基于Radon变换的多模态医学图像配准
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摘要
图像配准是图像熔合的基础,已经广泛应用于计算机视觉、遥感处理、运动估计、医学分析等领域。医学图像的配准与熔合是现代医疗中不可或缺的一部分。由于不同成像设备得到的医学图像各有其特点,将不同模式的医学图像进行配准,可以综合了解病变组织或器官的解剖和功能信息。
本文提出的医学图像配准算法主要分为两个部分,分别为粗配准和精配准。本文使用图像的质心估计平移参数,利用Radon变换估计旋转参数,此参数估计的过程为粗配准。再将得到的粗配准参数作为初始参数进行优化,此优化搜索过程为精配准。精配准过程中利用归一化互信息与梯度相似性相结合作为配准的相似性测度,使用Powell优化算法进行搜索,得到最终的配准参数。
本文首先介绍了医学图像配准的意义、应用和发展现状,对医学图像配准进行简单综述并介绍了配准的基本方法。然后对配准的各个组成部分进行了分析,如空间变换、插值算法、相似性测度和优化算法等。接着阐述了熵和互信息的概念以及基于互信息的配准算法原理。最后介绍了本文的创新部分,首先引出了Radon变换的概念并介绍如何利用Radon变换对图像进行旋转参数的估计,然后介绍了梯度相似性的定义,提出利用梯度相似性和归一化互信息相结合作为本文的相似性测度,实验结果表明了该算法的有效性和准确性。
Image registration is the basic of image fusion, it is widely used in computer vision, remote sensing, movement estimation, medical analysis and many other areas. Medical image registration and fusion is an indispensable part of modern medical treatment. Medical image from different imaging equipment has its special characteristics, the registration of different modality medical images could integrate the anatomic and functional information of the pathologic structures and organs.
The medical image registration algorithm proposed in this paper is mainly divided into two parts, one is coarse registration and the other is precise registration. The centroid of image is used to estimate the translation parameter, and the Radon transform is used to estimate the rotation parameter. The translation and the rotation are optimized as the initial parameters. The metric of the precise registration is combining normalized mutual information and gradient similarity. Powell is used as the optimization to calculate the final parameters.
This paper introduces the significance, application and development of medical image registration first. Then it summarizes medical image registration briefly, introduces the basic methods of registration and analyses every part of the registration process, for example, the space transform, the interpolation, the metric and the optimization and so on. Then it introduces the concept of entropy, mutual information and the principle of registration algorithm based on mutual information. At last it introduces the innovation of this paper and introduces the concept of Radon transform and how to use Radon transform to estimate the rotation parameter, then it introduces the definition of gradient similarity and the metric used in this paper which combines mutual information and gradient similarity. The result of the experiment shows the validity and the veracity.
本文提出的医学图像配准算法主要分为两个部分,分别为粗配准和精配准。本文使用图像的质心估计平移参数,利用Radon变换估计旋转参数,此参数估计的过程为粗配准。再将得到的粗配准参数作为初始参数进行优化,此优化搜索过程为精配准。精配准过程中利用归一化互信息与梯度相似性相结合作为配准的相似性测度,使用Powell优化算法进行搜索,得到最终的配准参数。
本文首先介绍了医学图像配准的意义、应用和发展现状,对医学图像配准进行简单综述并介绍了配准的基本方法。然后对配准的各个组成部分进行了分析,如空间变换、插值算法、相似性测度和优化算法等。接着阐述了熵和互信息的概念以及基于互信息的配准算法原理。最后介绍了本文的创新部分,首先引出了Radon变换的概念并介绍如何利用Radon变换对图像进行旋转参数的估计,然后介绍了梯度相似性的定义,提出利用梯度相似性和归一化互信息相结合作为本文的相似性测度,实验结果表明了该算法的有效性和准确性。
Image registration is the basic of image fusion, it is widely used in computer vision, remote sensing, movement estimation, medical analysis and many other areas. Medical image registration and fusion is an indispensable part of modern medical treatment. Medical image from different imaging equipment has its special characteristics, the registration of different modality medical images could integrate the anatomic and functional information of the pathologic structures and organs.
The medical image registration algorithm proposed in this paper is mainly divided into two parts, one is coarse registration and the other is precise registration. The centroid of image is used to estimate the translation parameter, and the Radon transform is used to estimate the rotation parameter. The translation and the rotation are optimized as the initial parameters. The metric of the precise registration is combining normalized mutual information and gradient similarity. Powell is used as the optimization to calculate the final parameters.
This paper introduces the significance, application and development of medical image registration first. Then it summarizes medical image registration briefly, introduces the basic methods of registration and analyses every part of the registration process, for example, the space transform, the interpolation, the metric and the optimization and so on. Then it introduces the concept of entropy, mutual information and the principle of registration algorithm based on mutual information. At last it introduces the innovation of this paper and introduces the concept of Radon transform and how to use Radon transform to estimate the rotation parameter, then it introduces the definition of gradient similarity and the metric used in this paper which combines mutual information and gradient similarity. The result of the experiment shows the validity and the veracity.
引文
[1]张佳,张泾周,吴疆,等.医学图像配准的研究进展[J].陕西科技大学学报,2006,24(2):120-124.
[2]Zitova B,Flusser J.Image Registration Methods:a Survey[J].Image Vision Computing,2003(21):977-1000.
[3]Elsen P A,Pol E J D,Viergever M A.Medical Image matching-A review with classification [J].IEEE Transactions on Medical Imaging,1993,12(3):26-39.
[4]Maintz J B A,Viergever M A.A survey of medical image registration[J].Medical Image Analysis,1998,2(1):1-36.
[5]罗述谦.医学图像配准技术[J].国外医学生物医学工程分册,1999,22(1):1-8.
[6]田捷,包尚联,周明全.医学影像处理与分析[M].北京:电子工业出版社,2003.
[7]Studholme C,Hill D L G,Hawkes D J.Incorporating connected region labeling into automated image registration using mutual information[C].Proceedings of the 2nd IEEE Workshop on Mathematical Methods in Biomedical Image Analysis,1996.
[8]Pluim J B W,Maintz J B A,Viergever M A.Image registration by maximization of combined mutual information and gradient information[J].IEEE Transaction on medical imaging,2000,19(8):809-814.
[9]Pluim J B W.Mutual Information based registration of medical images[D].Netherlands:Utrecht University,2001.
[10]Butz T,Thiran J P.Affine registration with feature space mutual information[C].Berlin:Medical Image Computing and Computer-Assisted Intervention,2000.
[11]Rueckert D,Clarkson M J,Hill D L G,et al.Non-rigid registration using higher order mutual information[J].SPIE Medical Imaging:Image Processing,2000,3979:438-447.
[12]Brown L G.A survey of image registration techniques[J].ACM Computing surveys,1992,24(4):325-376.
[13]Riter N,Owens R,Copper J,et al.Registration of stereo and temporal images of the retina[J].IEEE Transactions on Medical imaging,1999,18(5):404-418.
[14]Penny G P,Weese J,Little J A,et al.A comparison of similarity measures for use in 2D-3D medical image registration[J].IEEE Transactions on Medical Imaging,1998,17(4):586-595.
[15]高智勇,李义兵,钱勇先,等.多模态医学图像配准技术的分类与研究进展[J].国外医学生物医学工程分册,2000,23(4):206-211.
[16]Maes F,Vandermeulen D,Suetens P.Medical image registration using mutual information [C].Proceedings of the IEEE,2003.
[17]Rangarajan A,Chui H,Duncan J S.Rigid point feature registration using mutual information[J].Medical Image Analysis,1999,3(4):425-440.
[18]周永新,罗述谦.基于形状特征点最大互信息的医学图像配准[J].计算机辅助设计与图形学学报,2002,14(7):654-658.
[19]Porter B C,Rubens D J,et al.Three dimensional registration and fusion of ultrasound and MRI using major vessel as fiducial markers[J].IEEE Transactions on Medical Imaging,2001,20(4):354-359.
[20]Maintz J B A,Elsen P A,Viergever M A.Comparison of edge-based and ridge-based registration of CT and MR brain images[J].Medical Image Analysis,1996,1(2):151-161.
[21]Hsu L Y,Loew M H.Fully automatic 3D feature-based registration of multi-modality medical images[J].Image and Vision Computing,2001,19(1-2):75-85.
[22]Pelizzari C A,Chen G T Y,Spelbring D R,et al.Accurate three dimensional registration of CT,PET and/or MR images of the brain[J].Journal of Computer Assisted Tomography,1989,13(1):20-26.
[23]Besl P J,McKay N D.A method for registration of 3D shapes[J].IEEE Transaction in Pattern Analysis and Machine Intelligence,1992,14(2):239-256.
[24]Collignon A,Vandermeulen D,Suetens P,et al.Registration of 3-D multimodality medical images using surfaces and point landmarks[J].Pattern Recognition,1994,15(4):461-467.
[25]Maurer C R,Maciunas R J,Fitzpatrick J M.Registration of head CT images to physical space using a weighted combination of points and surfaces[J].IEEE Transaction on Medical Imaging,1998,17(5):753-761.
[26]吴锋,钱宗才,杭洽时,等.基于轮廓的力矩主轴法在医学图像配准中的应用[J].第四军医大学学报,2001,22(6):567-569.
[27]Kaneko S,Satoh Y,Igarashi S.Using selective correlation coefficient for robust image registration[J].Pattern Recognition,2003,36(5):1165-1173.
[28]Roche A,Pennec X,Malandain G,et al.Rigid registration of 3-D ultrasound with MR images:A new approach combining intensity and gradient information[J].IEEE Transactions on Medical Imaging,2001,20(10):1038-1049.
[29]Elson P A,Maintz J B A,Pol E J D,et al.Automatic registration of CT and MR brain image using correlation of geometric features[J].IEEE Transaction on Medical Imaging,1995,14(2):384-396.
[30]Collignon A,Maes F,Delaere D,et al.Automated multi-modality image registration based on information theory[C].Proceedings of Information Processing in Medical Imaging Conference,Dordrechet Kluwer Academic Publishers,1995:263-274.
[31] Viola P, Wells W M. Alignment by maximization of mutual information [C]. Proceedings of the 5th International Conference on Computer Vision. LosAlamitos, CA: IEEE Press,1995:16-23.
[32] Maes F, Collignon A, Vandermeulen D, et al. Multimodality image registration by maximization of mutual information [J]. IEEE Transactions on Medical Imaging, 1997,16(2): 187-198.
[33] Studholme C, Hill D L G, Hawkes D J. An overlap invariant entropy measure of 3D medical image [J]. Pattern Recognition, 1999, 32:71-86.
[34] Wu J, Chung A C. Multimodality brain image registration based on wavelet transform using SAD and MI [J]. MIAR,2004, 3150:270-277.
[35] Moigne J L, Campbell W J, Cromp R F. An automated parallel image registration technique based on the correlation of wavelet features [J]. IEEE Transactions on Geoscience and Remote Sensing, 2002, 40:1849-1864.
[36] Tomiya M, Ageishi A. Registration of remote sensing image data based on wavelet transform [J]. ISPRS Archives, 2003, 8:17-19.
[37] Ji Zhen, Jiang Yifeng, Zhang Jihong. Automatic registration algorithm based on wavelet transform [C]. Signal Processing Proceedings, 2000, 2:979-982.
[38] Zavorin I, Le Moigne J. Use of multiresolution wavelet feature pyramids for automatic registration of multisensor imagery [J]. IEEE Transaction on Image Processing, 2005,14(6):770-782.
[39] Lehmann TM, Gonner C, Spitzer K. Survey: Interpolation methods in medical image processing [J]. IEEE Transactions on Medical Imaging, 1999, 18(11):1049-1075.
[40] Unser M. Splines-A Perfect Fit for Signal and Image Processing [J]. IEEE Signal Processing Magazine, 1999,22-38.
[41] Hsieh Hou, Andrews H. Cubic Splines for Image Interpolation and Digital Filtering [J].IEEE Transactions on Acoustics, Speech and Signal Processing, 1978,26(6):508-517.
[42] Meijering E H, Niessen W J, Pluim J P, et al. Quantitative comparision sinc-approximating kernels for medical image interpolation [C]. MICCAI98 First International Conference on Medical Image Computing and Computer-Assisted Intervention, Lecture Notes in Computer Science, Springer Verlag:972-980, 1999.
[43] Holden M, Hill D L G, Denton E R E, et al. Voxel similarity measures for 3D serial MR brain image registration [C]. Information Processing in Medical Imaging 1999(IPMI99):472-477.
[44] Penney G P, Wcese J, Little J A, et ah A comparison of similarity measures for use in 2D-3D medical image registration [J]. IEEE Transactions on Medical Imaging, 1998,17(4):586-595.
[45]Woods R P,Cherry S R,Mazziotta J C.Rapid automated algorithm for aligning and reslicing PET images[J].Journal of Computer Assistant Tomography,1992,16:620-633.
[46]Shannon C E.A mathematical theory of communication[J].Bell System Technical Journal,1948(27):379-423.
[47]百度百科.http://baike.baidu.com/view/401605.htm
[48]Wachowiak M P,Smolikova R,Tourassi G D,et al.Generalized mutual information similarity metrics for multimodal biomedical image registration[C].Annual International Conference of the IEEE Engineering in Medicine and Biology,Houston,2:1005-1006,2002.
[49]Wachowiaka M P,Smolikova R,Tourassib G D,et al.Similarity metrics based on nonadditive entropies for 2D-3D multimodal biomedical image registration[C].San Diego:Proceedings of SPIE,5032:1090-1100,2003.
[50]Wachowiak M P,Smolikova R,Zheng Yufeng,et al.An approach to multimodal biomedical image registration utilizing particle swarm optimization[J].IEEE Transactions on Evolutionary computation,2004,8(3):289-301.
[51]Shi Y H,Eberhart R C.A modified particle swarm optimizer[C].Proceedings of IEEE International Conference on Evolutionary Computation,USA:IEEE,1998:67-73.
[52]Matsopoulos G K,Mouravliansky N A,Delibasis K K,et al.Automatic retinal image registration scheme using global optimization techniques[J].IEEE Transactions on Information Technology in Biomedicine,1999,3(1):47-60.
[53]Shannon C E.The mathematical theory of communication(part 1 and 2)[M].Bell System Technical Journal,1948,27:379-423 and 623-656.
[54]罗述谦,李响.基于最大互信息的多模医学图像配准[J].中国图像图形学报,2000,5(7):551-558.
[55]刘哲星,李树祥.基于联合直方图区域计数的时间序列图像自动配准方法[J].中国图像图形学报,2002,7(5):450-456.
[56]付宜利,于晓龙,王跃华.基于最大互信息的人脑多模图像快速配准算法[J].生物医学工程研究,2006,25(2):71-74.
[57]张堤,刘哲星,李树祥,等.基于互信息量的医学图像自动弹性配准[J].中国生物医学工程学报,2004,23(3):279-281.
[58]Maes F,Vandermeulen D,Suetens P.Medical Image Registration Using Mutual Information [C].Proceedings of IEEE,2003,91(10).
[59]陈伟卿,欧宗瑛,李冠华,等.基于互信息与梯度相似性相结合的医学图像配准方法[J].大连理工大学学报,2009,49(3).
[2]Zitova B,Flusser J.Image Registration Methods:a Survey[J].Image Vision Computing,2003(21):977-1000.
[3]Elsen P A,Pol E J D,Viergever M A.Medical Image matching-A review with classification [J].IEEE Transactions on Medical Imaging,1993,12(3):26-39.
[4]Maintz J B A,Viergever M A.A survey of medical image registration[J].Medical Image Analysis,1998,2(1):1-36.
[5]罗述谦.医学图像配准技术[J].国外医学生物医学工程分册,1999,22(1):1-8.
[6]田捷,包尚联,周明全.医学影像处理与分析[M].北京:电子工业出版社,2003.
[7]Studholme C,Hill D L G,Hawkes D J.Incorporating connected region labeling into automated image registration using mutual information[C].Proceedings of the 2nd IEEE Workshop on Mathematical Methods in Biomedical Image Analysis,1996.
[8]Pluim J B W,Maintz J B A,Viergever M A.Image registration by maximization of combined mutual information and gradient information[J].IEEE Transaction on medical imaging,2000,19(8):809-814.
[9]Pluim J B W.Mutual Information based registration of medical images[D].Netherlands:Utrecht University,2001.
[10]Butz T,Thiran J P.Affine registration with feature space mutual information[C].Berlin:Medical Image Computing and Computer-Assisted Intervention,2000.
[11]Rueckert D,Clarkson M J,Hill D L G,et al.Non-rigid registration using higher order mutual information[J].SPIE Medical Imaging:Image Processing,2000,3979:438-447.
[12]Brown L G.A survey of image registration techniques[J].ACM Computing surveys,1992,24(4):325-376.
[13]Riter N,Owens R,Copper J,et al.Registration of stereo and temporal images of the retina[J].IEEE Transactions on Medical imaging,1999,18(5):404-418.
[14]Penny G P,Weese J,Little J A,et al.A comparison of similarity measures for use in 2D-3D medical image registration[J].IEEE Transactions on Medical Imaging,1998,17(4):586-595.
[15]高智勇,李义兵,钱勇先,等.多模态医学图像配准技术的分类与研究进展[J].国外医学生物医学工程分册,2000,23(4):206-211.
[16]Maes F,Vandermeulen D,Suetens P.Medical image registration using mutual information [C].Proceedings of the IEEE,2003.
[17]Rangarajan A,Chui H,Duncan J S.Rigid point feature registration using mutual information[J].Medical Image Analysis,1999,3(4):425-440.
[18]周永新,罗述谦.基于形状特征点最大互信息的医学图像配准[J].计算机辅助设计与图形学学报,2002,14(7):654-658.
[19]Porter B C,Rubens D J,et al.Three dimensional registration and fusion of ultrasound and MRI using major vessel as fiducial markers[J].IEEE Transactions on Medical Imaging,2001,20(4):354-359.
[20]Maintz J B A,Elsen P A,Viergever M A.Comparison of edge-based and ridge-based registration of CT and MR brain images[J].Medical Image Analysis,1996,1(2):151-161.
[21]Hsu L Y,Loew M H.Fully automatic 3D feature-based registration of multi-modality medical images[J].Image and Vision Computing,2001,19(1-2):75-85.
[22]Pelizzari C A,Chen G T Y,Spelbring D R,et al.Accurate three dimensional registration of CT,PET and/or MR images of the brain[J].Journal of Computer Assisted Tomography,1989,13(1):20-26.
[23]Besl P J,McKay N D.A method for registration of 3D shapes[J].IEEE Transaction in Pattern Analysis and Machine Intelligence,1992,14(2):239-256.
[24]Collignon A,Vandermeulen D,Suetens P,et al.Registration of 3-D multimodality medical images using surfaces and point landmarks[J].Pattern Recognition,1994,15(4):461-467.
[25]Maurer C R,Maciunas R J,Fitzpatrick J M.Registration of head CT images to physical space using a weighted combination of points and surfaces[J].IEEE Transaction on Medical Imaging,1998,17(5):753-761.
[26]吴锋,钱宗才,杭洽时,等.基于轮廓的力矩主轴法在医学图像配准中的应用[J].第四军医大学学报,2001,22(6):567-569.
[27]Kaneko S,Satoh Y,Igarashi S.Using selective correlation coefficient for robust image registration[J].Pattern Recognition,2003,36(5):1165-1173.
[28]Roche A,Pennec X,Malandain G,et al.Rigid registration of 3-D ultrasound with MR images:A new approach combining intensity and gradient information[J].IEEE Transactions on Medical Imaging,2001,20(10):1038-1049.
[29]Elson P A,Maintz J B A,Pol E J D,et al.Automatic registration of CT and MR brain image using correlation of geometric features[J].IEEE Transaction on Medical Imaging,1995,14(2):384-396.
[30]Collignon A,Maes F,Delaere D,et al.Automated multi-modality image registration based on information theory[C].Proceedings of Information Processing in Medical Imaging Conference,Dordrechet Kluwer Academic Publishers,1995:263-274.
[31] Viola P, Wells W M. Alignment by maximization of mutual information [C]. Proceedings of the 5th International Conference on Computer Vision. LosAlamitos, CA: IEEE Press,1995:16-23.
[32] Maes F, Collignon A, Vandermeulen D, et al. Multimodality image registration by maximization of mutual information [J]. IEEE Transactions on Medical Imaging, 1997,16(2): 187-198.
[33] Studholme C, Hill D L G, Hawkes D J. An overlap invariant entropy measure of 3D medical image [J]. Pattern Recognition, 1999, 32:71-86.
[34] Wu J, Chung A C. Multimodality brain image registration based on wavelet transform using SAD and MI [J]. MIAR,2004, 3150:270-277.
[35] Moigne J L, Campbell W J, Cromp R F. An automated parallel image registration technique based on the correlation of wavelet features [J]. IEEE Transactions on Geoscience and Remote Sensing, 2002, 40:1849-1864.
[36] Tomiya M, Ageishi A. Registration of remote sensing image data based on wavelet transform [J]. ISPRS Archives, 2003, 8:17-19.
[37] Ji Zhen, Jiang Yifeng, Zhang Jihong. Automatic registration algorithm based on wavelet transform [C]. Signal Processing Proceedings, 2000, 2:979-982.
[38] Zavorin I, Le Moigne J. Use of multiresolution wavelet feature pyramids for automatic registration of multisensor imagery [J]. IEEE Transaction on Image Processing, 2005,14(6):770-782.
[39] Lehmann TM, Gonner C, Spitzer K. Survey: Interpolation methods in medical image processing [J]. IEEE Transactions on Medical Imaging, 1999, 18(11):1049-1075.
[40] Unser M. Splines-A Perfect Fit for Signal and Image Processing [J]. IEEE Signal Processing Magazine, 1999,22-38.
[41] Hsieh Hou, Andrews H. Cubic Splines for Image Interpolation and Digital Filtering [J].IEEE Transactions on Acoustics, Speech and Signal Processing, 1978,26(6):508-517.
[42] Meijering E H, Niessen W J, Pluim J P, et al. Quantitative comparision sinc-approximating kernels for medical image interpolation [C]. MICCAI98 First International Conference on Medical Image Computing and Computer-Assisted Intervention, Lecture Notes in Computer Science, Springer Verlag:972-980, 1999.
[43] Holden M, Hill D L G, Denton E R E, et al. Voxel similarity measures for 3D serial MR brain image registration [C]. Information Processing in Medical Imaging 1999(IPMI99):472-477.
[44] Penney G P, Wcese J, Little J A, et ah A comparison of similarity measures for use in 2D-3D medical image registration [J]. IEEE Transactions on Medical Imaging, 1998,17(4):586-595.
[45]Woods R P,Cherry S R,Mazziotta J C.Rapid automated algorithm for aligning and reslicing PET images[J].Journal of Computer Assistant Tomography,1992,16:620-633.
[46]Shannon C E.A mathematical theory of communication[J].Bell System Technical Journal,1948(27):379-423.
[47]百度百科.http://baike.baidu.com/view/401605.htm
[48]Wachowiak M P,Smolikova R,Tourassi G D,et al.Generalized mutual information similarity metrics for multimodal biomedical image registration[C].Annual International Conference of the IEEE Engineering in Medicine and Biology,Houston,2:1005-1006,2002.
[49]Wachowiaka M P,Smolikova R,Tourassib G D,et al.Similarity metrics based on nonadditive entropies for 2D-3D multimodal biomedical image registration[C].San Diego:Proceedings of SPIE,5032:1090-1100,2003.
[50]Wachowiak M P,Smolikova R,Zheng Yufeng,et al.An approach to multimodal biomedical image registration utilizing particle swarm optimization[J].IEEE Transactions on Evolutionary computation,2004,8(3):289-301.
[51]Shi Y H,Eberhart R C.A modified particle swarm optimizer[C].Proceedings of IEEE International Conference on Evolutionary Computation,USA:IEEE,1998:67-73.
[52]Matsopoulos G K,Mouravliansky N A,Delibasis K K,et al.Automatic retinal image registration scheme using global optimization techniques[J].IEEE Transactions on Information Technology in Biomedicine,1999,3(1):47-60.
[53]Shannon C E.The mathematical theory of communication(part 1 and 2)[M].Bell System Technical Journal,1948,27:379-423 and 623-656.
[54]罗述谦,李响.基于最大互信息的多模医学图像配准[J].中国图像图形学报,2000,5(7):551-558.
[55]刘哲星,李树祥.基于联合直方图区域计数的时间序列图像自动配准方法[J].中国图像图形学报,2002,7(5):450-456.
[56]付宜利,于晓龙,王跃华.基于最大互信息的人脑多模图像快速配准算法[J].生物医学工程研究,2006,25(2):71-74.
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