基于共形几何代数的3D医学图像配准

Abstract

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.