Three dimensional medical images can help doctors in diagnosis and treatment, and the registered medical images of different modalities can provide more comprehensive information about the patient for doctors. However, the traditional 3D multimodal medical image registration is less precise, time-consuming and susceptible to interference. This article first establishes the Hessian fourdimensional scale space, and extends the SURF framework to 3D. Then, a 3D feature point descriptor with gradient angle invariance is constructed based on geometric algebra to enrich feature point information. Meanwhile, a fast spatial optimization algorithm is designed, which can not only ensure the registration accuracy, but also improve the registration stability. Finally, the experiments are carried out using the RIRE public data set with good data consistency and the personalized clinical instance data provided by the cooperative affiliated hospitals. In the experimental evaluation, with manual registration as the gold standard, the average registration error of the public library and clinical example images does not exceed 3 mm, and the registration similarity exceeds 99. 1% . Gaussian noise is mixed in the anti-interference experiment, the mean error still does not exceed 3. 5 mm, and the similarity exceeds 98. 9% . Experimental results show that the 3D registration method based on geometric algebra SURF has higher accuracy and stability, which can provide theoretical basis and treatment plan for clinical application.