基于几何代数理论的医学图像配准研究
|
摘要
生物医学图像配准技术广泛应用于临床医学研究及临床诊断和治疗。采用不同医学设备获取的医学图像称为多模态医学影像,其数据反映了机体组织不同的、互补的和重叠的生理信息。将不同模态的医学影像数据进行配准与融合,可方便医生实现治疗计划制定、病灶的定位、病情进展判断、治疗效果评定,并可为后续更高层次的医学图形图像自动处理提供更完整的信息。近年来,随着医学设备综合性能的提升,成像信息逐渐向多分辨率的彩色、多维方向发展,本文称之为多信息医学影像数据。
本文对多信息医学影像数据配准技术展开研究,研究对象包括2D彩色多模态医学图像、3D颅位医学图像,涉及到的成像模态有SPECT/CT2D彩色医学图像,CT/mr-PD3D颅位医学图像。针对上述配准对象,提出基于非经典数学理论——几何代数(Geometric Algebra,GA)分析与计算理论的配准方法。针对不同数据维医学图像配准,提出具有通用性的几何不变量的概念、几何代数计算模型及对应的计算方法。不同模态医学图像的几何不变量可以表征其在空间分布的几何位置,以该几何位置作为参考和基准,构造几何代数域上的几何平移算子及几何旋转算子,实现浮动模态医学影像数据的几何变换,完成与参考模态的配准,这也是本文配准的核心思想。正文部分提出4类不同几何不变量,实现了基于这些几何不变量的2D/2D、3D/3D医学图像配准。配准实验结果表明,基于几何代数理论和几何不变量的配准方法具有运算简单、几何意义直观、配准精度较高等优点,并且配准结果不易陷入局部最优点,适合于多信息医学图像配准。本文的主要工作及相关研究结果如下：
1、完成SPECT/CT彩色医学图像配准。鉴于传统体外定位标记法,外标记支架与病体的固定检查较繁琐,本文提出一种几何代数G3子空间下建立的RGB色彩空间,提出SPECT/CT医学图像四元数几何矩的计算方法,根据四元数图像质量分布情况,利用2D彩色医学图像转动惯量几何不变量的性质,求取两模态图像的相对旋转角度；利用两质心对齐的思路求取相对平移量,获得了良好配准与融合结果。
2、对CT/mr-PD3D颅位医学图像配准问题,提出3D医学图像点云集的转动惯量不变量的几何代数计算模型与计算方法,求取两个模态的转动惯量几何不变量及质心坐标向量。对齐质心后,以参考模态(3D-CT)的转动惯量几何不变量作为参考轴,构造几何代数空间上旋转算子,实现浮动图像全体点云(mr-PD)的旋转,进而实现配准。
3、在几何代数点云数据转动惯量几何不变量的基础上,本文提出基于点云集投影的二重向量不变量。从几何意义上分析,点云集投影的二重向量不变量可以视为平面,以点云集投影向量范数均方值最小(最大)作为度量的不变量,不同医学图像的3D模态点云集均具有这样的几何不变量。本文分别从一般几何代数与共形几何代数(Conformal Geometrical Algebra, CGA)两个思路上建立二重向量投影不变量的数学模型及计算方法,实现基于二重向量几何不变量的3D CT/mr-PD医学图像数据的配准,实验结果表明,该方法的配准同效于上述转动惯量几何不变量方法。
4、最后本文提出几何代数空间G3上的角度不变量,首先给出任意两个子空间夹角计算的几何代数统一形式(包括相等维度、不等维度的子空间)。对于3D医学图像数据的点云集,相对于直线(向量)、平面(二重向量)导出两个角度不变量。本文分别对这2个角度不变量进行几何代数建模与求解,求取3D CT/mr-PD医学图像数据2个角度不变量,并且以上述两角度不变量为基点,用对应的2种途径实现3D CT/mr-PD医学图像配准。其配准过程运算简单,配准精度高。
本文提出的几何不变量的几何要素是一般刚体所固有的几何特性,它(们)在空间上的几何分布及位置特性可以表征其所在刚体(可视为无穷带质量点云组成)在空间上的几何位置信息。对于2D、3D医学图像数据点云集(可视为有限个离散点云组成的刚体),对应的几何不变量同样具备描述其几何位置信息的几何特性与表征功能,为此提出的几何不变量配准策略是可行的,也是科学的,有效的。本文提出的基于几何代数理论的配准方法,采用基于独立坐标系统的几何描述方法与科学计算语言,与2D、3D医学图像配准思路相结合,实现了稳定、快速、直观与高效配准,为医学图像配准研究提供一种新的思路。
The registration technology of biomedical images is widely utilized in the fields of clinical research, diagnosis and treatment. The medical images acquired by different medical devices are called multi-modality medical images, and the data of which reflect the different, complementary and overlapping physiological information of tissues. The registration and fusion for different modality medical images has significant advantages in treatment plan decision, lesion localization, disease progress estimation and therapeutic effects evaluation. In addition, it can also provide adequate information for the subsequent automatic processing of medical images. Recently, medical equipments with higher performance have ability to provide multi-resolution and multi-dimensional images that are named multi-information medical image data in this paper.
Registration of multi-information medical image data is researched in this paper, and the objects include2D color multi-modality medical images and3D craniofacial medical images. The imaging modalities consist of SPECT/CT2D color medical images and CT/mr-PD3D craniofacial medical images. A registration method based on non-classical mathematical theory——Geometric Algebra (GA) analyses and theory of computation is proposed in this paper for registration objects listed above. For the registration of different data dimensions medical images, both a universal geometric invariant concept and a GA calculation model and its corresponding calculation methodology are present in this paper. The geometric invariant of different modality medical images can be characterized as different geometric positions in spatial. Taking these geometric positions as the reference and baseline, the geometry-displacement operators and geometry-rotation operators in GA domain are structured, which are utilized for geometric transformation of floating modal medical image data. The registration of reference modality is subsequently accomplished. The context described above is the core idea of registration in this paper. Four kinds of different geometric invariants are put forward in order to realize the registration of2D/2D,3D/3D medical images. The registration experiment results demonstrate the advantages of the methodology proposed here, which include optimization capability in global area, little computation burden, intuitive geometric meaning and high registration precision. Consequently, it is suitable for the registration of multi-information medical images. Main contributions of this paper are described as follows:
1. The registration of SPECT/CT color medical images is realized. Since the vitro labeling bracket and fixed check of sick body of the traditional vitro positioning notation are relatively burdensome, the RGB color space established in the subspace of GA G3is proposed. And the calculation method of quaternion geometric moment for SPECT/CT medical images is present, in which the relative rotation angle of two modal images can be calculated on the basis of the distribution of quaternion image mass and the property of the rotational inertia geometric invariant of2D color medical images. In addition, the relative translation amount can be computed by the thought that the two centers of mass are aligned, and the registration and fusion effect is ideal.
2. In order to cope with the registration of CT/mr-PD3D cranial medical images, a GA calculation model and algorithm of the rotational inertia invariant of the3D cranial medical image point set are proposed for calculating the rotational inertia geometric invariant and the coordinate vector of the center of mass of the two modes. After aligning the mass center, the twiddle factor in GA space is constructed by taking the geometric invariants of rotational inertia of reference mode (3D-CT) as a reference axis. Subsequently, the rotation of point cloud (mr-PD) of floating image is realized, and the registration is completed.
3. On the basis of the rotational inertia geometric invariant of the GA point cloud data, a dual-vector invariant based on the projection of point cloud set is proposed in this paper. In a viewpoint of geometric aspect, the dual-vector invariant can be regarded as a plane. If the minimum (maximum) norm mean square value of the point cloud set projection vector is chosen as a invariant, all3D modal point cloud sets for different medical images have the geometric invariant like this. The mathematical model and calculation method of dual-vector projection invariant are established by the two thoughts of general GA and conformal geometrical algebra(CGA) respectively to realize the registration of3D CT/mr-PD medical image data based on the dual vector geometric invariant. The experiment results show that the registration effect of this method is equal to the rotational inertia geometric invariants method mentioned above.
4. Finally, an angle invariant in the GA space G3is presented in this paper. By given the calculation unified form of the arbitrary angle between two subspaces (including the subspaces with equal dimension and unequal dimension), two angle invariants for the point cloud sets of3D medical image data are derived corresponding to the straight line (vector) and plane (dual vector). A modeling and solving technique of the two angle invariants of3D CT/mr-PD medical image date are conducted. And then, two corresponding methods are applied to achieve the registration of the3D CT/mr-PD medical images. It is a registration process with low computation burden and high precision.
The geometric elements of geometric invariant proposed here are inherent geometric characteristics of the general rigid body. Its or their spatial geometric distributions and geometric location information can characterize the spatial geometric location information of the rigid body which can be considered as the infinite brand mass point clouds. For the point cloud sets, which can be considered as a rigid body composed of finite discrete point clouds, of2D,3D medical image data, the corresponding geometric invariant also have geometric properties and function of characterization to describe its geometric location information. Therefore, the strategy of geometric invariant registration proposed in this paper is feasible, scientific and effective. The registration method based on the GA theory adopts the geometric description method and scientific computer language of the independent coordinate system. The2D,3D medical image registration methods put forward here have characteristics of stable, fast, intuitive and efficient, which provide new research ways for medical images registration.
本文对多信息医学影像数据配准技术展开研究,研究对象包括2D彩色多模态医学图像、3D颅位医学图像,涉及到的成像模态有SPECT/CT2D彩色医学图像,CT/mr-PD3D颅位医学图像。针对上述配准对象,提出基于非经典数学理论——几何代数(Geometric Algebra,GA)分析与计算理论的配准方法。针对不同数据维医学图像配准,提出具有通用性的几何不变量的概念、几何代数计算模型及对应的计算方法。不同模态医学图像的几何不变量可以表征其在空间分布的几何位置,以该几何位置作为参考和基准,构造几何代数域上的几何平移算子及几何旋转算子,实现浮动模态医学影像数据的几何变换,完成与参考模态的配准,这也是本文配准的核心思想。正文部分提出4类不同几何不变量,实现了基于这些几何不变量的2D/2D、3D/3D医学图像配准。配准实验结果表明,基于几何代数理论和几何不变量的配准方法具有运算简单、几何意义直观、配准精度较高等优点,并且配准结果不易陷入局部最优点,适合于多信息医学图像配准。本文的主要工作及相关研究结果如下：
1、完成SPECT/CT彩色医学图像配准。鉴于传统体外定位标记法,外标记支架与病体的固定检查较繁琐,本文提出一种几何代数G3子空间下建立的RGB色彩空间,提出SPECT/CT医学图像四元数几何矩的计算方法,根据四元数图像质量分布情况,利用2D彩色医学图像转动惯量几何不变量的性质,求取两模态图像的相对旋转角度；利用两质心对齐的思路求取相对平移量,获得了良好配准与融合结果。
2、对CT/mr-PD3D颅位医学图像配准问题,提出3D医学图像点云集的转动惯量不变量的几何代数计算模型与计算方法,求取两个模态的转动惯量几何不变量及质心坐标向量。对齐质心后,以参考模态(3D-CT)的转动惯量几何不变量作为参考轴,构造几何代数空间上旋转算子,实现浮动图像全体点云(mr-PD)的旋转,进而实现配准。
3、在几何代数点云数据转动惯量几何不变量的基础上,本文提出基于点云集投影的二重向量不变量。从几何意义上分析,点云集投影的二重向量不变量可以视为平面,以点云集投影向量范数均方值最小(最大)作为度量的不变量,不同医学图像的3D模态点云集均具有这样的几何不变量。本文分别从一般几何代数与共形几何代数(Conformal Geometrical Algebra, CGA)两个思路上建立二重向量投影不变量的数学模型及计算方法,实现基于二重向量几何不变量的3D CT/mr-PD医学图像数据的配准,实验结果表明,该方法的配准同效于上述转动惯量几何不变量方法。
4、最后本文提出几何代数空间G3上的角度不变量,首先给出任意两个子空间夹角计算的几何代数统一形式(包括相等维度、不等维度的子空间)。对于3D医学图像数据的点云集,相对于直线(向量)、平面(二重向量)导出两个角度不变量。本文分别对这2个角度不变量进行几何代数建模与求解,求取3D CT/mr-PD医学图像数据2个角度不变量,并且以上述两角度不变量为基点,用对应的2种途径实现3D CT/mr-PD医学图像配准。其配准过程运算简单,配准精度高。
本文提出的几何不变量的几何要素是一般刚体所固有的几何特性,它(们)在空间上的几何分布及位置特性可以表征其所在刚体(可视为无穷带质量点云组成)在空间上的几何位置信息。对于2D、3D医学图像数据点云集(可视为有限个离散点云组成的刚体),对应的几何不变量同样具备描述其几何位置信息的几何特性与表征功能,为此提出的几何不变量配准策略是可行的,也是科学的,有效的。本文提出的基于几何代数理论的配准方法,采用基于独立坐标系统的几何描述方法与科学计算语言,与2D、3D医学图像配准思路相结合,实现了稳定、快速、直观与高效配准,为医学图像配准研究提供一种新的思路。
The registration technology of biomedical images is widely utilized in the fields of clinical research, diagnosis and treatment. The medical images acquired by different medical devices are called multi-modality medical images, and the data of which reflect the different, complementary and overlapping physiological information of tissues. The registration and fusion for different modality medical images has significant advantages in treatment plan decision, lesion localization, disease progress estimation and therapeutic effects evaluation. In addition, it can also provide adequate information for the subsequent automatic processing of medical images. Recently, medical equipments with higher performance have ability to provide multi-resolution and multi-dimensional images that are named multi-information medical image data in this paper.
Registration of multi-information medical image data is researched in this paper, and the objects include2D color multi-modality medical images and3D craniofacial medical images. The imaging modalities consist of SPECT/CT2D color medical images and CT/mr-PD3D craniofacial medical images. A registration method based on non-classical mathematical theory——Geometric Algebra (GA) analyses and theory of computation is proposed in this paper for registration objects listed above. For the registration of different data dimensions medical images, both a universal geometric invariant concept and a GA calculation model and its corresponding calculation methodology are present in this paper. The geometric invariant of different modality medical images can be characterized as different geometric positions in spatial. Taking these geometric positions as the reference and baseline, the geometry-displacement operators and geometry-rotation operators in GA domain are structured, which are utilized for geometric transformation of floating modal medical image data. The registration of reference modality is subsequently accomplished. The context described above is the core idea of registration in this paper. Four kinds of different geometric invariants are put forward in order to realize the registration of2D/2D,3D/3D medical images. The registration experiment results demonstrate the advantages of the methodology proposed here, which include optimization capability in global area, little computation burden, intuitive geometric meaning and high registration precision. Consequently, it is suitable for the registration of multi-information medical images. Main contributions of this paper are described as follows:
1. The registration of SPECT/CT color medical images is realized. Since the vitro labeling bracket and fixed check of sick body of the traditional vitro positioning notation are relatively burdensome, the RGB color space established in the subspace of GA G3is proposed. And the calculation method of quaternion geometric moment for SPECT/CT medical images is present, in which the relative rotation angle of two modal images can be calculated on the basis of the distribution of quaternion image mass and the property of the rotational inertia geometric invariant of2D color medical images. In addition, the relative translation amount can be computed by the thought that the two centers of mass are aligned, and the registration and fusion effect is ideal.
2. In order to cope with the registration of CT/mr-PD3D cranial medical images, a GA calculation model and algorithm of the rotational inertia invariant of the3D cranial medical image point set are proposed for calculating the rotational inertia geometric invariant and the coordinate vector of the center of mass of the two modes. After aligning the mass center, the twiddle factor in GA space is constructed by taking the geometric invariants of rotational inertia of reference mode (3D-CT) as a reference axis. Subsequently, the rotation of point cloud (mr-PD) of floating image is realized, and the registration is completed.
3. On the basis of the rotational inertia geometric invariant of the GA point cloud data, a dual-vector invariant based on the projection of point cloud set is proposed in this paper. In a viewpoint of geometric aspect, the dual-vector invariant can be regarded as a plane. If the minimum (maximum) norm mean square value of the point cloud set projection vector is chosen as a invariant, all3D modal point cloud sets for different medical images have the geometric invariant like this. The mathematical model and calculation method of dual-vector projection invariant are established by the two thoughts of general GA and conformal geometrical algebra(CGA) respectively to realize the registration of3D CT/mr-PD medical image data based on the dual vector geometric invariant. The experiment results show that the registration effect of this method is equal to the rotational inertia geometric invariants method mentioned above.
4. Finally, an angle invariant in the GA space G3is presented in this paper. By given the calculation unified form of the arbitrary angle between two subspaces (including the subspaces with equal dimension and unequal dimension), two angle invariants for the point cloud sets of3D medical image data are derived corresponding to the straight line (vector) and plane (dual vector). A modeling and solving technique of the two angle invariants of3D CT/mr-PD medical image date are conducted. And then, two corresponding methods are applied to achieve the registration of the3D CT/mr-PD medical images. It is a registration process with low computation burden and high precision.
The geometric elements of geometric invariant proposed here are inherent geometric characteristics of the general rigid body. Its or their spatial geometric distributions and geometric location information can characterize the spatial geometric location information of the rigid body which can be considered as the infinite brand mass point clouds. For the point cloud sets, which can be considered as a rigid body composed of finite discrete point clouds, of2D,3D medical image data, the corresponding geometric invariant also have geometric properties and function of characterization to describe its geometric location information. Therefore, the strategy of geometric invariant registration proposed in this paper is feasible, scientific and effective. The registration method based on the GA theory adopts the geometric description method and scientific computer language of the independent coordinate system. The2D,3D medical image registration methods put forward here have characteristics of stable, fast, intuitive and efficient, which provide new research ways for medical images registration.
引文
[1]周振环.医学图像分割与配准[M].成都：电子科技大学出版社,2007.
[2]郑亚琴,田心.医学图像配准技术研究进展[J].国际生物医学工程杂志,2006,29(2)：88-92.
[3]彭文.基于特征的医学图像配准中若干关键技术的研究[D][博士学位论文].杭州：浙江大学,计算机科学与技术学院,2007.
[4]Shao Y, Cherry S R, Farahani K, et al. Development of a PET detector system compatible with MRI/NMR systems[J]. IEEE Transactions on Nuclear Science,1997,44(3):1167-1171.
[5]宋智礼.图像配准技术及其应用的研究[D][博士学位论文].上海：复旦大学,计算机科学技术学院,2010.
[6]Brown L G. A survey of image registration techniques[J]. ACM computing surveys (CSUR),1992,24(4): 325-376.
[7]Marc Vaillant, Christos Davatzikos, Russell H. Taylor.et al. A path-planning algorithm for image-guided neurosurgery[A].CVRMed-MRCAS'97[C]. Berlin Heidelberg:Springer Berlin Heidelberg,1997, 467-476.
[8]杜亚娟.基于不变矩理论的自动目标识别技术研究[D][博士学位论文].西安：西北工业大学,自动化学院,2000.
[9]Chong C W, Raveendran P, Mukundan R. Translation and scale invariants of Legendre moments[J]. Pattern Recognition,2004,37(1):119-129.
[10]Mukundan R, Ong S H, Lee P A. Image analysis by Tchebichef moments[J]. IEEE Transactions on Image Processing,2001,10(9):1357-1364.
[11]冉冉,杨唐文,阮秋琦.结合HSL模型与傅里叶描述子的三维彩色物体识别[J].智能系统学报,2011,6(1)：73-78.
[12]Rahtu E, Salo M, Heikkila J. Affine invariant pattern recognition using multiscale autoconvolution[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(6):908-918.
[13]李军宏,陈玉春,潘泉等.一种基于高阶统计量的不变量图像识别算法[J].计算机工程,2004,30(20)：7-8.
[14]Zhang Jianguo, Tan Tieniu. Affine invariant texture analysis based on structural properties[C].Proceedings of the Fifth Asian Conference on Computer Vision (ACCV 2002), Australia, Melbourne, MA,2002, pp.216-221.
[15]Yang Z, Cohen F S. Image registration and object recognition using affine invariants and convex hulls[J]. IEEE Transactions on Image Processing,1999,8(7):934-946.
[16]Lowe D G. Distinctive image features from scale-invariant keypoints[J]. International journal of computer vision,2004,60(2):91-110.
[17]Zhu S, Ma K K. A new diamond search algorithm for fast block-matching motion estimation[J]. IEEE Transactions on Image Processing,2000,9(2):287-290.
[18]Bay H, Ess A, Tuytelaars T, et al. Speeded-up robust features (SURF)[J]. Computer vision and image understanding,2008,110(3):346-359.
[19]Mikolajczyk K, Schmid C. A performance evaluation of local descriptors[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(10):1615-1630.
[20]雷琳,陈涛,李智勇等.全局仿射变换条件下图像不变量提取新方法[J].国防科技大学学报,2008,30(4)：64-70.
[21]Bentoutou Y, Taleb N, Chikr El Mezouar M, et al. An invariant approach for image registration in digital subtraction angiography[J]. Pattern Recognition,2002,35(12):2853-2865.
[22]戴修斌,张辉,舒华忠等.基于正交矩混合不变量的离焦模糊图像配准[J].应用科学学报,2010,28(5)：476-484.
[23]李斌,叶昊.基于仿射几何不变量的鲁棒图像配准算法[J].上海交通大学学报,2012,46(12)：1881-1884.
[24]Lee J H, Kim Y S, Lee D, et al. Robust CCD and IR image registration using gradient-based statistical information[J]. Signal Processing Letters, IEEE,2010,17(4):347-350.
[25]Jiang H, Yu S X, Martin D R. Linear scale and rotation invariant matching[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2011,33(7):1339-1355.
[26]Jiang H, Tian T P, Sclaroff S. Scale and rotation invariant matching using linearly augmented trees[C]. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), America, Providence, RI,2011, pp.2473-2480.
[27]Tsolakis A, Falelakis M, Delopoulos A. A framework for efficient correspondence using feature interrelations[C].19th International Conference on Pattern Recognition, Americam, Tampa,2008, pp.1-4.
[28]Caetano T S, Caelli T. A unified formulation of invariant point pattern matching[C].18th International Conference on Pattern Recognition, China, Hong Kong,2006,pp.121-124.
[29]Maintz J B, Viergever M A. A survey of medical image registration[J]. Medical image analysis,1998, 2(1):1-36.
[30]Michel A. Audette,Frank P. Ferrieb, Terry M. Peters. An algorithmic overview of surface registration techniques for medical imaging[J].Medical Image Analysis,2000,4(3):201-217.
[31]Van den Elsen P A, Pol E J D, Viergever M A. Medical image matching-a review with classification[J]. Engineering in Medicine and Biology Magazine, IEEE,1993,12(1):26-39.
[32]Zhang Huisheng, Liu Xinyu, Li Ling, et al. Accurate Multi-spectral Image Registration Based on Scale Invariant Feature[C].2nd International Conference on Computer Science and Network Technology (ICCSNT), China, Changchun,2012,29(31):847-852.
[33]T.D.Zuk,M S.Atkins. A comparison of manual and automatic methods for registering scans of the head[J]. IEEE Transactions on Medical Imaging,1996,15(5):732-744.
[34]张锐娟.图像配准理论及算法研究[D][硕士学位论文].西安：西安电子科技大学,物理与光电工程学院,2009.
[35]Makela,T.,Clarysse,P.,Sipila,O.,et al. A review of cardiac image registration methods[J].IEEE Transactions on Medical Imaging,2002,21(9):1011-1021.
[36]Zitova B, Flusser J. Image registration methods:a survey[J]. Image and vision computing,2003,21(11): 977-1000.
[37]Holden M. A review of geometric transformations for nonrigid body registration[J]. IEEE Transactions on Medical Imaging,2008,27(1):111-128.
[38]Lu X, Ma H, Zhang B, et al. A review of algorithm research progress for non-rigid medical image registration[C].2011 International Conference on Consumer Electronics, Communications and Networks (CECNet), China, XianNing,2011:3863-3866.
[39]Sotiras A.,Davatzikos C.,Paragios N. Deformable Medical Image Registration:A Survey[J]. IEEE Transactions on Medical Imaging,2013,32(7):1153-1190.
[40]申艳平.医学图像配准技术[J].中国医学物理学杂志,2013,30(001)：3885-3889.
[41]Plishker W, Dandekar O, Bhattacharyya S, et al. A taxonomy for medical image registration acceleration techniques[C]. Life Science Systems and Applications Workshop,2007. IEEE/NIH, America, Bethesda, MD,2007,160-163.
[42]Luo Shuqian, Li Xiang. Implementation of mutual information based multi-modality medical image registration[C]. Engineering in Medicine and Biology Society,2000. Proceedings of the 22nd Annual International Conference of the IEEE, America, Chicago, IL,2000,2:1447-1450.
[43]曹炬,马杰,谭毅华等.基于像素抽样的快速互相关图像匹配算法[J].宇航学报.2004,25(2),173-178.
[44]秦斌杰,庄天戈.基于体素灰度3D多模医学图像配准中的相似性测度[J].上海交通大学学报,2002,36(7),942-945.
[45]梁玮.2D-3D医学图像配准研究[D][硕士学位论文].南京：东南大学,生物科学与医学工程学院2004.
[46]Chengfen Jiang. Ticheng Lu, Shuping Sun. Interactive image registration tool for positioning verification in head and neck radiotherapy [J]. Computers in Biology and Medicine,2008,38(1): 90-100.
[47]R.P.Woods,S.R.Cherry,J.C.Mazziotta. Rapid Automated Algorithm for Aligning and Reslicing PET Images[J].Journal of Computer Assisted Tomography,1992,16(4):620-633.
[48]吴锋,钱宗才,杭恰时.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.
[49]Pluim J P W, Maintz J B A, Viergever M A. Mutual-information-based registration of medical images:a survey[J]. IEEE Transactions on Medical Imaging,2003,22(8):986-1004.
[50]M.M.Emma,C.Ruben,L.G.Rodriqo,et al.Image Registration Based on Automatic Detection of Anatomical Landmarks for Bone Age Assessment[J].WSEAS Transactions on Computers,2005,4(11): 1596-1603.
[51]N.Ryan,C.Heneghan,P.Chazal. Registration of Digital Retinal Images Using Landmark Correspondence by Expectation Maximization [J].Image and Vision Computing,2004,22 (11):883-898.
[52]王秀英等.弹性的二维医学图像配准算法[J],吉林大学学报(信息科学版),2003 21(5)：73-79.
[53]Chen J, Tian J, Lee N, et al. A partial intensity invariant feature descriptor for multimodal retinal image registration[J]. IEEE Transactions on Biomedical Engineering,2010,57(7):1707-1718.
[54]Zheng Lintao, Qian Guiping. A SIFT-Based Approach for Image Registration[A].Green Communications and Networks[C]. Berlin Heidelberg:Springer Netherlands,2012,277-287.
[55]Faysal Boughorbel, Muharrem Mercimek, Andreas Koschan, et al. A new method for the registration of three-dimensional point-sets:The Gaussian Fields framework[J]. Image and Vision Computing,2010, 28(1):124-137.
[56]Yingxuan Zhu, Samuel Cheng, Vladimir Stankovic, et al. Image registration using BP-SIFT[J]. Journal of Visual Communication and Image Representation,2013,24(4):448-457.
[57]Lu Xiaoqi, Zhao Yongjie, Zhang Baohua, et al. A non-rigid cardiac image registration method based on an optical flow model[J]. International Journal for Light and Electron Optics,2013,124(20):4266-4273.
[58]Edgar RArce-Santana, Alfonso Alba. Image registration using Markov random coefficient and geometric transformation fields[J]. Pattern Recognition,2009,42(8):1660-1671.
[59]Li Hao, Yang Hansheng, Shi Guohua, et al. Adaptive optics retinal image registration from scale-invariant feature transform[J]. International Journal for Light and Electron Optics, 2011,22(9):839-841.
[60]GT.Y.Chen,C.A.Pelizzari. Image Correlation Techniques in Radiation Therapy Planning[J].Computerized Medical Imaging and Graphics,1989,13(3):235-240.
[61]Penney 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.
[62]张密.放射治疗中2D/3D医学图像配准算法研究[D][硕士学位论文].广州：华南理工大学,生物 科学与工程学院,2010.
[63]Khamene A, Bloch P, Wein W, et al. Automatic registration of portal images and volumetric CT for patient positioning in radiation therapy[J]. Medical Image Analysis,2006,10(1):96-112.
[64]Galvin J M, Sims C.The use of digitally reconstructed radiographs for three-dimensional treatment planning and CT-simulation[J].International Journal of Radiation Oncology Biology Physics,1995, 31(4):935-942.
[65]R. Harmouche, F. Cheriet, H. Labelle, et al.3D registration of MR and X-ray spine images using an articulated model[J].Computerized Medical Imaging and Graphics,2012,36(5):410-418.
[66]Gholipour A, Kehtarnavaz N, Briggs R, et al. Brain functional localization:a survey of image registration techniques[J]. IEEE Transactions on Medical Imaging,2007,26(4):427-451.
[67]Schweikard A., Glosser G., Bodduluri M., et al. Robotic Motion Compensation for Respiratory Movement during Radiosurgery [J]. Computer-Aided Surgery,2000,5(4):263-277.
[68]LaRose D A. Iterative X-ray/CT Registration using accelerated volume rendering [D][doctoral dissertation].Pittsburgh:Carnegie Mellon University, Robotics Institute,2001.
[69]Chen X, Varley M R, Shark L K, et al. An extension of iterative closest point algorithm for 3d-2d registration for pre-treatment validation in radiotherapy[C]. International Conference on Medical Information Visualisation-BioMedical Visualisation,2006, USA, Washington, DC,2006:3-8.
[70]Cui Haihua, Dai Ning, Liao Wenhe, et al. Intraoral 3D optical measurement system for tooth restoration[J]. International Journal for Light and Electron Optics,2013,124(12):1142-1147.
[71]Livyatan H, Yaniv Z, Joskowicz L. Gradient-based 2-D/3-D rigid registration of fluoroscopic X-ray to CT[J]. IEEE Transactions on Medical Imaging,2003,22(11):1395-1406.
[72]Tzimiropoulos G, Argyriou V, Zafeiriou S, et al. Robust FFT-based scale-invariant image registration with image gradients[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2010,32(10): 1899-1906.
[73]X. Chen, M. R. Varley, L.K.Shark, et al. A computationally efficient method for automatic registration of orthogonal x-ray images with volumetric CT data [J].Physics in Medicine and Biology,2008, 53(4):967-983.
[74]Ali Khamene, Peter Bloch, Wolfgang Wein, et al. Automatic registration of portal images and volumetric CT for patient positioning in radiation therapy [J]. Medical Image Analysis,2006,10(1):96-112.
[75]Charles Florin, James Williams, Ali Khamene, et al. Registration of 3D angiographic and X-ray images using sequential monte carlo sampling[A].Computer Vision for Biomedical Image Applications[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2005,427-436.
[76]Zheng Guoyan. Unifying energy minimization and mutual information maximization for robust 2D/3D registration of X-ray and CT images[A].Pattern Recognition[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2007,547-557.
[77]Yoshito Otake, Mehran Armand, Ofri Sadowsky, et al. An iterative framework for improving the accuracy of intraoperative intensity-based 2D/3D registration for image-guided orthopedic surgery [A].Information Processing in Computer-Assisted Interventions[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2010,23-33.
[78]Lei Peng, Dandekar Omkar, Widlus David, et al. Incorporation of Preprocedural PET into CT-Guided Radiofrequency Ablation of Hepatic Metastases:a Nonrigid Image Registration Validation Study[J]. Journal of Digital Imaging,2010,23 (6):780-792.
[79]Marcelo Elias de Oliveira,Harri Hallila,Antti Ritvanen,et al. Feature-invariant image registration method for quantification of surgical outcomes in patients with craniosynostosis:a preliminary study[J]. Journal of Pediatric Surgery,2011,46(1O):E1-E8.
[80]Andre G, Wu K. Providing visual information to validate 2-D to 3-D registration [J].Medical Image Analysis,2000,4(4):357-368.
[81]A.Rangarajan, H. Chui, J. S. Duncan. Rigid point feature registration using mutual information[J].Medical Image Analysis,1999,3(4):425-440.
[82]Porter B C, Rubens D J, Strang J G, et al. Three-dimensional registration and fusion of ultrasound and MRI using major vessels as fiducial markers[J]. IEEE Transactions on Medical Imaging,2001,20(4): 354-359.
[83]Besl P Makay. A Method for Registration of 3D Shapes[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1992,14(2):239-256.
[84]Chen Y, Medioni G. Object Modeling by Registration of Multiple Range Images[J].Image and Vision Computing,1992,10(3):145-155.
[85]Fitzgibbon A W. Robust registration of 2D and 3D point sets[J]. Image and Vision Computing,2003, 21(13):1145-1153.
[86]Du S, Zheng N, Ying S, et al. Affine iterative closest point algorithm for point set registration[J]. Pattern Recognition Letters,2010,31(9):791-799.
[87]Du S, Zheng N, Meng G, et al. Affine registration of point sets using ICP and ICA[J]. Signal Processing Letters, IEEE,2008,15:689-692.
[88]Sharp G C, Lee S W, Wehe D K. ICP registration using invariant features[J]., IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(1):90-102.
[89]屈建勤.基于代数和几何不变量的点集配准方法[D][博士学位论文].长春：吉林大学,2012.
[90]Li Gang, Guo Lei, Liu Tianming. Deformation invariant attribute vector for deformable registration of longitudinal brain MR images[J]. Computerized Medical Imaging and Graphics,2009,33(5):384-398.
[91]Pluim, J.P.W., Maintz, J.B.A., Viergever, M.A.. Image registration by maximization of combined mutual information and gradient information[A].Medical Image Computing and Computer-Assisted Intervention[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2000:452-461.
[92]Liu Liping, Ke Li, Zhongguo Liu.Medical image registration by maximization of combined mutual information and edge correlative deviation[C]. Engineering in Medicine and Biology Society,2005. IEEE-EMBS 2005.27th Annual International Conference, China, Shanghai,2005,6:6379-6382.
[93]Chen W.Q., Ou Z.Y., Song W.W.A Coarse-to-Refined Approach of Medical Image Registration Based on Combining Mutual Information and Shape Information[C]. International Conference on Neural Networks and Brain,2005. China, Beijing,2005,2:816-820.
[94]Li Guang, Xie Huchen, Ning Holly, et al. Accuracy of 3D volumetric image registration based on CT,MR and PET/CT phantom experiments[J].Journal of Applied Clinical Medical Physics,2008, 9(4):17-36.
[95]Pluim J P W, Maintz J B A, Viergever M A. f-Information measures in medical image registration[J]. IEEE Transactions on Medical Imaging,2004,23(12):1508-1516.
[96]M. Babaie-Zadeh, C. Jutten, K.Nayebi.Differential of the mutual information[J]. Signal Processing Letters, IEEE,2004,11(1):48-51.
[97]吕晓琪,李娜,张宝华等.基于体素相似性的三维多模脑图像配准研究[J].中国医学影像学杂志,2013,21(2)：146-151.
[98]王远军,周密,查珊珊等.多模态医学图像配准技术研究[J].中国医学物理学杂志,2013,30(003)：4125-4129.
[99]Laura Fernandez-de-Manuel, Gert Wollny, Jan Kybic, et al. Organ-focused mutual information for nonrigid multimodal registration of liver CT and Gd-EOB-DTPA-enhanced MRI[J]. Medical Image Analysis,2014(18):22-35.
[100]L. Y. Hsu, M. H. Loew. Fully automatic 3D feature-based registration of multi-modality medical images[J].Image and Vision Computing,2001,19(1):75-85.
[101]李文龙,程流泉,李军等.基于自由形变的3D非线性医学图像配准[J].中国医学影像技术,2011,27(12)：2536-2540.
[102]R.Sharman, J.M. Tyler, O S.Pianykh. A fast and accurate method to register medical images using Wavelet Modulus Maxima[J]. Pattern Recognition Letters,2000,21(6):447-462.
[103]Salomon M, Heitz F, Perrin G R, et al. A massively parallel approach to deformable matching of 3D medical images via stochastic differential equations[J]. Parallel Computing,2005,31(1):45-71.
[104]Cordon O, Damas S, Santamaria J. A fast and accurate approach for 3D image registration using the scatter search evolutionary algorithm[J]. Pattern Recognition Letters,2006,27(11):1191-1200.
[105]Blackall J M, Rueckert D, Maurer Jr C R, et al. An image registration approach to automated calibration for freehand 3D ultrasound[A]. Medical Image Computing and Computer-Assisted Intervention-MICCAI 2000[C].Berlin Heidelberg:Springer Berlin Heidelberg,2000,462-471.
[106]Thirion J P. New feature points based on geometric invariants for 3D image registration[J]. International journal of computer vision,1996,18(2):121-137.
[107]Huang X, Hill N A, Ren J, et al. Dynamic 3D ultrasound and MR image registration of the beating heart[A].Medical Image Computing and Computer-Assisted Intervention-MICCAI 2005[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2005,171-178.
[108]Walimbe V, Shekhar R. Automatic elastic image registration by interpolation of 3D rotations and translations from discrete rigid-body transformations[J]. Medical Image Analysis,2006,10(6):899-914.
[109]Renjie He, et al.Global optimization of mutual information:application to three dimensional retrospective registration of magnetic resonance images[J].Computerized Medical Imaging and Graphics,2002,26(4):277-292.
[110]刘爱菱.3D医学图像配准方法研究[D][硕士学位论文].武汉：华中科技大学,2007.
[111]Yang S, Illner D, Teller K, et al. Statistical Shape Theory and Registration Methods for Analyzing the 3D Architecture of Chromatin in Interphase Cell Nuclei[M]. Springer Netherlands:Advances in Nuclear Architecture,2011:131-147.
[112]Diego Thomas, Akihiro Sugimoto. Robustly registering range images using local distribution of albedo[J]. Computer Vision and Image Understanding,2011,115(5):649-667.
[113]Jiang Jun, Cheng Jun, Chen Xinglin. Registration for 3-D point cloud using angular-invariant feature[J]. Neurocomputing,2009,72(16-18):3839-3844.
[114]He Bingwei, Lin Zeming, Li Y.F. An automatic registration algorithm for the scattered point clouds based on the curvature feature[J]. Optics&Laser Technology,2013,46(3):53-60.
[115]Joaquim Salvi,Carles Matabosch,David Fofi,et al.A review of recent range image registration methods with accuracy evaluation[J].Image and Vision Computing,2007,25(5):578-596.
[116]Jannin, P., J.M.Fitzpatrick, D.J.Hawkes, et al. Validation of medical image processing in image-guided therapy[J]. IEEE Transactions on Medical Imaging,2002,21(12):1445-9.
[117]Reuben R. Shamir, Leo Joskowicz. Geometrical analysis of registration errors in point-based rigid-body registration using invariants[J]. Medical Image Analysis,2011,15(1):85-95.
[118]Plattarp D,Soret M.Patient Set-up Using Portal Images:2D/2D Image Registration Using Mutual Information[J].Computer Aided Surgery,2000,5(4):246-262.
[119]van de Kraats E B, Penney G P, Tomazevic D, et al. Standardized evaluation methodology for 2-D-3-D registration[J]. IEEE Transactions on Medical Imaging,2005,24(9):1177-1189.
[120]Reuben R S.Leo J.Sergey S, et al.Localization and registration accuracy in image guided neurosurgery:a clinical study[J].International Journal of Computer Assisted Radiology and Surgery,2009,4(1):45-52.
[121]Artin E. Geometric algebra[M]. John Wiley & Sons,2011.
[122]Zaharia M D, Dorst L. Modeling and visualization of 3D polygonal mesh surfaces using geometric algebra[J]. Computers & Graphics,2004,28(4):519-526.
[123]Dorst L, Fontijne D, Mann S. Geometric Algebra for Computer Science (Revised Edition):An Object-Oriented Approach to Geometry[M]. San Francisco:Morgan Kaufmann,2009.
[124]Bayro-Corrochano E, Vallejo R, Arana-Daniel N. Geometric preprocessing, geometric feedforward neural networks and Clifford support vector machines for visual learning[J]. Neurocomputing,2005, 67:54-105.
[125]李洪波.Clifford代数,几何计算和几何推理[J].数学进展,2003,32(4)：405-415.
[126]倪庆.几何代数在计算机视觉三维重建中的应用[D][硕士学位论文].国防科学技术大学,机电工程与自动化学院,2011.
[127]Rivera-Rovelo Jorge, Bayro-Corrochano Eduardo. Medical image segmentation, volume representation and registration using spheres in the geometric algebra framework[J]. Pattern Recognition,2007, 40(l):171-188.
[128]徐晨,刘辉,欧阳春娟等.多光谱图像Clifford拟微分算子及应用[J].中国科学：信息科学,2011,41(12)：1423-1435.
[129]Orozco-Aguirre R, Rivera-Rovelo J, Bayro-Corrochano E. Medical image segmentation and the use of geometric algebras in medical applications[M]. Berlin:Springer Berlin Heidelberg,2005:729-740.
[130]韩国良.几何变换及配准和运动估计的几何代数方法研究[D][硕士学位论文].青岛：中国石油大学,计算机与通信工程学院,2008.
[131]Leo Reyes, Gerard Medioni, Eduardo Bayro. Registration of 3D Points Using Geometric Algebra and Tensor Voting[J]. International Journal of Computer Vision,2007,75(3):351-369.
[132]Subakan 6 N, Vemuri B C. Quaternion-Based Color Image Smoothing Using a Spatially Varying Kernel[A]. Energy Minimization Methods in Computer Vision and Pattern Recognition[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2009:415-428.
[133]Bayro-Corrochano E, Rivera-Rovelo J. The use of geometric algebra for 3D modeling and registration of medical data[J]. Journal of Mathematical Imaging and Vision,2009,34(1):48-60.
[134]刘辉,徐晨,曹文明.基于Clifford代数的多光谱图像边缘检测[J].东南大学学报(自然科学版),2012,42(2)：244-248.
[135]Franchini S, Gentile A, Sorbello F, et al. Clifford Algebra Based Edge Detector for Color Images[C]. Sixth International Conference on Complex, Intelligent and Software Intensive Systems (CISIS). Italy: Palermo,2012, pp.84-91.
[136]He T, Xie W, Cao W. Target Detection in Three-Dimension Sensor Networks Based on Clifford Algebra[J]. Wireless Sensor Network,2009, 1(2):82-89.
[137]Sangwine S J. Colour image edge detector based on quaternion convolution[J]. Electronics Letters,1998, 34(10):969-971.
[138]Sangwine S J. Fourier transforms of colour images using quaternion or hypercomplex, numbers[J]. Electronics letters,1996,32(21):1979-1980.
[139]Hua Liang, Feng Hao, Yu Kean, Liu Yuqing, Ding Lijun, Gu Juping. Edge Detection for Color Medical Image Based on Quaternion and SOFM-NN[J]. International Journal of Advancements in Computing Technology,2013,5(8):870-878.
[140]Bas P, Le Bihan,N., Chassery J. M. Color Image Watermarking using Quaternion Fourier Transform[C]. IEEE International Conference on Aeoustics, Speech, and Signal Processing (ICASSP), China:Hong Kong,2003, pp.521-524.
[141]Alexiadis D S, Sergiadis G D. Estimation of motions in color image sequences using hypercomplex Fourier transforms[J]. IEEE Transactions on Image Processing,2009,18(1):168-187.
[142]Shi L, Funt B. Quaternion color texture segmentation[J]. Computer Vision and Image Understanding, 2007,107(1):88-96.
[143]Denis P, Carre P, Fernandez-Maloigne C. Spatial and spectral quaternionic approaches for colour images[J]. Computer Vision and Image Understanding,2007,107(1):74-87.
[144]Tsui T K, Zhang X P, Androutsos D. Color image watermarking using multidimensional Fourier transforms[J]. IEEE Transactions on Information Forensics and Security,2008,3(1):16-28.
[145]王勇,马立元,王忠强.四元数法在计算机图形学中的应用[J].军械工程学院学报,2001,13(2)：48-51.
[146]Chou J C K, Kamel M. Finding the position and orientation of a sensor on a robot manipulator using quaternions[J]. The international journal of robotics research,1991,10(3):240-254.
[147]杨现辉.基于对偶四元数的点云配准算法研究[D][硕士学位论文],南京：南京航空航天大学,自动化学院,2010.
[148]Rohde G K, Aldroubi A, Healy D M. Interpolation artifacts in sub-pixel image registration[J]. IEEE Transactions on Image Processing,2009,18(2):333-345.
[149]Moxey C E, Sangwine S J, Ell T A. Hypercomplex correlation techniques for vector images[J]. IEEE Transactions on Signal Processing,2003,51(7):1941-1953.
[150]Feng W, Hu B, Yang C. A subpixel color image registration algorithm using quaternion phase-only correlation[C]. International Conference on Audio, Language and Image Processing, China:Shanghai, 2008, pp.1045-1049.
[151]Lu Z, Xu Y, Yang X, et al.2D quaternion Fourier transform:the spectrum properties and its application in color image registration[C]. IEEE International Conference on Multimedia and Expo, China:Beijing, 2007,pp.1715-1718.
[152]Yang C, Zhang J, Yang D, et al. Discrete-quatemion-Fourier-transform-based registration method for color images[C].2010 International Conference on Audio Language and Image Processing, China:Shang,2010, pp.1184-1189.
[153]Liu H, Guo B, Feng Z. Pseudo-log-polar Fourier transform for image registration[J]. Signal Processing Letters, IEEE,2006,13(1):17-20.
[154]Reddy B S, Chatterji B N. An FFT-based technique for translation, rotation, and scale-invariant image registration[J]. IEEE Transactions on Image Processing,1996,5(8):1266-1271.
[155]Lin L, Liu Y, Zheng W, et al. Registration algorithm based on image matching for outdoor AR system with fixed viewing position[J]. IEE Proceedings-Vision, Image and Signal Processing,2006,153(1): 57-62.
[156]杨轶璐,徐心和.四元数在手术导航系统中的应用[J].东北大学学报(自然科学版),2005,26(1)：21-24.
[157]Qu Jianqin, Gong Leiguang.Yang Lin. A 3D point matching algorithm for affine registration[J]. International Journal of Computer Assisted Radiology and Surgery,2011,6(2):229-236.
[158]Pan J, Fei S, Zou W, et al. Color image registration via quaternion Fourier transform and parametric template method[C].8th World Congress on Intelligent Control and Automation (WCICA), China:Jinan, 2010,pp.1006-1011.
[159]Feng W, Hu B, Yang C. A subpixel color image registration algorithm using quaternion phase-only correlation[C]. International Conference on Audio, Language and Image Processing, China:Shanghai, 2008, pp.1045-1049.
[160]Ahmad F H, Natarajan S, Jiang J L. Feature based non-rigid registration using quaternion subdivision[M]. Berlin:Springer Berlin Heidelberg,2010.
[161]Hongbo L, Hestenes D. Rockwood A. Spherical conformal geometry with geometric algebra[J]. Geometric Computing with Clifford Algebras:theoretical foundations and applications in computer vision and robotics, Springer-Verlag Telos,2001.61-76.
[162]Hildenbrand D. Geometric Computing in Computer Graphics using Conformal Geometric Algebra[J]. Computers&Graphics,2005,29(5):795-803.
[163]Lopez-Franco C, Bayro-Corrochano E. Omnidirectional vision and invariant theory for robot navigation using conformal geometric algebra[C].18th International Conference on Pattern Recognition, China:Hong Kong,2006, pp.570-573.
[164]Zamora J, Bayro-Corrochano E. Inverse kinematics, fixation and grasping using conformal geometric algebra[C]. IEEE/RSJ International Conference on Intelligent Robots and Systems, Japan:Sendai,2004, pp.3841-3846.
[165]邢燕,檀结庆.图形变换和运动的共形几何代数表示方法[J].计算机应用研究,2008,25(9)：2842-2844.
[166]杜娟,郝矿荣,黄新等.基于共形几何代数的三维人体骨架运动序列[J].计算机工程与设计,2012,33(10)：3887-3891.
[167]Jorge Rivera Rovelo, Eduardo Bayro Corrochano. Medical Image Segmentation using a Self-organizing Neural Network and Clifford Geometric Algebra[C]. International Joint Conference on Neural Networks, Canada:Vancouver, BC,2006,pp.3538-3545.
[168]曹文明,刘辉,徐晨等.基于共形几何代数的3D医学图像配准[J].中国科学：信息科学,2013,43(2)：254-274.
[169]李茂宽,关键.基于共形几何代数与Radon变换的圆检测方法[J].光电工程,2010,37(4)：72-76.
[170]Clifford W K. On the classification of geometric algebras[J]. Mathematical Papers by William Kingdon Clifford,1882:397-401.
[171]Leo Dorst, Chris Doran, Joan Lasenby. Applications of geometric algebra in computer science and engineering[M]. New York:Hamilton Printing Company,2002.
[172]Dorst L. Honing geometric algebra for its use in the computer sciences[J]. Geometric Computing with Clifford Algebra,2001:127-151.
[173]Hestenes D. New foundations for classical mechanics[M]. Berlin:Springer,1999.
[174]Hestenes D. A unified language for mathematics and physics[M]. Berlin:Springer Netherlands,1986.
[175]王耀明.图像的矩函数[M].上海：华东理工大学出版社,2002.
[176]Mindru F, Tuytelaars T, Gool L V, et al. Moment invariants for recognition under changing viewpoint and illumination[J]. Computer Vision and Image Understanding,2004,94(1):3-27.
[177]朱明,孙继刚,郭立.彩色图像四元数矩不变量的研究[J].中国光学,2011,4(5)：497-502.
[178]Guo Liqiang, Zhu Ming. Quaternion Fourier-Mellin moments for color images[J]. Pattern Recognition, 2011,44(2):187-195.
[179]刘恋,刘伟宁,陈晓曦等.彩色图像的四元数径向矩仿射不变量[J].激光与红外,2012,42(4)：463-467.
[180]Sivaramakrishna R..3D breast image registration--a review[J]. Technol Cancer Res Treat,2005, 4(1):39-48.
[181]Zana F, Klein JC. A multimodal registration algorithm of eye fundus images using vessels detection and Hough transform[J]. IEEE Transactions on Medical Imaging,1999,18(5):419-428.
[182]Wyawahare M V, Patil P M, Abhyankar H K. Image registration techniques:an overview[J]. International Journal of Signal Processing, Image Processing and Pattern Recognition,2009,2(3):11-28.
[183]Batler J M, Pelizarri C A, Chen GTY. Correlation of projection radiographs in radiation therapy using open curve segments and points[J]. MED PHYS(S0094-2405),1992,19(2):329-334.
[184]Betting F, Feldmar J.3D-2D projective registration of anatomical surfaces with their projections[M]. Springer.Information Processing in Medical Imaging, Kluwer Academic Publishers, Dordrecht,1995: 275-286.
[185]Gueziec A, Kazanzides P, Williamson B, et al. Anatomy-based registration of CT-scan and intraoperative X-ray images for guiding a surgical robot[J].IEEE Transactions on Medical Imaging,1998, 17(5):715-728.
[186]De Castro E, Morandi C. Registration of translated and rotated images using finite Fourier transforms[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1987, Volume:PAMI-9(5):700-703.
[187]Chen Q, Defrise M, Deconinck F. Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1994,16(12):1156-1168.
[188]Lemieux L, Jagoe R, Fish D R,et al. A patient-to-computed-tomography image registration method based on digitally reconstructed radiographs[J]. MED PHYS,1994,21(11):1749-1760.
[189]Collignon A, Maes F, Delaere D, et al. Automated multi-modality image registration based on informatio n theory[J]. Information processing in medical imaging,1995:263-274.
[190]Viola P, Wells III W M. Alignment by maximization of mutual information[J]. International journal of computer vision,1997,24(2):137-154.
[191]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.
[192]Mattes D, Haynor D R, Vesselle H, et al. PET-CT image registration in the chest using free-form deformations[J]. IEEE Transactions on Medical Imaging,2003,22(1):120-128.
[193]Harry Loats. CT and SPECT image registration and fusion for spatial localization of metastatic processes using Radiolabeled Monoclonals [J]. The Journal of Nuclear Medicine (SO161-5505),1993, 34(3 Suppl):562-566.
[194]夏伟,吕中伟,蔡海东等.盆腹部SPECT与CT图像融合配准框架的设计与应用[J].中国临床医学影像杂志,2009,20(1)：26-28.
[195]章毓晋.图像处理和分析[M].北京：清华大学出版社,1999.
[196]李雄飞,张存利,李鸿鹏等.医学图像配准技术进展[J].计算机科学,2010,37(7)：27-33.
[197]Lu Xiaoqi, Ma Hongli, Zhang Baohua. A non-rigid medical image registration method based on improved linear elastic model[J]. International Journal for Light and Electron Optics,2012, 123(20):1867-1873.
[198]D L G Hill, P G Batchelor, M Holden, et al. Medical image registration [J]. Physics in Medicine and Biology,2001,46(3):1-45.
[199]M.Fornefett, K. Rohr, H.S.Stiehl. Radial basis functions with compact support for elastic registration of medical images[J]. Image and Vision Computing,2001,19(1-2):87-96.
[200]Yang Xuan, Pei Ji-hong, Sun Wei. Elastic image registration using hierarchical spatially based mean shift [J]. Computers in Biology and Medicine,2013,43(9):1086-1097.
[201]Pluim J, Maintz J, Viergever M. Mutual-information-based registration of medical images:A survey [J]. IEEE Trans on Medical Imaging,2003,22(8):986-1004.
[202]王婕好,王加俊,张静亚.基于改进光流场和尺度不变特征变换的非刚性医学图像配准[J].电子与信息学报,2013,35(5)：1222-1228.
[203]许鸿奎,江铭炎,杨明强.基于改进光流场模型的脑部多模医学图像配准[J].电子学报,2012,40(3)：525-529.
[204]潘晓光,李宏,康雁等.双向梯度归一化互信息医学图像配准方法[J].东北大学学报(自然科学版),2012,33(8)：1107-1110.
[205]杜晓刚,党建武,王阳萍等.基于萤火虫算法的互信息医学图像配准[J].计算机科学,2013,40(7)：273-276.
[206]William M.Wells Ⅲ, Paul Viola, Hideki Atsumi, Shin Nakajima, Ron.Kikinis. Multi-modal volume registration by maximization of mutual information[J]. Medical Image Analysis,1996,1(1):35-51.
[207]葛永新,杨丹,雷明.基于良分布的亚像素定位角点的图像配准[J].电子与信息学报,2010,32(2)：427-431.
[208]Collignon A M F, Vandermeulen D, Suetens P, et al. Surface-based registration of 3D medical images[J]. Proc. SPIE 1898, Medical Imaging 1993:Image Processing,1993,32:pp.32-42.
[209]Hava Lester,Simon R.Arridge. A survey of hierarchical non-linear medical image registration[J]. Pattern Recognition,1999,32(1):129-149.
[210]李洪波.共形几何代数域运动形状的刻画[J].计算机辅助设计与图形学学报,2006,18(7)：895-901.
[211]俞肇元,袁林旺,罗文.GIS时空分析系统的Clifford代数设计与实现[J].武汉大学学报：信息科学版,2011,36(12)：1397-1401.
[212]李洪波.共形几何代数-几何代数的新理论和计算框架[J].计算机辅助设计与图形学报,2005,17(11)：2383-2393.
[213]李谭.多模态医学图像配准算法研究[D][硕士学位论文].天津大学,计算机科学与技术学院,2007.
[2]郑亚琴,田心.医学图像配准技术研究进展[J].国际生物医学工程杂志,2006,29(2)：88-92.
[3]彭文.基于特征的医学图像配准中若干关键技术的研究[D][博士学位论文].杭州：浙江大学,计算机科学与技术学院,2007.
[4]Shao Y, Cherry S R, Farahani K, et al. Development of a PET detector system compatible with MRI/NMR systems[J]. IEEE Transactions on Nuclear Science,1997,44(3):1167-1171.
[5]宋智礼.图像配准技术及其应用的研究[D][博士学位论文].上海：复旦大学,计算机科学技术学院,2010.
[6]Brown L G. A survey of image registration techniques[J]. ACM computing surveys (CSUR),1992,24(4): 325-376.
[7]Marc Vaillant, Christos Davatzikos, Russell H. Taylor.et al. A path-planning algorithm for image-guided neurosurgery[A].CVRMed-MRCAS'97[C]. Berlin Heidelberg:Springer Berlin Heidelberg,1997, 467-476.
[8]杜亚娟.基于不变矩理论的自动目标识别技术研究[D][博士学位论文].西安：西北工业大学,自动化学院,2000.
[9]Chong C W, Raveendran P, Mukundan R. Translation and scale invariants of Legendre moments[J]. Pattern Recognition,2004,37(1):119-129.
[10]Mukundan R, Ong S H, Lee P A. Image analysis by Tchebichef moments[J]. IEEE Transactions on Image Processing,2001,10(9):1357-1364.
[11]冉冉,杨唐文,阮秋琦.结合HSL模型与傅里叶描述子的三维彩色物体识别[J].智能系统学报,2011,6(1)：73-78.
[12]Rahtu E, Salo M, Heikkila J. Affine invariant pattern recognition using multiscale autoconvolution[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(6):908-918.
[13]李军宏,陈玉春,潘泉等.一种基于高阶统计量的不变量图像识别算法[J].计算机工程,2004,30(20)：7-8.
[14]Zhang Jianguo, Tan Tieniu. Affine invariant texture analysis based on structural properties[C].Proceedings of the Fifth Asian Conference on Computer Vision (ACCV 2002), Australia, Melbourne, MA,2002, pp.216-221.
[15]Yang Z, Cohen F S. Image registration and object recognition using affine invariants and convex hulls[J]. IEEE Transactions on Image Processing,1999,8(7):934-946.
[16]Lowe D G. Distinctive image features from scale-invariant keypoints[J]. International journal of computer vision,2004,60(2):91-110.
[17]Zhu S, Ma K K. A new diamond search algorithm for fast block-matching motion estimation[J]. IEEE Transactions on Image Processing,2000,9(2):287-290.
[18]Bay H, Ess A, Tuytelaars T, et al. Speeded-up robust features (SURF)[J]. Computer vision and image understanding,2008,110(3):346-359.
[19]Mikolajczyk K, Schmid C. A performance evaluation of local descriptors[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(10):1615-1630.
[20]雷琳,陈涛,李智勇等.全局仿射变换条件下图像不变量提取新方法[J].国防科技大学学报,2008,30(4)：64-70.
[21]Bentoutou Y, Taleb N, Chikr El Mezouar M, et al. An invariant approach for image registration in digital subtraction angiography[J]. Pattern Recognition,2002,35(12):2853-2865.
[22]戴修斌,张辉,舒华忠等.基于正交矩混合不变量的离焦模糊图像配准[J].应用科学学报,2010,28(5)：476-484.
[23]李斌,叶昊.基于仿射几何不变量的鲁棒图像配准算法[J].上海交通大学学报,2012,46(12)：1881-1884.
[24]Lee J H, Kim Y S, Lee D, et al. Robust CCD and IR image registration using gradient-based statistical information[J]. Signal Processing Letters, IEEE,2010,17(4):347-350.
[25]Jiang H, Yu S X, Martin D R. Linear scale and rotation invariant matching[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2011,33(7):1339-1355.
[26]Jiang H, Tian T P, Sclaroff S. Scale and rotation invariant matching using linearly augmented trees[C]. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), America, Providence, RI,2011, pp.2473-2480.
[27]Tsolakis A, Falelakis M, Delopoulos A. A framework for efficient correspondence using feature interrelations[C].19th International Conference on Pattern Recognition, Americam, Tampa,2008, pp.1-4.
[28]Caetano T S, Caelli T. A unified formulation of invariant point pattern matching[C].18th International Conference on Pattern Recognition, China, Hong Kong,2006,pp.121-124.
[29]Maintz J B, Viergever M A. A survey of medical image registration[J]. Medical image analysis,1998, 2(1):1-36.
[30]Michel A. Audette,Frank P. Ferrieb, Terry M. Peters. An algorithmic overview of surface registration techniques for medical imaging[J].Medical Image Analysis,2000,4(3):201-217.
[31]Van den Elsen P A, Pol E J D, Viergever M A. Medical image matching-a review with classification[J]. Engineering in Medicine and Biology Magazine, IEEE,1993,12(1):26-39.
[32]Zhang Huisheng, Liu Xinyu, Li Ling, et al. Accurate Multi-spectral Image Registration Based on Scale Invariant Feature[C].2nd International Conference on Computer Science and Network Technology (ICCSNT), China, Changchun,2012,29(31):847-852.
[33]T.D.Zuk,M S.Atkins. A comparison of manual and automatic methods for registering scans of the head[J]. IEEE Transactions on Medical Imaging,1996,15(5):732-744.
[34]张锐娟.图像配准理论及算法研究[D][硕士学位论文].西安：西安电子科技大学,物理与光电工程学院,2009.
[35]Makela,T.,Clarysse,P.,Sipila,O.,et al. A review of cardiac image registration methods[J].IEEE Transactions on Medical Imaging,2002,21(9):1011-1021.
[36]Zitova B, Flusser J. Image registration methods:a survey[J]. Image and vision computing,2003,21(11): 977-1000.
[37]Holden M. A review of geometric transformations for nonrigid body registration[J]. IEEE Transactions on Medical Imaging,2008,27(1):111-128.
[38]Lu X, Ma H, Zhang B, et al. A review of algorithm research progress for non-rigid medical image registration[C].2011 International Conference on Consumer Electronics, Communications and Networks (CECNet), China, XianNing,2011:3863-3866.
[39]Sotiras A.,Davatzikos C.,Paragios N. Deformable Medical Image Registration:A Survey[J]. IEEE Transactions on Medical Imaging,2013,32(7):1153-1190.
[40]申艳平.医学图像配准技术[J].中国医学物理学杂志,2013,30(001)：3885-3889.
[41]Plishker W, Dandekar O, Bhattacharyya S, et al. A taxonomy for medical image registration acceleration techniques[C]. Life Science Systems and Applications Workshop,2007. IEEE/NIH, America, Bethesda, MD,2007,160-163.
[42]Luo Shuqian, Li Xiang. Implementation of mutual information based multi-modality medical image registration[C]. Engineering in Medicine and Biology Society,2000. Proceedings of the 22nd Annual International Conference of the IEEE, America, Chicago, IL,2000,2:1447-1450.
[43]曹炬,马杰,谭毅华等.基于像素抽样的快速互相关图像匹配算法[J].宇航学报.2004,25(2),173-178.
[44]秦斌杰,庄天戈.基于体素灰度3D多模医学图像配准中的相似性测度[J].上海交通大学学报,2002,36(7),942-945.
[45]梁玮.2D-3D医学图像配准研究[D][硕士学位论文].南京：东南大学,生物科学与医学工程学院2004.
[46]Chengfen Jiang. Ticheng Lu, Shuping Sun. Interactive image registration tool for positioning verification in head and neck radiotherapy [J]. Computers in Biology and Medicine,2008,38(1): 90-100.
[47]R.P.Woods,S.R.Cherry,J.C.Mazziotta. Rapid Automated Algorithm for Aligning and Reslicing PET Images[J].Journal of Computer Assisted Tomography,1992,16(4):620-633.
[48]吴锋,钱宗才,杭恰时.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.
[49]Pluim J P W, Maintz J B A, Viergever M A. Mutual-information-based registration of medical images:a survey[J]. IEEE Transactions on Medical Imaging,2003,22(8):986-1004.
[50]M.M.Emma,C.Ruben,L.G.Rodriqo,et al.Image Registration Based on Automatic Detection of Anatomical Landmarks for Bone Age Assessment[J].WSEAS Transactions on Computers,2005,4(11): 1596-1603.
[51]N.Ryan,C.Heneghan,P.Chazal. Registration of Digital Retinal Images Using Landmark Correspondence by Expectation Maximization [J].Image and Vision Computing,2004,22 (11):883-898.
[52]王秀英等.弹性的二维医学图像配准算法[J],吉林大学学报(信息科学版),2003 21(5)：73-79.
[53]Chen J, Tian J, Lee N, et al. A partial intensity invariant feature descriptor for multimodal retinal image registration[J]. IEEE Transactions on Biomedical Engineering,2010,57(7):1707-1718.
[54]Zheng Lintao, Qian Guiping. A SIFT-Based Approach for Image Registration[A].Green Communications and Networks[C]. Berlin Heidelberg:Springer Netherlands,2012,277-287.
[55]Faysal Boughorbel, Muharrem Mercimek, Andreas Koschan, et al. A new method for the registration of three-dimensional point-sets:The Gaussian Fields framework[J]. Image and Vision Computing,2010, 28(1):124-137.
[56]Yingxuan Zhu, Samuel Cheng, Vladimir Stankovic, et al. Image registration using BP-SIFT[J]. Journal of Visual Communication and Image Representation,2013,24(4):448-457.
[57]Lu Xiaoqi, Zhao Yongjie, Zhang Baohua, et al. A non-rigid cardiac image registration method based on an optical flow model[J]. International Journal for Light and Electron Optics,2013,124(20):4266-4273.
[58]Edgar RArce-Santana, Alfonso Alba. Image registration using Markov random coefficient and geometric transformation fields[J]. Pattern Recognition,2009,42(8):1660-1671.
[59]Li Hao, Yang Hansheng, Shi Guohua, et al. Adaptive optics retinal image registration from scale-invariant feature transform[J]. International Journal for Light and Electron Optics, 2011,22(9):839-841.
[60]GT.Y.Chen,C.A.Pelizzari. Image Correlation Techniques in Radiation Therapy Planning[J].Computerized Medical Imaging and Graphics,1989,13(3):235-240.
[61]Penney 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.
[62]张密.放射治疗中2D/3D医学图像配准算法研究[D][硕士学位论文].广州：华南理工大学,生物 科学与工程学院,2010.
[63]Khamene A, Bloch P, Wein W, et al. Automatic registration of portal images and volumetric CT for patient positioning in radiation therapy[J]. Medical Image Analysis,2006,10(1):96-112.
[64]Galvin J M, Sims C.The use of digitally reconstructed radiographs for three-dimensional treatment planning and CT-simulation[J].International Journal of Radiation Oncology Biology Physics,1995, 31(4):935-942.
[65]R. Harmouche, F. Cheriet, H. Labelle, et al.3D registration of MR and X-ray spine images using an articulated model[J].Computerized Medical Imaging and Graphics,2012,36(5):410-418.
[66]Gholipour A, Kehtarnavaz N, Briggs R, et al. Brain functional localization:a survey of image registration techniques[J]. IEEE Transactions on Medical Imaging,2007,26(4):427-451.
[67]Schweikard A., Glosser G., Bodduluri M., et al. Robotic Motion Compensation for Respiratory Movement during Radiosurgery [J]. Computer-Aided Surgery,2000,5(4):263-277.
[68]LaRose D A. Iterative X-ray/CT Registration using accelerated volume rendering [D][doctoral dissertation].Pittsburgh:Carnegie Mellon University, Robotics Institute,2001.
[69]Chen X, Varley M R, Shark L K, et al. An extension of iterative closest point algorithm for 3d-2d registration for pre-treatment validation in radiotherapy[C]. International Conference on Medical Information Visualisation-BioMedical Visualisation,2006, USA, Washington, DC,2006:3-8.
[70]Cui Haihua, Dai Ning, Liao Wenhe, et al. Intraoral 3D optical measurement system for tooth restoration[J]. International Journal for Light and Electron Optics,2013,124(12):1142-1147.
[71]Livyatan H, Yaniv Z, Joskowicz L. Gradient-based 2-D/3-D rigid registration of fluoroscopic X-ray to CT[J]. IEEE Transactions on Medical Imaging,2003,22(11):1395-1406.
[72]Tzimiropoulos G, Argyriou V, Zafeiriou S, et al. Robust FFT-based scale-invariant image registration with image gradients[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2010,32(10): 1899-1906.
[73]X. Chen, M. R. Varley, L.K.Shark, et al. A computationally efficient method for automatic registration of orthogonal x-ray images with volumetric CT data [J].Physics in Medicine and Biology,2008, 53(4):967-983.
[74]Ali Khamene, Peter Bloch, Wolfgang Wein, et al. Automatic registration of portal images and volumetric CT for patient positioning in radiation therapy [J]. Medical Image Analysis,2006,10(1):96-112.
[75]Charles Florin, James Williams, Ali Khamene, et al. Registration of 3D angiographic and X-ray images using sequential monte carlo sampling[A].Computer Vision for Biomedical Image Applications[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2005,427-436.
[76]Zheng Guoyan. Unifying energy minimization and mutual information maximization for robust 2D/3D registration of X-ray and CT images[A].Pattern Recognition[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2007,547-557.
[77]Yoshito Otake, Mehran Armand, Ofri Sadowsky, et al. An iterative framework for improving the accuracy of intraoperative intensity-based 2D/3D registration for image-guided orthopedic surgery [A].Information Processing in Computer-Assisted Interventions[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2010,23-33.
[78]Lei Peng, Dandekar Omkar, Widlus David, et al. Incorporation of Preprocedural PET into CT-Guided Radiofrequency Ablation of Hepatic Metastases:a Nonrigid Image Registration Validation Study[J]. Journal of Digital Imaging,2010,23 (6):780-792.
[79]Marcelo Elias de Oliveira,Harri Hallila,Antti Ritvanen,et al. Feature-invariant image registration method for quantification of surgical outcomes in patients with craniosynostosis:a preliminary study[J]. Journal of Pediatric Surgery,2011,46(1O):E1-E8.
[80]Andre G, Wu K. Providing visual information to validate 2-D to 3-D registration [J].Medical Image Analysis,2000,4(4):357-368.
[81]A.Rangarajan, H. Chui, J. S. Duncan. Rigid point feature registration using mutual information[J].Medical Image Analysis,1999,3(4):425-440.
[82]Porter B C, Rubens D J, Strang J G, et al. Three-dimensional registration and fusion of ultrasound and MRI using major vessels as fiducial markers[J]. IEEE Transactions on Medical Imaging,2001,20(4): 354-359.
[83]Besl P Makay. A Method for Registration of 3D Shapes[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1992,14(2):239-256.
[84]Chen Y, Medioni G. Object Modeling by Registration of Multiple Range Images[J].Image and Vision Computing,1992,10(3):145-155.
[85]Fitzgibbon A W. Robust registration of 2D and 3D point sets[J]. Image and Vision Computing,2003, 21(13):1145-1153.
[86]Du S, Zheng N, Ying S, et al. Affine iterative closest point algorithm for point set registration[J]. Pattern Recognition Letters,2010,31(9):791-799.
[87]Du S, Zheng N, Meng G, et al. Affine registration of point sets using ICP and ICA[J]. Signal Processing Letters, IEEE,2008,15:689-692.
[88]Sharp G C, Lee S W, Wehe D K. ICP registration using invariant features[J]., IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(1):90-102.
[89]屈建勤.基于代数和几何不变量的点集配准方法[D][博士学位论文].长春：吉林大学,2012.
[90]Li Gang, Guo Lei, Liu Tianming. Deformation invariant attribute vector for deformable registration of longitudinal brain MR images[J]. Computerized Medical Imaging and Graphics,2009,33(5):384-398.
[91]Pluim, J.P.W., Maintz, J.B.A., Viergever, M.A.. Image registration by maximization of combined mutual information and gradient information[A].Medical Image Computing and Computer-Assisted Intervention[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2000:452-461.
[92]Liu Liping, Ke Li, Zhongguo Liu.Medical image registration by maximization of combined mutual information and edge correlative deviation[C]. Engineering in Medicine and Biology Society,2005. IEEE-EMBS 2005.27th Annual International Conference, China, Shanghai,2005,6:6379-6382.
[93]Chen W.Q., Ou Z.Y., Song W.W.A Coarse-to-Refined Approach of Medical Image Registration Based on Combining Mutual Information and Shape Information[C]. International Conference on Neural Networks and Brain,2005. China, Beijing,2005,2:816-820.
[94]Li Guang, Xie Huchen, Ning Holly, et al. Accuracy of 3D volumetric image registration based on CT,MR and PET/CT phantom experiments[J].Journal of Applied Clinical Medical Physics,2008, 9(4):17-36.
[95]Pluim J P W, Maintz J B A, Viergever M A. f-Information measures in medical image registration[J]. IEEE Transactions on Medical Imaging,2004,23(12):1508-1516.
[96]M. Babaie-Zadeh, C. Jutten, K.Nayebi.Differential of the mutual information[J]. Signal Processing Letters, IEEE,2004,11(1):48-51.
[97]吕晓琪,李娜,张宝华等.基于体素相似性的三维多模脑图像配准研究[J].中国医学影像学杂志,2013,21(2)：146-151.
[98]王远军,周密,查珊珊等.多模态医学图像配准技术研究[J].中国医学物理学杂志,2013,30(003)：4125-4129.
[99]Laura Fernandez-de-Manuel, Gert Wollny, Jan Kybic, et al. Organ-focused mutual information for nonrigid multimodal registration of liver CT and Gd-EOB-DTPA-enhanced MRI[J]. Medical Image Analysis,2014(18):22-35.
[100]L. Y. Hsu, M. H. Loew. Fully automatic 3D feature-based registration of multi-modality medical images[J].Image and Vision Computing,2001,19(1):75-85.
[101]李文龙,程流泉,李军等.基于自由形变的3D非线性医学图像配准[J].中国医学影像技术,2011,27(12)：2536-2540.
[102]R.Sharman, J.M. Tyler, O S.Pianykh. A fast and accurate method to register medical images using Wavelet Modulus Maxima[J]. Pattern Recognition Letters,2000,21(6):447-462.
[103]Salomon M, Heitz F, Perrin G R, et al. A massively parallel approach to deformable matching of 3D medical images via stochastic differential equations[J]. Parallel Computing,2005,31(1):45-71.
[104]Cordon O, Damas S, Santamaria J. A fast and accurate approach for 3D image registration using the scatter search evolutionary algorithm[J]. Pattern Recognition Letters,2006,27(11):1191-1200.
[105]Blackall J M, Rueckert D, Maurer Jr C R, et al. An image registration approach to automated calibration for freehand 3D ultrasound[A]. Medical Image Computing and Computer-Assisted Intervention-MICCAI 2000[C].Berlin Heidelberg:Springer Berlin Heidelberg,2000,462-471.
[106]Thirion J P. New feature points based on geometric invariants for 3D image registration[J]. International journal of computer vision,1996,18(2):121-137.
[107]Huang X, Hill N A, Ren J, et al. Dynamic 3D ultrasound and MR image registration of the beating heart[A].Medical Image Computing and Computer-Assisted Intervention-MICCAI 2005[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2005,171-178.
[108]Walimbe V, Shekhar R. Automatic elastic image registration by interpolation of 3D rotations and translations from discrete rigid-body transformations[J]. Medical Image Analysis,2006,10(6):899-914.
[109]Renjie He, et al.Global optimization of mutual information:application to three dimensional retrospective registration of magnetic resonance images[J].Computerized Medical Imaging and Graphics,2002,26(4):277-292.
[110]刘爱菱.3D医学图像配准方法研究[D][硕士学位论文].武汉：华中科技大学,2007.
[111]Yang S, Illner D, Teller K, et al. Statistical Shape Theory and Registration Methods for Analyzing the 3D Architecture of Chromatin in Interphase Cell Nuclei[M]. Springer Netherlands:Advances in Nuclear Architecture,2011:131-147.
[112]Diego Thomas, Akihiro Sugimoto. Robustly registering range images using local distribution of albedo[J]. Computer Vision and Image Understanding,2011,115(5):649-667.
[113]Jiang Jun, Cheng Jun, Chen Xinglin. Registration for 3-D point cloud using angular-invariant feature[J]. Neurocomputing,2009,72(16-18):3839-3844.
[114]He Bingwei, Lin Zeming, Li Y.F. An automatic registration algorithm for the scattered point clouds based on the curvature feature[J]. Optics&Laser Technology,2013,46(3):53-60.
[115]Joaquim Salvi,Carles Matabosch,David Fofi,et al.A review of recent range image registration methods with accuracy evaluation[J].Image and Vision Computing,2007,25(5):578-596.
[116]Jannin, P., J.M.Fitzpatrick, D.J.Hawkes, et al. Validation of medical image processing in image-guided therapy[J]. IEEE Transactions on Medical Imaging,2002,21(12):1445-9.
[117]Reuben R. Shamir, Leo Joskowicz. Geometrical analysis of registration errors in point-based rigid-body registration using invariants[J]. Medical Image Analysis,2011,15(1):85-95.
[118]Plattarp D,Soret M.Patient Set-up Using Portal Images:2D/2D Image Registration Using Mutual Information[J].Computer Aided Surgery,2000,5(4):246-262.
[119]van de Kraats E B, Penney G P, Tomazevic D, et al. Standardized evaluation methodology for 2-D-3-D registration[J]. IEEE Transactions on Medical Imaging,2005,24(9):1177-1189.
[120]Reuben R S.Leo J.Sergey S, et al.Localization and registration accuracy in image guided neurosurgery:a clinical study[J].International Journal of Computer Assisted Radiology and Surgery,2009,4(1):45-52.
[121]Artin E. Geometric algebra[M]. John Wiley & Sons,2011.
[122]Zaharia M D, Dorst L. Modeling and visualization of 3D polygonal mesh surfaces using geometric algebra[J]. Computers & Graphics,2004,28(4):519-526.
[123]Dorst L, Fontijne D, Mann S. Geometric Algebra for Computer Science (Revised Edition):An Object-Oriented Approach to Geometry[M]. San Francisco:Morgan Kaufmann,2009.
[124]Bayro-Corrochano E, Vallejo R, Arana-Daniel N. Geometric preprocessing, geometric feedforward neural networks and Clifford support vector machines for visual learning[J]. Neurocomputing,2005, 67:54-105.
[125]李洪波.Clifford代数,几何计算和几何推理[J].数学进展,2003,32(4)：405-415.
[126]倪庆.几何代数在计算机视觉三维重建中的应用[D][硕士学位论文].国防科学技术大学,机电工程与自动化学院,2011.
[127]Rivera-Rovelo Jorge, Bayro-Corrochano Eduardo. Medical image segmentation, volume representation and registration using spheres in the geometric algebra framework[J]. Pattern Recognition,2007, 40(l):171-188.
[128]徐晨,刘辉,欧阳春娟等.多光谱图像Clifford拟微分算子及应用[J].中国科学：信息科学,2011,41(12)：1423-1435.
[129]Orozco-Aguirre R, Rivera-Rovelo J, Bayro-Corrochano E. Medical image segmentation and the use of geometric algebras in medical applications[M]. Berlin:Springer Berlin Heidelberg,2005:729-740.
[130]韩国良.几何变换及配准和运动估计的几何代数方法研究[D][硕士学位论文].青岛：中国石油大学,计算机与通信工程学院,2008.
[131]Leo Reyes, Gerard Medioni, Eduardo Bayro. Registration of 3D Points Using Geometric Algebra and Tensor Voting[J]. International Journal of Computer Vision,2007,75(3):351-369.
[132]Subakan 6 N, Vemuri B C. Quaternion-Based Color Image Smoothing Using a Spatially Varying Kernel[A]. Energy Minimization Methods in Computer Vision and Pattern Recognition[C]. Berlin Heidelberg:Springer Berlin Heidelberg,2009:415-428.
[133]Bayro-Corrochano E, Rivera-Rovelo J. The use of geometric algebra for 3D modeling and registration of medical data[J]. Journal of Mathematical Imaging and Vision,2009,34(1):48-60.
[134]刘辉,徐晨,曹文明.基于Clifford代数的多光谱图像边缘检测[J].东南大学学报(自然科学版),2012,42(2)：244-248.
[135]Franchini S, Gentile A, Sorbello F, et al. Clifford Algebra Based Edge Detector for Color Images[C]. Sixth International Conference on Complex, Intelligent and Software Intensive Systems (CISIS). Italy: Palermo,2012, pp.84-91.
[136]He T, Xie W, Cao W. Target Detection in Three-Dimension Sensor Networks Based on Clifford Algebra[J]. Wireless Sensor Network,2009, 1(2):82-89.
[137]Sangwine S J. Colour image edge detector based on quaternion convolution[J]. Electronics Letters,1998, 34(10):969-971.
[138]Sangwine S J. Fourier transforms of colour images using quaternion or hypercomplex, numbers[J]. Electronics letters,1996,32(21):1979-1980.
[139]Hua Liang, Feng Hao, Yu Kean, Liu Yuqing, Ding Lijun, Gu Juping. Edge Detection for Color Medical Image Based on Quaternion and SOFM-NN[J]. International Journal of Advancements in Computing Technology,2013,5(8):870-878.
[140]Bas P, Le Bihan,N., Chassery J. M. Color Image Watermarking using Quaternion Fourier Transform[C]. IEEE International Conference on Aeoustics, Speech, and Signal Processing (ICASSP), China:Hong Kong,2003, pp.521-524.
[141]Alexiadis D S, Sergiadis G D. Estimation of motions in color image sequences using hypercomplex Fourier transforms[J]. IEEE Transactions on Image Processing,2009,18(1):168-187.
[142]Shi L, Funt B. Quaternion color texture segmentation[J]. Computer Vision and Image Understanding, 2007,107(1):88-96.
[143]Denis P, Carre P, Fernandez-Maloigne C. Spatial and spectral quaternionic approaches for colour images[J]. Computer Vision and Image Understanding,2007,107(1):74-87.
[144]Tsui T K, Zhang X P, Androutsos D. Color image watermarking using multidimensional Fourier transforms[J]. IEEE Transactions on Information Forensics and Security,2008,3(1):16-28.
[145]王勇,马立元,王忠强.四元数法在计算机图形学中的应用[J].军械工程学院学报,2001,13(2)：48-51.
[146]Chou J C K, Kamel M. Finding the position and orientation of a sensor on a robot manipulator using quaternions[J]. The international journal of robotics research,1991,10(3):240-254.
[147]杨现辉.基于对偶四元数的点云配准算法研究[D][硕士学位论文],南京：南京航空航天大学,自动化学院,2010.
[148]Rohde G K, Aldroubi A, Healy D M. Interpolation artifacts in sub-pixel image registration[J]. IEEE Transactions on Image Processing,2009,18(2):333-345.
[149]Moxey C E, Sangwine S J, Ell T A. Hypercomplex correlation techniques for vector images[J]. IEEE Transactions on Signal Processing,2003,51(7):1941-1953.
[150]Feng W, Hu B, Yang C. A subpixel color image registration algorithm using quaternion phase-only correlation[C]. International Conference on Audio, Language and Image Processing, China:Shanghai, 2008, pp.1045-1049.
[151]Lu Z, Xu Y, Yang X, et al.2D quaternion Fourier transform:the spectrum properties and its application in color image registration[C]. IEEE International Conference on Multimedia and Expo, China:Beijing, 2007,pp.1715-1718.
[152]Yang C, Zhang J, Yang D, et al. Discrete-quatemion-Fourier-transform-based registration method for color images[C].2010 International Conference on Audio Language and Image Processing, China:Shang,2010, pp.1184-1189.
[153]Liu H, Guo B, Feng Z. Pseudo-log-polar Fourier transform for image registration[J]. Signal Processing Letters, IEEE,2006,13(1):17-20.
[154]Reddy B S, Chatterji B N. An FFT-based technique for translation, rotation, and scale-invariant image registration[J]. IEEE Transactions on Image Processing,1996,5(8):1266-1271.
[155]Lin L, Liu Y, Zheng W, et al. Registration algorithm based on image matching for outdoor AR system with fixed viewing position[J]. IEE Proceedings-Vision, Image and Signal Processing,2006,153(1): 57-62.
[156]杨轶璐,徐心和.四元数在手术导航系统中的应用[J].东北大学学报(自然科学版),2005,26(1)：21-24.
[157]Qu Jianqin, Gong Leiguang.Yang Lin. A 3D point matching algorithm for affine registration[J]. International Journal of Computer Assisted Radiology and Surgery,2011,6(2):229-236.
[158]Pan J, Fei S, Zou W, et al. Color image registration via quaternion Fourier transform and parametric template method[C].8th World Congress on Intelligent Control and Automation (WCICA), China:Jinan, 2010,pp.1006-1011.
[159]Feng W, Hu B, Yang C. A subpixel color image registration algorithm using quaternion phase-only correlation[C]. International Conference on Audio, Language and Image Processing, China:Shanghai, 2008, pp.1045-1049.
[160]Ahmad F H, Natarajan S, Jiang J L. Feature based non-rigid registration using quaternion subdivision[M]. Berlin:Springer Berlin Heidelberg,2010.
[161]Hongbo L, Hestenes D. Rockwood A. Spherical conformal geometry with geometric algebra[J]. Geometric Computing with Clifford Algebras:theoretical foundations and applications in computer vision and robotics, Springer-Verlag Telos,2001.61-76.
[162]Hildenbrand D. Geometric Computing in Computer Graphics using Conformal Geometric Algebra[J]. Computers&Graphics,2005,29(5):795-803.
[163]Lopez-Franco C, Bayro-Corrochano E. Omnidirectional vision and invariant theory for robot navigation using conformal geometric algebra[C].18th International Conference on Pattern Recognition, China:Hong Kong,2006, pp.570-573.
[164]Zamora J, Bayro-Corrochano E. Inverse kinematics, fixation and grasping using conformal geometric algebra[C]. IEEE/RSJ International Conference on Intelligent Robots and Systems, Japan:Sendai,2004, pp.3841-3846.
[165]邢燕,檀结庆.图形变换和运动的共形几何代数表示方法[J].计算机应用研究,2008,25(9)：2842-2844.
[166]杜娟,郝矿荣,黄新等.基于共形几何代数的三维人体骨架运动序列[J].计算机工程与设计,2012,33(10)：3887-3891.
[167]Jorge Rivera Rovelo, Eduardo Bayro Corrochano. Medical Image Segmentation using a Self-organizing Neural Network and Clifford Geometric Algebra[C]. International Joint Conference on Neural Networks, Canada:Vancouver, BC,2006,pp.3538-3545.
[168]曹文明,刘辉,徐晨等.基于共形几何代数的3D医学图像配准[J].中国科学：信息科学,2013,43(2)：254-274.
[169]李茂宽,关键.基于共形几何代数与Radon变换的圆检测方法[J].光电工程,2010,37(4)：72-76.
[170]Clifford W K. On the classification of geometric algebras[J]. Mathematical Papers by William Kingdon Clifford,1882:397-401.
[171]Leo Dorst, Chris Doran, Joan Lasenby. Applications of geometric algebra in computer science and engineering[M]. New York:Hamilton Printing Company,2002.
[172]Dorst L. Honing geometric algebra for its use in the computer sciences[J]. Geometric Computing with Clifford Algebra,2001:127-151.
[173]Hestenes D. New foundations for classical mechanics[M]. Berlin:Springer,1999.
[174]Hestenes D. A unified language for mathematics and physics[M]. Berlin:Springer Netherlands,1986.
[175]王耀明.图像的矩函数[M].上海：华东理工大学出版社,2002.
[176]Mindru F, Tuytelaars T, Gool L V, et al. Moment invariants for recognition under changing viewpoint and illumination[J]. Computer Vision and Image Understanding,2004,94(1):3-27.
[177]朱明,孙继刚,郭立.彩色图像四元数矩不变量的研究[J].中国光学,2011,4(5)：497-502.
[178]Guo Liqiang, Zhu Ming. Quaternion Fourier-Mellin moments for color images[J]. Pattern Recognition, 2011,44(2):187-195.
[179]刘恋,刘伟宁,陈晓曦等.彩色图像的四元数径向矩仿射不变量[J].激光与红外,2012,42(4)：463-467.
[180]Sivaramakrishna R..3D breast image registration--a review[J]. Technol Cancer Res Treat,2005, 4(1):39-48.
[181]Zana F, Klein JC. A multimodal registration algorithm of eye fundus images using vessels detection and Hough transform[J]. IEEE Transactions on Medical Imaging,1999,18(5):419-428.
[182]Wyawahare M V, Patil P M, Abhyankar H K. Image registration techniques:an overview[J]. International Journal of Signal Processing, Image Processing and Pattern Recognition,2009,2(3):11-28.
[183]Batler J M, Pelizarri C A, Chen GTY. Correlation of projection radiographs in radiation therapy using open curve segments and points[J]. MED PHYS(S0094-2405),1992,19(2):329-334.
[184]Betting F, Feldmar J.3D-2D projective registration of anatomical surfaces with their projections[M]. Springer.Information Processing in Medical Imaging, Kluwer Academic Publishers, Dordrecht,1995: 275-286.
[185]Gueziec A, Kazanzides P, Williamson B, et al. Anatomy-based registration of CT-scan and intraoperative X-ray images for guiding a surgical robot[J].IEEE Transactions on Medical Imaging,1998, 17(5):715-728.
[186]De Castro E, Morandi C. Registration of translated and rotated images using finite Fourier transforms[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1987, Volume:PAMI-9(5):700-703.
[187]Chen Q, Defrise M, Deconinck F. Symmetric phase-only matched filtering of Fourier-Mellin transforms for image registration and recognition[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1994,16(12):1156-1168.
[188]Lemieux L, Jagoe R, Fish D R,et al. A patient-to-computed-tomography image registration method based on digitally reconstructed radiographs[J]. MED PHYS,1994,21(11):1749-1760.
[189]Collignon A, Maes F, Delaere D, et al. Automated multi-modality image registration based on informatio n theory[J]. Information processing in medical imaging,1995:263-274.
[190]Viola P, Wells III W M. Alignment by maximization of mutual information[J]. International journal of computer vision,1997,24(2):137-154.
[191]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.
[192]Mattes D, Haynor D R, Vesselle H, et al. PET-CT image registration in the chest using free-form deformations[J]. IEEE Transactions on Medical Imaging,2003,22(1):120-128.
[193]Harry Loats. CT and SPECT image registration and fusion for spatial localization of metastatic processes using Radiolabeled Monoclonals [J]. The Journal of Nuclear Medicine (SO161-5505),1993, 34(3 Suppl):562-566.
[194]夏伟,吕中伟,蔡海东等.盆腹部SPECT与CT图像融合配准框架的设计与应用[J].中国临床医学影像杂志,2009,20(1)：26-28.
[195]章毓晋.图像处理和分析[M].北京：清华大学出版社,1999.
[196]李雄飞,张存利,李鸿鹏等.医学图像配准技术进展[J].计算机科学,2010,37(7)：27-33.
[197]Lu Xiaoqi, Ma Hongli, Zhang Baohua. A non-rigid medical image registration method based on improved linear elastic model[J]. International Journal for Light and Electron Optics,2012, 123(20):1867-1873.
[198]D L G Hill, P G Batchelor, M Holden, et al. Medical image registration [J]. Physics in Medicine and Biology,2001,46(3):1-45.
[199]M.Fornefett, K. Rohr, H.S.Stiehl. Radial basis functions with compact support for elastic registration of medical images[J]. Image and Vision Computing,2001,19(1-2):87-96.
[200]Yang Xuan, Pei Ji-hong, Sun Wei. Elastic image registration using hierarchical spatially based mean shift [J]. Computers in Biology and Medicine,2013,43(9):1086-1097.
[201]Pluim J, Maintz J, Viergever M. Mutual-information-based registration of medical images:A survey [J]. IEEE Trans on Medical Imaging,2003,22(8):986-1004.
[202]王婕好,王加俊,张静亚.基于改进光流场和尺度不变特征变换的非刚性医学图像配准[J].电子与信息学报,2013,35(5)：1222-1228.
[203]许鸿奎,江铭炎,杨明强.基于改进光流场模型的脑部多模医学图像配准[J].电子学报,2012,40(3)：525-529.
[204]潘晓光,李宏,康雁等.双向梯度归一化互信息医学图像配准方法[J].东北大学学报(自然科学版),2012,33(8)：1107-1110.
[205]杜晓刚,党建武,王阳萍等.基于萤火虫算法的互信息医学图像配准[J].计算机科学,2013,40(7)：273-276.
[206]William M.Wells Ⅲ, Paul Viola, Hideki Atsumi, Shin Nakajima, Ron.Kikinis. Multi-modal volume registration by maximization of mutual information[J]. Medical Image Analysis,1996,1(1):35-51.
[207]葛永新,杨丹,雷明.基于良分布的亚像素定位角点的图像配准[J].电子与信息学报,2010,32(2)：427-431.
[208]Collignon A M F, Vandermeulen D, Suetens P, et al. Surface-based registration of 3D medical images[J]. Proc. SPIE 1898, Medical Imaging 1993:Image Processing,1993,32:pp.32-42.
[209]Hava Lester,Simon R.Arridge. A survey of hierarchical non-linear medical image registration[J]. Pattern Recognition,1999,32(1):129-149.
[210]李洪波.共形几何代数域运动形状的刻画[J].计算机辅助设计与图形学学报,2006,18(7)：895-901.
[211]俞肇元,袁林旺,罗文.GIS时空分析系统的Clifford代数设计与实现[J].武汉大学学报：信息科学版,2011,36(12)：1397-1401.
[212]李洪波.共形几何代数-几何代数的新理论和计算框架[J].计算机辅助设计与图形学报,2005,17(11)：2383-2393.
[213]李谭.多模态医学图像配准算法研究[D][硕士学位论文].天津大学,计算机科学与技术学院,2007.