【作者】 华亮；

【导师】 冯浩；

【作者基本信息】 浙江工业大学 ， 控制理论与控制工程， 2013， 博士

【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。更多还原

【Abstract】 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.更多还原