Medical Image Registration Based On Geometrical Algebra Theory

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.