星载SAR图像与光学图像配准方法研究
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摘要
图像配准技术在机器视觉、模式识别、医学图像分析、遥感图像处理等诸多领域中已成为研究热点。本文在分析与探讨多源卫星图像配准技术难点的基础上,以星载SAR(synthetic aperture radar)图像与光学图像配准技术为工作重点,确定了本文的研究方案,相关工作及主要贡献如下:
1.SAR图像的分割。SAR图像分割作为提取SAR图像中的闭合区域的关键步骤在本文得到重点讨论。针对SAR图像斑点噪声的特点,对目前国际上较为流行的分割方法进行分析,提出了联合MAP(Maximum a Posterior)准则与规则化SRAD(Speckle Reducing Anisotropic Diffusion)模型的分割方法和基于自适应规则化非线性扩散滤波的C均值分割两种分割方法,前者属于结合SAR图像结构与强度信息的分割方法,即在分割的过程中抑制斑点噪声,有着较高的分割精度,适用于视数较高的SAR图像数据;后者属于基于滤波的分割方法,算法时间复杂度低于前者,适用于视数较低的大幅SAR图像数据。在文中根据不同的SAR图像数据使用不同的分割方法,取得了较好的折衷。
2.光学图像的滤波与分类。光学图像较SAR图像具有较高的图像质量,但有时仍受到高斯热噪声的污染。因此,仍需要通过滤波和增强来改善图像质量。针对二阶偏微分方程在对光学图像滤波时带来的不足,本文使用四阶偏微分方程对光学遥感影像进行预处理,因为四阶偏微分方程的处理结果是分段线性的,因此视觉效果优于二阶偏微分方程视觉效果,能较好地反映图像的真实信息。在好的滤波基础上对图像进行C均值分类得到好的分类结果。
3.基于Hausdorff距离与遗传算法的配准。提出了基于Hausdorff距离与遗传算法搜索策略的配准方法,在分别提取出SAR图像和光学图像闭合区域边缘作为特征后,使用Hausdorff距离作为两组特征间的相似性度量,使用遗传算法估算出映射参数。配准过程中,将由遗传算法解算五个映射参数的过程分为两步,保证每次使用遗传算法时适应度函数的变量不超过三维,这使得遗传算法即使在搜索范围较大的情况下也能较快地收敛到全局最优。最后使用二值图像相关度进行精配准来解决轻微扭曲的情况。
Image registration is a research focus in many fields such as computer vision, pattern recognition, medical image analysis and remote sensing image processing, etc. After analyzing the difficulty of multi-sensor images registration, we focus on the study of automatic registration for SAR and optical satellite images. The related work and mainly contribution as follows:
1. SAR images segmentation. SAR images segmentation as the most important step of closed-region abstracting is been emphasized in this thesis. Based on an analytical review of several classic segmentation methods, two novel algorithms are proposed for SAR segmentation. The first one is named combine MAP (Maximum a Posterior) criterion and SRAD (Speckles Reducing Anisotropic Diffusion) model which belong to the kinds of method segmenting SAR images using structures and intensity information. These kinds of method reducing speckle during the process of segmentation and having a high accuracy are fit for greater number of looks SAR images segmentation. The second one is called segmentation based on adaptive regularizing non-linear diffusion equations which belong to the other kinds of method that segment SAR images despeckled using method segmenting optical images. These methods are applied for big size and lower number of looks SAR images. We compromise these two methods according to the size and resolution of images.
2. Optical image filtering and segmentation. Optical images always corrupted by additive Gaussian white noise, so we have to improve quantity of images by filtering and enhancing. A class of fourth-order partial differential equations is used to optimize the trade-off between noise removal and edge preservation. Since the Laplacian of an image at a pixel is zero if the image is planar in its neighborhood, these PDEs attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image. Piecewise planar images look more nature than step images. Then C-means is used for segmenting filtered optical image.
3. Registration using Hausdorff distance and Genetic Algorithm. A registration method using Hausdorff distance and Genetic Algorithm is proposed. After exstrcting closed regions from SAR and optical satellite image, Hausdorff distance and genetic algorithm are applied to estimate the parameters of transformation between two images. We separate the process of searching five parameters in two steps in order to ensure that there are no more than three parameters in each search step. This way can enhance the searching speed. At the last, registration refinement based on binary correlation is used for solving mild distortion problem.
1.SAR图像的分割。SAR图像分割作为提取SAR图像中的闭合区域的关键步骤在本文得到重点讨论。针对SAR图像斑点噪声的特点,对目前国际上较为流行的分割方法进行分析,提出了联合MAP(Maximum a Posterior)准则与规则化SRAD(Speckle Reducing Anisotropic Diffusion)模型的分割方法和基于自适应规则化非线性扩散滤波的C均值分割两种分割方法,前者属于结合SAR图像结构与强度信息的分割方法,即在分割的过程中抑制斑点噪声,有着较高的分割精度,适用于视数较高的SAR图像数据;后者属于基于滤波的分割方法,算法时间复杂度低于前者,适用于视数较低的大幅SAR图像数据。在文中根据不同的SAR图像数据使用不同的分割方法,取得了较好的折衷。
2.光学图像的滤波与分类。光学图像较SAR图像具有较高的图像质量,但有时仍受到高斯热噪声的污染。因此,仍需要通过滤波和增强来改善图像质量。针对二阶偏微分方程在对光学图像滤波时带来的不足,本文使用四阶偏微分方程对光学遥感影像进行预处理,因为四阶偏微分方程的处理结果是分段线性的,因此视觉效果优于二阶偏微分方程视觉效果,能较好地反映图像的真实信息。在好的滤波基础上对图像进行C均值分类得到好的分类结果。
3.基于Hausdorff距离与遗传算法的配准。提出了基于Hausdorff距离与遗传算法搜索策略的配准方法,在分别提取出SAR图像和光学图像闭合区域边缘作为特征后,使用Hausdorff距离作为两组特征间的相似性度量,使用遗传算法估算出映射参数。配准过程中,将由遗传算法解算五个映射参数的过程分为两步,保证每次使用遗传算法时适应度函数的变量不超过三维,这使得遗传算法即使在搜索范围较大的情况下也能较快地收敛到全局最优。最后使用二值图像相关度进行精配准来解决轻微扭曲的情况。
Image registration is a research focus in many fields such as computer vision, pattern recognition, medical image analysis and remote sensing image processing, etc. After analyzing the difficulty of multi-sensor images registration, we focus on the study of automatic registration for SAR and optical satellite images. The related work and mainly contribution as follows:
1. SAR images segmentation. SAR images segmentation as the most important step of closed-region abstracting is been emphasized in this thesis. Based on an analytical review of several classic segmentation methods, two novel algorithms are proposed for SAR segmentation. The first one is named combine MAP (Maximum a Posterior) criterion and SRAD (Speckles Reducing Anisotropic Diffusion) model which belong to the kinds of method segmenting SAR images using structures and intensity information. These kinds of method reducing speckle during the process of segmentation and having a high accuracy are fit for greater number of looks SAR images segmentation. The second one is called segmentation based on adaptive regularizing non-linear diffusion equations which belong to the other kinds of method that segment SAR images despeckled using method segmenting optical images. These methods are applied for big size and lower number of looks SAR images. We compromise these two methods according to the size and resolution of images.
2. Optical image filtering and segmentation. Optical images always corrupted by additive Gaussian white noise, so we have to improve quantity of images by filtering and enhancing. A class of fourth-order partial differential equations is used to optimize the trade-off between noise removal and edge preservation. Since the Laplacian of an image at a pixel is zero if the image is planar in its neighborhood, these PDEs attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image. Piecewise planar images look more nature than step images. Then C-means is used for segmenting filtered optical image.
3. Registration using Hausdorff distance and Genetic Algorithm. A registration method using Hausdorff distance and Genetic Algorithm is proposed. After exstrcting closed regions from SAR and optical satellite image, Hausdorff distance and genetic algorithm are applied to estimate the parameters of transformation between two images. We separate the process of searching five parameters in two steps in order to ensure that there are no more than three parameters in each search step. This way can enhance the searching speed. At the last, registration refinement based on binary correlation is used for solving mild distortion problem.
引文
[1].Brown,L.G,A Survey of Image Registration Techniques,ACM Computer surveys,1992,24(4).
[2].Li,H.,Manjunath,B.S.and Mitra,S.K.,A Contour-Based Approach to Multi-sensor Image Registration,IEEE Transactions on Image Processing,1995,4(3):320-334.
[3].Thepaut,O.,Kpalma,K.and Ronsin,J.,Automatic Registration of ERS and SPOT Multi-sensor Images in A Data Fusion Context,Forest Ecology and Management,2000,93-100.
[4].Dowman,I.,and Dare,P.,Automated Procedures for Multi-sensor Registration and Orthorectification of Satellite Images,International Archives of Photogrammetry and Remote Sensing,1999,32(7-4-3 W6):37-44.
[5].Lisa Gottesfeld Brown.,A survey of image registration techniques,ACM computing Surveys,1992,24(4):326-376
[6].Kuglin C D,Hines D C.,The phase correlation image alignment method,In proceeding of the IEEE 1975 International Conference on Cybernetics and Society(sept).New York,1975,63-165.
[7].Brown,L.G,A Survey of Image Registration Techniques,ACM Computer Surveys,1992,24(4).
[8].Stockman,G,Kopstein,S.and Benett,S.,Matching Images to Models for Registration and Object via Clustering,IEEE Transactions on Pattern Analysis and Machine Intelligence,1982,4(3):229-241.
[9].Goshtasby,A.,Stockman,G C,and Page,C V.,A Region-Based Approach to Digital Image Registration with Subpixel Accuracy,IEEE Transactions on Geoscience and Remote Sensing,1986,GE-24(3):390-399.
[10].Flusser,J.and Suk,T.,A Moment-Based Approach to Registration of Images with Affine Geometric Distortion,IEEE Transactions on Geoscience and Remote Sensing,1994,32(2):382-387.
[11].Yosi Keller,Amir averbuch,A New Approach to Multi-sensor Image Registration,Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2003,1-6.
[12].Q.Zheng and R.Chellappa,A computational vision approach to image registration,IEEE Trans.Image Processing,1993,331-326.
[13].A.Ventura,A.Rampini,and R.Schettini,Image registration by recognition of corresponding structures.IEEE Trans.Ceosti.Remote Sensing,1990,28:305-314.
[14].J.Greenfeld,An operator-based matching system,Photogrammetric Eng.,Remote Sensing,1991,57:1049-1055.
[15].于秋则,基于改进Hausdorff测度和遗传算法的SAR图像与光学图像匹配,宇航学报,2005,27(1):130-134.
[16].R.Cook,I.McConnell,MUM(Merge Using Moments) Segmentation for SAR Images,Proc.SPIE 2316,1994,92-103.
[17].R.Cook,I.McConnell,D.Stewart,Segmentation and Simulated Annealing,Euopto Conf. On SAR Image Analysis,Simulation and Modelling Ⅱ,SPIE Proc.,1996,2958:30-37.
[18].R.Touzi,A.Lopes,P.Bousquet,A Statistical and Geometrical Edge Detector for SAR Images,IEEE Trans.Geosci.Remote Sensing,1988,26(6):764-773.
[19].Robert A.Weisenseel,W.Clem Karl,et al.Markov Random Filed Segmentation Methods for SAR Target Chips.1999,SPIE 3721.
[20].Dane P.Kottke,Paul D.Fiore,et al.A Design for HMM-Based SAR ATR,Proc,1998,SPIE 3370:541-551.
[21].Robert A.Weisenseel,W.Clem Kar,et al.MRF-Based Algorithms for Segmentation of SAR Images,the Proceeding of the 1998 International Conference on Image Processing,IEEE,1998,3:770-774.
[22].Geman S,Geman D.,Stochastic relaxation,Gibbs distribution and the Bayesian restoration of images,IEEE Trans.on Pattern Analysis and Machine Intelligence,1984,6(6):721-741.
[23].Charles H.Fosgate,Hamid Krim,et.al.Multi-scale Segmentation and Anomaly Enhancement of SAR Imagery.IEEE Transactions on Image Processing,1997,6(1):7-20.
[24].Hyeokhq Choi,Richard G.Baraniuk.Multi-scale Image Segmentation Using Wavelet-Domain Hidden Markov Models.IEEE Transactions on Image Processing,2001.9,10(9):1309-1321.
[25].王正明,朱炬波,SAR图像提高分辨率技术,科学出版社,北京,2006.
[26].Frerry A C,Muller H J,Yannasse C C F,Sant'Anna S J S.A model for extremely heterogeneous clutter.IEEE Trans.Geosci.Remote Sensing,1986,GE-24:234-245.
[27].Ulaby F T,Kouyate F,Brisco B,Williams T M.Textural information in SAR images.IEEE Transactions on Geoscience and Remote Sensing,1986,GE-24:234-245.
[28].Jakeman E,Tough.Generalized K-distribution:a stastical model for weak scattering.J.Opt.Soc.Am.A,1987,4(9):1764-1772.
[29].A.Witldn,Scale-space filtering,Int.Joint Conf.Artificial Imtelligence,Karlsruhe,Germany,1983,1019-1021.
[30].J.Koenderink,The structure of images,Biol.Cybem.,1984,50:363-370.
[31].A.Hummel,Representation based on zero-crossings in scale-space,Proc.IEEE Computer Vision and Pattern Recognition Conf.,1986,204-209.
[32].L.Alvazrez,F.Guichard,P.L.Lions,J.M.Morel,Axioms and fundamental equations of image processing,Archive for Rational Mechanics and Analysis,1993,199-257.
[33].Perona P,Malik J.Scale-space and edge detection using anisotropic diffusion.IEEE Transaction on Pattem Analysis and Machine Intelligence,1990,12(7):629-639.
[34].Yongjian Yu,Scot T Acton.Speckle reduction anisotropic diffusion.IEEE Transaction on Image processing,2002,11(11):1260-1270.
[35].F.CATTE,P.L.Lions,J.M.Morel,T.Coil,Image selective smoothing and edge detection diffusion Ⅱ,SIAM J.Numer.Anal,1992,29:845-866.
[36].S.Teboul,L.Blanc-Feraud,G.Aubert,et al.,Variational approach for edge-preserving regularization using coupled PDE's,IEEE Trans.Image Proc.,1998,7(3),pp:387-397.
[37].Michael Struwe.Variational Methods.Berlin:Springer_Verlag,1996.
[38].李荣华,冯果忱,微分方程数值解法,北京,人民教育出版社,1980.
[39].高贵,基于各向异性热扩散方程的SAR图像分割方法,信号处理,2006,22(1):105-109.
[40].Lee S J.Refined filtering of image noise using local statistic.Computer graphic and image processing,1981,15(4):380-389.
[41].Kuan T D.et al.Adaptive resolution of images with speckle.IEEE Trans.ASSP.,1987, 35(3):373-383.
[42].Frost S V.et al.A model for radar images and its application to adaptive digital filtering of multiplieative noise.IEEE Trans.Pattern Analysis and Machine Intelligence,1982,4(2):157-166.
[43].R.Touzi,A.Lopes,P.Bousquet,A statistical and geometrical edge detector for SAR images,IEEE Trans.Geosci.And Remote Sensing,1988,26(6),764-773.
[44].刘振华,毛士艺,自适应SAR图像边缘检测算法,电子与信息学报,2003,25(4):467-472.
[45].孙即祥,现代模式识别,长沙,国防科技大学出版社,2002.
[46].Y.L.You,W.Xu,A.Tannenbaum,and M.Kaveh,Behavioral analysis of anisotropic diffusion in image processing,IEEE Trans.Image Processing,1996,5:1539-1553.
[47].Yu-Li You,M.Kaveh,Fourth-Order Partial Differential Equations for Noise Removal,IEEE Transactions on image processing,2000,9(10):1723-1730.
[48].L.I.Rudin,S.Osher,and E.Fatemi,Nonlinear total variation based noise removal algorithms,Physica D,1992,60:259-268.
[49].Dong-Gyn Sim etl.Object matching algorithms using robust hausdorff distance measures.IEEE Transaction on Image Processing,1999,8(1):425-429.
[50].Huttenlocher D P,Klanderman G A and Rucklidge W J.Comparing images using the Hausdorff distance.IEEE Trans Pattem Anal Machine Intelligence,1993,15:850-863.
[51].Fogel,L.J.,Owens,A.J.,and Walsh,M.J.Artificial intelligence through simulated evolution.NewYork John Wiley & Sons,1996.
[52].刘勇,康立山,非数值并行算法,北京,科学出版社,2003.
[2].Li,H.,Manjunath,B.S.and Mitra,S.K.,A Contour-Based Approach to Multi-sensor Image Registration,IEEE Transactions on Image Processing,1995,4(3):320-334.
[3].Thepaut,O.,Kpalma,K.and Ronsin,J.,Automatic Registration of ERS and SPOT Multi-sensor Images in A Data Fusion Context,Forest Ecology and Management,2000,93-100.
[4].Dowman,I.,and Dare,P.,Automated Procedures for Multi-sensor Registration and Orthorectification of Satellite Images,International Archives of Photogrammetry and Remote Sensing,1999,32(7-4-3 W6):37-44.
[5].Lisa Gottesfeld Brown.,A survey of image registration techniques,ACM computing Surveys,1992,24(4):326-376
[6].Kuglin C D,Hines D C.,The phase correlation image alignment method,In proceeding of the IEEE 1975 International Conference on Cybernetics and Society(sept).New York,1975,63-165.
[7].Brown,L.G,A Survey of Image Registration Techniques,ACM Computer Surveys,1992,24(4).
[8].Stockman,G,Kopstein,S.and Benett,S.,Matching Images to Models for Registration and Object via Clustering,IEEE Transactions on Pattern Analysis and Machine Intelligence,1982,4(3):229-241.
[9].Goshtasby,A.,Stockman,G C,and Page,C V.,A Region-Based Approach to Digital Image Registration with Subpixel Accuracy,IEEE Transactions on Geoscience and Remote Sensing,1986,GE-24(3):390-399.
[10].Flusser,J.and Suk,T.,A Moment-Based Approach to Registration of Images with Affine Geometric Distortion,IEEE Transactions on Geoscience and Remote Sensing,1994,32(2):382-387.
[11].Yosi Keller,Amir averbuch,A New Approach to Multi-sensor Image Registration,Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2003,1-6.
[12].Q.Zheng and R.Chellappa,A computational vision approach to image registration,IEEE Trans.Image Processing,1993,331-326.
[13].A.Ventura,A.Rampini,and R.Schettini,Image registration by recognition of corresponding structures.IEEE Trans.Ceosti.Remote Sensing,1990,28:305-314.
[14].J.Greenfeld,An operator-based matching system,Photogrammetric Eng.,Remote Sensing,1991,57:1049-1055.
[15].于秋则,基于改进Hausdorff测度和遗传算法的SAR图像与光学图像匹配,宇航学报,2005,27(1):130-134.
[16].R.Cook,I.McConnell,MUM(Merge Using Moments) Segmentation for SAR Images,Proc.SPIE 2316,1994,92-103.
[17].R.Cook,I.McConnell,D.Stewart,Segmentation and Simulated Annealing,Euopto Conf. On SAR Image Analysis,Simulation and Modelling Ⅱ,SPIE Proc.,1996,2958:30-37.
[18].R.Touzi,A.Lopes,P.Bousquet,A Statistical and Geometrical Edge Detector for SAR Images,IEEE Trans.Geosci.Remote Sensing,1988,26(6):764-773.
[19].Robert A.Weisenseel,W.Clem Karl,et al.Markov Random Filed Segmentation Methods for SAR Target Chips.1999,SPIE 3721.
[20].Dane P.Kottke,Paul D.Fiore,et al.A Design for HMM-Based SAR ATR,Proc,1998,SPIE 3370:541-551.
[21].Robert A.Weisenseel,W.Clem Kar,et al.MRF-Based Algorithms for Segmentation of SAR Images,the Proceeding of the 1998 International Conference on Image Processing,IEEE,1998,3:770-774.
[22].Geman S,Geman D.,Stochastic relaxation,Gibbs distribution and the Bayesian restoration of images,IEEE Trans.on Pattern Analysis and Machine Intelligence,1984,6(6):721-741.
[23].Charles H.Fosgate,Hamid Krim,et.al.Multi-scale Segmentation and Anomaly Enhancement of SAR Imagery.IEEE Transactions on Image Processing,1997,6(1):7-20.
[24].Hyeokhq Choi,Richard G.Baraniuk.Multi-scale Image Segmentation Using Wavelet-Domain Hidden Markov Models.IEEE Transactions on Image Processing,2001.9,10(9):1309-1321.
[25].王正明,朱炬波,SAR图像提高分辨率技术,科学出版社,北京,2006.
[26].Frerry A C,Muller H J,Yannasse C C F,Sant'Anna S J S.A model for extremely heterogeneous clutter.IEEE Trans.Geosci.Remote Sensing,1986,GE-24:234-245.
[27].Ulaby F T,Kouyate F,Brisco B,Williams T M.Textural information in SAR images.IEEE Transactions on Geoscience and Remote Sensing,1986,GE-24:234-245.
[28].Jakeman E,Tough.Generalized K-distribution:a stastical model for weak scattering.J.Opt.Soc.Am.A,1987,4(9):1764-1772.
[29].A.Witldn,Scale-space filtering,Int.Joint Conf.Artificial Imtelligence,Karlsruhe,Germany,1983,1019-1021.
[30].J.Koenderink,The structure of images,Biol.Cybem.,1984,50:363-370.
[31].A.Hummel,Representation based on zero-crossings in scale-space,Proc.IEEE Computer Vision and Pattern Recognition Conf.,1986,204-209.
[32].L.Alvazrez,F.Guichard,P.L.Lions,J.M.Morel,Axioms and fundamental equations of image processing,Archive for Rational Mechanics and Analysis,1993,199-257.
[33].Perona P,Malik J.Scale-space and edge detection using anisotropic diffusion.IEEE Transaction on Pattem Analysis and Machine Intelligence,1990,12(7):629-639.
[34].Yongjian Yu,Scot T Acton.Speckle reduction anisotropic diffusion.IEEE Transaction on Image processing,2002,11(11):1260-1270.
[35].F.CATTE,P.L.Lions,J.M.Morel,T.Coil,Image selective smoothing and edge detection diffusion Ⅱ,SIAM J.Numer.Anal,1992,29:845-866.
[36].S.Teboul,L.Blanc-Feraud,G.Aubert,et al.,Variational approach for edge-preserving regularization using coupled PDE's,IEEE Trans.Image Proc.,1998,7(3),pp:387-397.
[37].Michael Struwe.Variational Methods.Berlin:Springer_Verlag,1996.
[38].李荣华,冯果忱,微分方程数值解法,北京,人民教育出版社,1980.
[39].高贵,基于各向异性热扩散方程的SAR图像分割方法,信号处理,2006,22(1):105-109.
[40].Lee S J.Refined filtering of image noise using local statistic.Computer graphic and image processing,1981,15(4):380-389.
[41].Kuan T D.et al.Adaptive resolution of images with speckle.IEEE Trans.ASSP.,1987, 35(3):373-383.
[42].Frost S V.et al.A model for radar images and its application to adaptive digital filtering of multiplieative noise.IEEE Trans.Pattern Analysis and Machine Intelligence,1982,4(2):157-166.
[43].R.Touzi,A.Lopes,P.Bousquet,A statistical and geometrical edge detector for SAR images,IEEE Trans.Geosci.And Remote Sensing,1988,26(6),764-773.
[44].刘振华,毛士艺,自适应SAR图像边缘检测算法,电子与信息学报,2003,25(4):467-472.
[45].孙即祥,现代模式识别,长沙,国防科技大学出版社,2002.
[46].Y.L.You,W.Xu,A.Tannenbaum,and M.Kaveh,Behavioral analysis of anisotropic diffusion in image processing,IEEE Trans.Image Processing,1996,5:1539-1553.
[47].Yu-Li You,M.Kaveh,Fourth-Order Partial Differential Equations for Noise Removal,IEEE Transactions on image processing,2000,9(10):1723-1730.
[48].L.I.Rudin,S.Osher,and E.Fatemi,Nonlinear total variation based noise removal algorithms,Physica D,1992,60:259-268.
[49].Dong-Gyn Sim etl.Object matching algorithms using robust hausdorff distance measures.IEEE Transaction on Image Processing,1999,8(1):425-429.
[50].Huttenlocher D P,Klanderman G A and Rucklidge W J.Comparing images using the Hausdorff distance.IEEE Trans Pattem Anal Machine Intelligence,1993,15:850-863.
[51].Fogel,L.J.,Owens,A.J.,and Walsh,M.J.Artificial intelligence through simulated evolution.NewYork John Wiley & Sons,1996.
[52].刘勇,康立山,非数值并行算法,北京,科学出版社,2003.