基于Hausdorff距离和遗传算法的图像配准方法研究
|
摘要
图像配准是图像处理的基本任务之一,它的主要作用是将不同时间、不同传感器、不同视角及不同拍摄条件下获取的两幅或多幅图像进行匹配(主要是几何意义上的)。近年来对图像配准技术的研究涵盖了多个应用领域,在计算机视觉、模式识别、医学图像分析和遥感数据处理等学科中图像配准技术均占有举足轻重的地位,图像配准己成为很多研究课题的必备环节。
图像配准中的一个关键的问题是如何利用一种行之有效的方法来评价图像间的相似程度。自1991年,一种基于Hausdorff距离的计算图像间的相似度的方法提出后,Hausdorff距离作为一种评价两个图形位置关系的量化标准已被大量应用到图像配准的研究领域中,其良好的配准精度也被大量的实验和研究所证明。然而在图像配准中,单纯的Hausdorff距离在计算上存在着一个比较大的缺点,就是对于噪声和孤立点的敏感性,但是由Hausdorrff距离改进的LTS(Least Trimmed Square)Hausdorff距离却可以很好的克服这些问题,作为一种改进方法,LTS Hausdorff距离在数字图像配准中具有比较理想的精确度和健壮性。
该文提出了一种基于改进的Hausdorff距离(LTS Hausdorff距离)与遗传算法的图像配准方法。算法首先是对参考图像和待配准图像进行预处理,然后在此基础上结合遗传算法对待配准图像进行配准操作,遗传算法的执行过程中利用LTS Hausdorff距离作为适应度函数,最终的目的是通过遗传算法搜索到最优变换参数,本文的主要内容如下:
(1)在分析和阐述了传统的Hausdorff距离的概念、原理以及在图像配准中的缺点的基础上,引入了LTS Hausdorff距离。并且将LTS Hausdorff距离作为衡量图像相似程度的主要度量应用到图像配准中,很好的解决了传统的Hausdorff距离在图像配准中所出现的对于噪声和孤立点过于敏感的问题,而且可以保证整个配准的精度。
(2)完整的阐述了遗传算法结合LTS Hausdorff距离进行图像配准的算法的流程。在图像预处理的环节中对图像进行了锐化、平滑、二值化以及边缘检测等操作。首先,在比较关键的边缘检测的处理中使用了Butterworth滤波方法进行图像点特征的提取,使图像经过预处理的环节后,能够呈现更清晰和准确的轮廓点图像。然后,将遗传算法应用到图像配准中,并且根据图像配准的特点对遗传算法进行了一些改进,例如:放弃传统的二进制的编码形式,采用实数编码;根据具体的配准实验情况确定种群大小和遗传代数;最重要的是,将LTS Hausdorff距离作为适应度函数应用到遗传算法当中,这样使得整个算法在抵抗噪声和孤立点方面有了很大的优势。
对于128×128像素的人体脑部MRI图和PET图的配准实验结果证明了,本文算法具有比较好的配准精度。并且笔者还用本文的算法和采用了传统的Hausdorff距离的算法进行了比较。在几种算法对于同样的加入了噪声的图像进行配准实验后,实验的结果表明:本文采用的方法具有更好的健壮性。
Image registration is one of the basic digital image processing methods, which mainly registers two or more digital images, mostly geometrically, obtained at different time, by different sensors, on different angle of view or on different filming conditions. In recent years, image registration is studied in many different applying domains, so that it plays a very important role in computer vision, pattern recognition, medical image analysis and remote sensing. Image registration has become an essential part during many studies and researches.
A key problem in image registration is to find an effective way in which we can evaluate the similarities of the digital images. In 1991, a method based on Hausdorff distance was proposed, which is about the computing of the image similarities. From then on the Hausdorff distance has been utilizing in many experiments and researches, and as a standard of measuring the positions of images, it has been proved to be a good method in registration accuracy. However the naive Hausdorff distance has a defect during image registration, which is the sensitivity of noise and outliers. While as the improved Hausdorff distance, the LTS (Least Trimmed Square) Hausdorff distance can overcome these problems easily. So the accuracy and stability of image registration which is based on LTS Hausdorff distance is more preferable.
In this paper, an image registration algorithm based on LTS Hausdorff distance and genetic algorithm is proposed. Before the algorithm begins, the reference image and the unregistered image are processed using image sharpening, image smoothing, image binarization and edge detection. Then on the result of the pre-processing, the processed images are registered using genetic operations, during which the LTS Hausdorff distance is used as the fitness function; finally the goal is to find the best transformation parameters by genetic algorithm. The main contents are as follows:
(1)It introduces the LTS Hausdroff distance after explaining the definition, theorem, as well as the problems which may come out during the image registration. Moreover, as the main standard measuring the similarities during the image registration, it can perfectly solve the problems caused by the sensitivity of noise and outliers, which mainly appear in na?ve Hausdorff distance. More importantly it can guarantee the accuracy of image registration.
(2)It narrates the whole procedure of the image registration based on genetic algorithms and LTS Hausdorff distance. During the process of pre-solving of the images, the images are processed by the operation of sharpening, smoothing, binarization and edge detection. First, it is because of the methods of Butterworth filter which used in edge detection to get the point features of images that the sketches of the images can show more clearly and accurately. Then the GA is applied to the image registration, and the GA used in the algorithm is improved on the ground of the features of image registration. The improvement including: using real number encoding instead of the orthodox binary encoding; determining the group and the generations by the practical experimental statistics; and using self-adapted crossover rate and mutation rate. Finally the LTS Hausdorff distance is applied as the fitness function in the improved genetic algorithms, so that it dramatically improves the resistance to the impacts of noise and outliers in the algorithm.
The author has made enough experiments using medical MRI and PET 128×128 pixel image to prove that the algorithm proposed by this paper can guarantee a good accuracy during the registration. The author also compared the algorithm proposed in this paper and the algorithms based on orthodox Hausdorff distance, and made a contrast of the differences which caused by the algorithms, after solving the same images interfered by noise and outliers. The results of the experiments proved that the algorithm is really more robust.
图像配准中的一个关键的问题是如何利用一种行之有效的方法来评价图像间的相似程度。自1991年,一种基于Hausdorff距离的计算图像间的相似度的方法提出后,Hausdorff距离作为一种评价两个图形位置关系的量化标准已被大量应用到图像配准的研究领域中,其良好的配准精度也被大量的实验和研究所证明。然而在图像配准中,单纯的Hausdorff距离在计算上存在着一个比较大的缺点,就是对于噪声和孤立点的敏感性,但是由Hausdorrff距离改进的LTS(Least Trimmed Square)Hausdorff距离却可以很好的克服这些问题,作为一种改进方法,LTS Hausdorff距离在数字图像配准中具有比较理想的精确度和健壮性。
该文提出了一种基于改进的Hausdorff距离(LTS Hausdorff距离)与遗传算法的图像配准方法。算法首先是对参考图像和待配准图像进行预处理,然后在此基础上结合遗传算法对待配准图像进行配准操作,遗传算法的执行过程中利用LTS Hausdorff距离作为适应度函数,最终的目的是通过遗传算法搜索到最优变换参数,本文的主要内容如下:
(1)在分析和阐述了传统的Hausdorff距离的概念、原理以及在图像配准中的缺点的基础上,引入了LTS Hausdorff距离。并且将LTS Hausdorff距离作为衡量图像相似程度的主要度量应用到图像配准中,很好的解决了传统的Hausdorff距离在图像配准中所出现的对于噪声和孤立点过于敏感的问题,而且可以保证整个配准的精度。
(2)完整的阐述了遗传算法结合LTS Hausdorff距离进行图像配准的算法的流程。在图像预处理的环节中对图像进行了锐化、平滑、二值化以及边缘检测等操作。首先,在比较关键的边缘检测的处理中使用了Butterworth滤波方法进行图像点特征的提取,使图像经过预处理的环节后,能够呈现更清晰和准确的轮廓点图像。然后,将遗传算法应用到图像配准中,并且根据图像配准的特点对遗传算法进行了一些改进,例如:放弃传统的二进制的编码形式,采用实数编码;根据具体的配准实验情况确定种群大小和遗传代数;最重要的是,将LTS Hausdorff距离作为适应度函数应用到遗传算法当中,这样使得整个算法在抵抗噪声和孤立点方面有了很大的优势。
对于128×128像素的人体脑部MRI图和PET图的配准实验结果证明了,本文算法具有比较好的配准精度。并且笔者还用本文的算法和采用了传统的Hausdorff距离的算法进行了比较。在几种算法对于同样的加入了噪声的图像进行配准实验后,实验的结果表明:本文采用的方法具有更好的健壮性。
Image registration is one of the basic digital image processing methods, which mainly registers two or more digital images, mostly geometrically, obtained at different time, by different sensors, on different angle of view or on different filming conditions. In recent years, image registration is studied in many different applying domains, so that it plays a very important role in computer vision, pattern recognition, medical image analysis and remote sensing. Image registration has become an essential part during many studies and researches.
A key problem in image registration is to find an effective way in which we can evaluate the similarities of the digital images. In 1991, a method based on Hausdorff distance was proposed, which is about the computing of the image similarities. From then on the Hausdorff distance has been utilizing in many experiments and researches, and as a standard of measuring the positions of images, it has been proved to be a good method in registration accuracy. However the naive Hausdorff distance has a defect during image registration, which is the sensitivity of noise and outliers. While as the improved Hausdorff distance, the LTS (Least Trimmed Square) Hausdorff distance can overcome these problems easily. So the accuracy and stability of image registration which is based on LTS Hausdorff distance is more preferable.
In this paper, an image registration algorithm based on LTS Hausdorff distance and genetic algorithm is proposed. Before the algorithm begins, the reference image and the unregistered image are processed using image sharpening, image smoothing, image binarization and edge detection. Then on the result of the pre-processing, the processed images are registered using genetic operations, during which the LTS Hausdorff distance is used as the fitness function; finally the goal is to find the best transformation parameters by genetic algorithm. The main contents are as follows:
(1)It introduces the LTS Hausdroff distance after explaining the definition, theorem, as well as the problems which may come out during the image registration. Moreover, as the main standard measuring the similarities during the image registration, it can perfectly solve the problems caused by the sensitivity of noise and outliers, which mainly appear in na?ve Hausdorff distance. More importantly it can guarantee the accuracy of image registration.
(2)It narrates the whole procedure of the image registration based on genetic algorithms and LTS Hausdorff distance. During the process of pre-solving of the images, the images are processed by the operation of sharpening, smoothing, binarization and edge detection. First, it is because of the methods of Butterworth filter which used in edge detection to get the point features of images that the sketches of the images can show more clearly and accurately. Then the GA is applied to the image registration, and the GA used in the algorithm is improved on the ground of the features of image registration. The improvement including: using real number encoding instead of the orthodox binary encoding; determining the group and the generations by the practical experimental statistics; and using self-adapted crossover rate and mutation rate. Finally the LTS Hausdorff distance is applied as the fitness function in the improved genetic algorithms, so that it dramatically improves the resistance to the impacts of noise and outliers in the algorithm.
The author has made enough experiments using medical MRI and PET 128×128 pixel image to prove that the algorithm proposed by this paper can guarantee a good accuracy during the registration. The author also compared the algorithm proposed in this paper and the algorithms based on orthodox Hausdorff distance, and made a contrast of the differences which caused by the algorithms, after solving the same images interfered by noise and outliers. The results of the experiments proved that the algorithm is really more robust.
引文
[1] L.G.Brown, A survey of image registration technique, ACM Computing surveys [J], 1992, 24(4):326-376.
[2] Barbara Zitova, Jan Flusser, Image registration methods: A survey, Image and Vision Computing [J], 2003, 21:977-1000.
[3] Huttenlocher D P, Klanderman G A, Rucklidge W J, Comparing images using the Hausdorf distance, IEEE Transactions on PAMI [J], 1993, 15(9): 850-863.
[4] Dong-Gyu Sim, Oh-Kyu Kwon, and Rae-Hong Park, Object Matching Algorithms Using Robust Hausdorff Distance Measures, IEEE Transactions On Image Processing [J], 2004,15(3):425-428.
[5] Chalermwat P, El-Ghazawi T, Le Moigne J. Two-Phase Genetic Algorithm-Based Image Registration on Parallel Clusters[J]. Journal of Future Generation Computing Systems, 2001, 17: 467-476.
[6] Brumby S, Theiler J, Perkins S, et al. Investigation of feature extraction by a genetic algorithm[J]. SPIE, 1999,3812: 24-31.
[7] Daniel P. Huttcnlocher and William J. Rucklidge, A multi-resolution technique for comparing images using the Hausdorff distance, IEEE Transactions un Pattern Analysis and Machine Intelligence[J], 1993,14: 705-706.
[8] Jialing C., James C.H.C., et al., CT and PET lung image registration and fusion in radiotherapy treatment planning using the chamfer-matching method, Int. J. Radiation Oncology Biol. Phys.[J] , March, 1999,43(4): 883-891.
[9] G. Borgefors, Hierarchical chamfer matching: A parametric edge matching algorithm, IEEE Trans. Pattern Anal. Machine Intelligence [J], Nov. 1988, 10:849–865.
[10] 徐建斌等,一种基于距离变换和遗传算法的遥感图像匹配,电子与信息学[J],2005,7(7):1010-1012.
[11] Health A., Sarkar S., Sanocki T., Comparison of Edge Detectors: A Methodology and Initial Study. Computer Vision and Image Understanding [J], 1998, 69(1): 38-54.
[12] 刑军,基于Sobel算子数字图像的边缘检测,微机发展[J],2005, 15(9):48-52.
[13] 刘彩 , 一种改进的 Sobel 图像边缘检测算法 , 贵州工业大学学报 ( 自然科学版)[J],2004,33(5):77-79.
[14] 黄 朝 兵 , 鲁 伟 , Butterworth 滤 波 和 Sobel 算 子 的 图 像 边 缘 检测,2006,http://www.xllw.net/show.aspx?id=9325&cid=10.
[15] 牛力丕,毛士艺,陈炜,基于Hausdorff距离的图像配准研究[J],电子与信息学报,2007,(01):56-59.
[1] L.G.Brown, A survey of image registration technique, ACM Computing surveys [J], 1992, 24(4):326-376.
[2] Barbara Zitova, Jan Flusser, Image registration methods: A survey, Image and Vision Computing [J], 2003, 21:977-1000.
[3] Huttenlocher D P, Klanderman G A, Rucklidge W J, Comparing images using the Hausdorf distance, IEEE Transactions on PAMI [J], 1993, 15(9): 850-863.
[4] Dong-Gyu Sim, Oh-Kyu Kwon, and Rae-Hong Park, Object Matching Algorithms Using Robust Hausdorff Distance Measures, IEEE Transactions On Image Processing [J], 2004,15(3):425-428.
[5] Chalermwat P, El-Ghazawi T, Le Moigne J. Two-Phase Genetic Algorithm-Based Image Registration on Parallel Clusters[J]. Journal of Future Generation Computing Systems, 2001, 17: 467-476.
[6] Brumby S, Theiler J, Perkins S, et al. Investigation of feature extraction by a genetic algorithm[J]. SPIE, 1999,3812: 24-31.
[7] Daniel P. Huttcnlocher and William J. Rucklidge, A multi-resolution technique for comparing images using the Hausdorff distance, IEEE Transactions un Pattern Analysis and Machine Intelligence[J], 1993,14: 705-706.
[8] Jialing C., James C.H.C., et al., CT and PET lung image registration and fusion in radiotherapy treatment planning using the chamfer-matching method, Int. J. Radiation Oncology Biol. Phys.[J] , March, 1999,43(4): 883-891.
[9] G. Borgefors, Hierarchical chamfer matching: A parametric edge matching algorithm, IEEE Trans. Pattern Anal. Machine Intelligence [J], Nov. 1988, 10:849–865.
[10] 徐建斌等,一种基于距离变换和遗传算法的遥感图像匹配,电子与信息学[J],2005,7(7):1010-1012.
[11] Health A., Sarkar S., Sanocki T., Comparison of Edge Detectors: A Methodology and Initial Study. Computer Vision and Image Understanding [J], 1998, 69(1): 38-54.
[12] 刑军,基于Sobel算子数字图像的边缘检测,微机发展[J],2005, 15(9):48-52.
[13] 刘彩 , 一种改进的 Sobel 图像边缘检测算法 , 贵州工业大学学报 ( 自然科学版)[J],2004,33(5):77-79.
[14] 黄 朝 兵 , 鲁 伟 , Butterworth 滤 波 和 Sobel 算 子 的 图 像 边 缘 检测,2006,http://www.xllw.net/show.aspx?id=9325&cid=10.
[15] 牛力丕,毛士艺,陈炜,基于Hausdorff距离的图像配准研究[J],电子与信息学报,2007,(01):56-59.
[32] 云庆夏,黄光球,王占权,遗传算法和遗传规划,北京:冶金工业出版社,1997.
[33] 周明,孙树栋,遗传算法原理与应用,北京:国防工业出版社,1999.
[34] 陈国良,王煦法,庄镇泉,遗传算法及其应用,北京:人民邮电出版社,1996.
[35] 管云峰 , 胡勇 , 李介谷 , 基于 Hausdorff 距离的图像匹配技术 , 红外与激光工程,1998,27(4):22-25.
[36] Holland J. H., Adaptation in Natural and Artificial System [M], Ann Arbor: University of Michigan Press, 1975:30-58.
[37] Ming H. Y., David J., Kriegman, Narendra A., Detecting Faces in Images: A Survey[J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(1):34-58.
[38] B.S.Reddy, zB.N.Chaterji, An FFT-based technique for image registration: rotation and scale-invariant image registration, IEEE Transaction on image Processing [J], 1996, 1266-1271.
[39] C.D.Kuglin and D.C.Hines, The phase correlation image alignment method, in Proc.Int.Conf on Cybernetics and society [C], 1975:163-165.
[40] 谌安军 , 陈炜 , 毛士艺 , 一种基于边缘的图像配准方法 [J], 电子与信息学报,2004,(05):34-42.
[41] G.Wolberg and S.Zokai, Robust image registration using log-polar transform, in Proc.of IEEEICIP2000[C], 2006:493-496.
[42] 史栋林,基于边缘的图像配准研究[D],南京理工大学,2006:23-24.
[43] L.Lucchese and G.M.Cortelazzo, A Noise-Robust Frequency domain technique for estimate planar roto-translations, IEEE Transaction on signal Processing [J], 2000, 48(6):1769-1786.
[44] L.Lucchese, A frequency domain technique based on energy radial Projections for robust estimation of global 2D affine transformations, Computer Vision and Image Understanding [J], 2001:72-116.
[45] L.Lucchese, G.Doreto, GM.Cortelazzo, A frequency domain technique for rage data registration, IEEE Transaction on medical imaging, 2002, 24: 1468-1484.
[46] 倪国强,刘琼,多源图像配准技术分析与展望,光电工程,第31卷第9期,2004,1-6.
[47] 李中科,吴乐南,基于霍夫变换和相位相关的图像配准方法,信号处理,第20 卷第 2 期,2004,166-169.
[48] Collignon, et al., Automated multimodality medical image registration using information theory, In Y. Bizais, et al. (Eds.) Proc. Information Processing in Medical Imaging, 263-558. 1995.
[49] Pelizzari, G.T.Chen, Y.Spelbring D. R., Weichselbaum R. R., Chen. C.T., Accurate three-dimensional registration of CT, PET, and/or MR images of the brain, J. Computer. Assist. Tomogram. Vol. 143, 20-26, 1989.
[50] Maurer C.R.Jr., Aboutanos. G.B., Dawant. B.M., Maciunas R.J., Fitzpatrick. J.M., Registration of 30Dimages using weighted geometrical features. IEEE Trans. Med. Imaging, Vol. 15, No.6, 836-849, Dec., 1996.
[51] Jialing C., James C.H.C., et al. CT and PET lung image registration and fusion in radiotherapy treatment planning using the chamfer-matching method, Int. J. Radiation Oncology Biol. Phys. Vol. 43, No. 4, 883-891, Match, 1999.
[52] Barrow H.G., Tenenbaum, J. M., Bolles, R.C. Wolf, H.C. Parametric correspondence and chamfer matching: Two new techniques for image matching, Proc. Int. Joint Conf. Artificial Intelligence, Cambridge, MA, 659-663. 1977.
[53] 王才诗,李德仁,舒宁,NOAA/AVHRR影像特征匹配,武汉测绘科技大学学报,1994年3月,第19卷第1期,37-43.
[2] Barbara Zitova, Jan Flusser, Image registration methods: A survey, Image and Vision Computing [J], 2003, 21:977-1000.
[3] Huttenlocher D P, Klanderman G A, Rucklidge W J, Comparing images using the Hausdorf distance, IEEE Transactions on PAMI [J], 1993, 15(9): 850-863.
[4] Dong-Gyu Sim, Oh-Kyu Kwon, and Rae-Hong Park, Object Matching Algorithms Using Robust Hausdorff Distance Measures, IEEE Transactions On Image Processing [J], 2004,15(3):425-428.
[5] Chalermwat P, El-Ghazawi T, Le Moigne J. Two-Phase Genetic Algorithm-Based Image Registration on Parallel Clusters[J]. Journal of Future Generation Computing Systems, 2001, 17: 467-476.
[6] Brumby S, Theiler J, Perkins S, et al. Investigation of feature extraction by a genetic algorithm[J]. SPIE, 1999,3812: 24-31.
[7] Daniel P. Huttcnlocher and William J. Rucklidge, A multi-resolution technique for comparing images using the Hausdorff distance, IEEE Transactions un Pattern Analysis and Machine Intelligence[J], 1993,14: 705-706.
[8] Jialing C., James C.H.C., et al., CT and PET lung image registration and fusion in radiotherapy treatment planning using the chamfer-matching method, Int. J. Radiation Oncology Biol. Phys.[J] , March, 1999,43(4): 883-891.
[9] G. Borgefors, Hierarchical chamfer matching: A parametric edge matching algorithm, IEEE Trans. Pattern Anal. Machine Intelligence [J], Nov. 1988, 10:849–865.
[10] 徐建斌等,一种基于距离变换和遗传算法的遥感图像匹配,电子与信息学[J],2005,7(7):1010-1012.
[11] Health A., Sarkar S., Sanocki T., Comparison of Edge Detectors: A Methodology and Initial Study. Computer Vision and Image Understanding [J], 1998, 69(1): 38-54.
[12] 刑军,基于Sobel算子数字图像的边缘检测,微机发展[J],2005, 15(9):48-52.
[13] 刘彩 , 一种改进的 Sobel 图像边缘检测算法 , 贵州工业大学学报 ( 自然科学版)[J],2004,33(5):77-79.
[14] 黄 朝 兵 , 鲁 伟 , Butterworth 滤 波 和 Sobel 算 子 的 图 像 边 缘 检测,2006,http://www.xllw.net/show.aspx?id=9325&cid=10.
[15] 牛力丕,毛士艺,陈炜,基于Hausdorff距离的图像配准研究[J],电子与信息学报,2007,(01):56-59.
[1] L.G.Brown, A survey of image registration technique, ACM Computing surveys [J], 1992, 24(4):326-376.
[2] Barbara Zitova, Jan Flusser, Image registration methods: A survey, Image and Vision Computing [J], 2003, 21:977-1000.
[3] Huttenlocher D P, Klanderman G A, Rucklidge W J, Comparing images using the Hausdorf distance, IEEE Transactions on PAMI [J], 1993, 15(9): 850-863.
[4] Dong-Gyu Sim, Oh-Kyu Kwon, and Rae-Hong Park, Object Matching Algorithms Using Robust Hausdorff Distance Measures, IEEE Transactions On Image Processing [J], 2004,15(3):425-428.
[5] Chalermwat P, El-Ghazawi T, Le Moigne J. Two-Phase Genetic Algorithm-Based Image Registration on Parallel Clusters[J]. Journal of Future Generation Computing Systems, 2001, 17: 467-476.
[6] Brumby S, Theiler J, Perkins S, et al. Investigation of feature extraction by a genetic algorithm[J]. SPIE, 1999,3812: 24-31.
[7] Daniel P. Huttcnlocher and William J. Rucklidge, A multi-resolution technique for comparing images using the Hausdorff distance, IEEE Transactions un Pattern Analysis and Machine Intelligence[J], 1993,14: 705-706.
[8] Jialing C., James C.H.C., et al., CT and PET lung image registration and fusion in radiotherapy treatment planning using the chamfer-matching method, Int. J. Radiation Oncology Biol. Phys.[J] , March, 1999,43(4): 883-891.
[9] G. Borgefors, Hierarchical chamfer matching: A parametric edge matching algorithm, IEEE Trans. Pattern Anal. Machine Intelligence [J], Nov. 1988, 10:849–865.
[10] 徐建斌等,一种基于距离变换和遗传算法的遥感图像匹配,电子与信息学[J],2005,7(7):1010-1012.
[11] Health A., Sarkar S., Sanocki T., Comparison of Edge Detectors: A Methodology and Initial Study. Computer Vision and Image Understanding [J], 1998, 69(1): 38-54.
[12] 刑军,基于Sobel算子数字图像的边缘检测,微机发展[J],2005, 15(9):48-52.
[13] 刘彩 , 一种改进的 Sobel 图像边缘检测算法 , 贵州工业大学学报 ( 自然科学版)[J],2004,33(5):77-79.
[14] 黄 朝 兵 , 鲁 伟 , Butterworth 滤 波 和 Sobel 算 子 的 图 像 边 缘 检测,2006,http://www.xllw.net/show.aspx?id=9325&cid=10.
[15] 牛力丕,毛士艺,陈炜,基于Hausdorff距离的图像配准研究[J],电子与信息学报,2007,(01):56-59.
[32] 云庆夏,黄光球,王占权,遗传算法和遗传规划,北京:冶金工业出版社,1997.
[33] 周明,孙树栋,遗传算法原理与应用,北京:国防工业出版社,1999.
[34] 陈国良,王煦法,庄镇泉,遗传算法及其应用,北京:人民邮电出版社,1996.
[35] 管云峰 , 胡勇 , 李介谷 , 基于 Hausdorff 距离的图像匹配技术 , 红外与激光工程,1998,27(4):22-25.
[36] Holland J. H., Adaptation in Natural and Artificial System [M], Ann Arbor: University of Michigan Press, 1975:30-58.
[37] Ming H. Y., David J., Kriegman, Narendra A., Detecting Faces in Images: A Survey[J], IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(1):34-58.
[38] B.S.Reddy, zB.N.Chaterji, An FFT-based technique for image registration: rotation and scale-invariant image registration, IEEE Transaction on image Processing [J], 1996, 1266-1271.
[39] C.D.Kuglin and D.C.Hines, The phase correlation image alignment method, in Proc.Int.Conf on Cybernetics and society [C], 1975:163-165.
[40] 谌安军 , 陈炜 , 毛士艺 , 一种基于边缘的图像配准方法 [J], 电子与信息学报,2004,(05):34-42.
[41] G.Wolberg and S.Zokai, Robust image registration using log-polar transform, in Proc.of IEEEICIP2000[C], 2006:493-496.
[42] 史栋林,基于边缘的图像配准研究[D],南京理工大学,2006:23-24.
[43] L.Lucchese and G.M.Cortelazzo, A Noise-Robust Frequency domain technique for estimate planar roto-translations, IEEE Transaction on signal Processing [J], 2000, 48(6):1769-1786.
[44] L.Lucchese, A frequency domain technique based on energy radial Projections for robust estimation of global 2D affine transformations, Computer Vision and Image Understanding [J], 2001:72-116.
[45] L.Lucchese, G.Doreto, GM.Cortelazzo, A frequency domain technique for rage data registration, IEEE Transaction on medical imaging, 2002, 24: 1468-1484.
[46] 倪国强,刘琼,多源图像配准技术分析与展望,光电工程,第31卷第9期,2004,1-6.
[47] 李中科,吴乐南,基于霍夫变换和相位相关的图像配准方法,信号处理,第20 卷第 2 期,2004,166-169.
[48] Collignon, et al., Automated multimodality medical image registration using information theory, In Y. Bizais, et al. (Eds.) Proc. Information Processing in Medical Imaging, 263-558. 1995.
[49] Pelizzari, G.T.Chen, Y.Spelbring D. R., Weichselbaum R. R., Chen. C.T., Accurate three-dimensional registration of CT, PET, and/or MR images of the brain, J. Computer. Assist. Tomogram. Vol. 143, 20-26, 1989.
[50] Maurer C.R.Jr., Aboutanos. G.B., Dawant. B.M., Maciunas R.J., Fitzpatrick. J.M., Registration of 30Dimages using weighted geometrical features. IEEE Trans. Med. Imaging, Vol. 15, No.6, 836-849, Dec., 1996.
[51] Jialing C., James C.H.C., et al. CT and PET lung image registration and fusion in radiotherapy treatment planning using the chamfer-matching method, Int. J. Radiation Oncology Biol. Phys. Vol. 43, No. 4, 883-891, Match, 1999.
[52] Barrow H.G., Tenenbaum, J. M., Bolles, R.C. Wolf, H.C. Parametric correspondence and chamfer matching: Two new techniques for image matching, Proc. Int. Joint Conf. Artificial Intelligence, Cambridge, MA, 659-663. 1977.
[53] 王才诗,李德仁,舒宁,NOAA/AVHRR影像特征匹配,武汉测绘科技大学学报,1994年3月,第19卷第1期,37-43.