Multi-modal Medical Image Registration Based On Geometric Algebra

With the rapid development of medical imaging technology,medical images are becoming more and more diverse,but each kind of images only contains partial information.Medical image registration technology can provide different,complementary,and overlapping mutil-modal image information for the doctor to help them develop more effective treatment programs.The existing medical image registration technologies are mainly divided into two categories.One is the registration method based on gray value information which is simple and has high registration accuracy,but it has poor robustness and low computational efficiency.The other one is the registration method based on feature information which has high computational efficiency,but it only considers feature information which results in lower registration accuracy than the registration method based on gray value information.These two methods are usually used in two-dimensional image registration.When they are used in three-dimensional image registration,there are many problems such as massive registration parameters,long time-consuming,and poor robustness.To solve these problems,this paper proposes a multi-model medical image registration algorithm based on geometric algebra framework,and details are as follows:1.Image invariants are the key factors of influencing registration while geometry algebra is a covariate algebraic system that does not depend on coordinates at all and conforms to the invariant system of geometric calculations.Therefore,this paper extends the speeded up robust features(SURF)algorithm based on Euclidean geometry to the geometrical algebra(GA)framework which is called the GA-SURF algorithm.This algorithm combines the advantages of geometric algebra with SURF algorithm.It not only has translation invariance,rotation invariance,stability and robustness,but also directly deals with high-dimensional information with high computational efficiency.When calculating the Hessian matrix of pixels and constructing descriptors of feature points,the new algorithm considers information of multiple dimensions.What more,the new algorithm extracts GA feature points in the scale space constructed by geometric algebra theory.These make the accuracy of registration results guaranteed with high computational efficiency.2.Since the human body structure is three-dimensional,the three-dimensional model can be more helpful for subsequent matching.In this paper,the GA feature spheres are constructed based on the GA feature points extracted by the above GA-SURF algorithm.The new construction algorithm is simple and easy to implement with low computational complexity.In the framework of conformal geometry algebra,descriptors of GA feature spheres are generated to implement registration of reference images and floating images.The advantage of registration in the conformal geometry algebraic framework is simple and unified,high computational efficiency without losing the dimensional information.In this paper,the real human brain image data(RIRE project of Vanderbilt University)and the simulated human brain data(BrainWeb)are used for registration.Experimental results show that the new algorithm can directly process high-dimensional information with high registration accuracy and computational efficiency.