensing,2014,52(10):6627-6638．
[41]Dong F,Peng J.Brain MR image segmentation based on local Gaussian mixture model and nonlocal spatial regularization[J].Journal of Visual Communication and Image Representation,2014,25(5):827-839．
[42]Zhao B,Zhong Y,Ma A,Zhang L.A Spatial Gaussian Mixture Model for Optical Remote Sensing Image Clustering[J].IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2016,9(12):5748-5759．
[43]Meena Prakash R,Kumari R S S.Gaussian Mixture Model with the Inclusion of Spatial Factor and Pixel Re-labelling:Application to MR Brain Image Segmentation[J].Arabian Journal for Science and Engineering,2017,42(2):595-605．
[44]Metropolis N,Ulam S.The Monte Carlo method[J].Journal of the American Statistical Association,1949,44(247):335-341.
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