基于共形几何代数的3D医学图像配准

随着医学图像处理技术的发展，3D／3D配准益受重视，尤其是在外科手术导航等医学应用中．学者们提出了各种3D／3D配准方法，但大多方法是采用传统代数方法进行配准，配准精度和效率都存在问题．本文利用非经典数学——共形几何代数重建了3D医学图像的位置关系约柬问题，分析了医学图像的共形几何变换，构造了新的3D医学图像配准相似测度，基于此提出了新的3D医学图像配准算法，用于CT和MR图像的3D配准．新算法中，以骨骼轮廓作为配准的基础点集，在骨骼轮廓的基础上采用共形几何代数构造共形几何体，接着采用新的3D医学图像配准相似测度进行三维数据的直接配准．实验表明新算法实现了三维数据的直接对齐，能较好地定位组织器官的三维位置．可以直观地体现配准结果．

3D medical image registration based on conformal geometric algebra

With the development of medical image processing technology, more attention has been paid to the registration of 3D/3D medical images, especially in medical applications such as surgical navigation. Many methods to register 3D/3D medical images have been proposed, but most are based on traditional algebra, and have some problems with registration accuracy and efficiency. Here we reconstruct the position constraints of a 3D medical image with conformal geometric algebra, which is a kind of neo-Classical algebra, and also analyze the conformal geometry transformation of medical images. We then construct a novel similarity measure for 3D medical image registration. We use this method to propose 3D medical image registration algorithms for the registration of 3D CT and MR images. In these algorithms, we regard the skeletal outline as the base point set of the registration, based on which conformal geometric entities were constructed with conformal geometric algebra. Then, using the new similarity measure, we prospectively register the 3D data directly. Finally, we present experiments to validate the new algorithms. The results show that the algorithm realizes the direct alignment of 3D data, which can better localize the 3D position of tissues and organs and intuitively reflect the registration results.