###### Abstract  
Multimodal image registration is an important component of medical image processing, allowing the integration of complementary information from various imaging modalities to improve clinical applications like diagnosis and treatment planning. We proposed a novel multistage neural network for three-dimensional multimodal medical image registration, which addresses the challenge of larger rigid deformations commonly present in medical images due to variations in patient positioning in different scanners and rigid anatomical structures. This multistage network combines rigid, affine and deformable transformations in three stages. The network was trained unsupervised with Mutual Information and Gradient L2 loss. We compared the results of our proposed multistage network with a rigid-affine-deformable registration with the classical registration method NiftyReg as a baseline and a multistage network, which combines affine and deformable transformation, as a benchmark. To evaluate the performance of the proposed multistage network, we used four three-dimensional multimodal in vivo datasets: three renal MR datasets consisting of T1-weighted and T2-weighted MR scans and one liver dataset containing CT and T1-weighted MR scans. Experimental results showed that combining rigid, affine and deformable transformations in a multistage network leads to registration results with a high structural similarity, overlap of the corresponding structures (Dice: 76.7 \(\pm\) 12.5, 61.1 \(\pm\) 14.0, 64.8 \(\pm\) 16.2, 68.1 \(\pm\) 24.6 for the four datasets) and a low level of image folding (\(|I|\leq\) 0: less than or equal to 1.1%), resulting in a medical plausible registration result. machine learning; image registration; multistage; deep learning; multimodal; medical images 20231  
number of cysts. By fusing the images of the two MR modalities and thereby combining complementary information, the determination of the two biomarkers can be significantly improved [8]. Furthermore, images from multiple time points can be fused, e.g., images before, during and after a therapy, to monitor the therapy's progress. For this, registration of the images is necessary. Another example of a clinical application that benefits from image registration is the treatment of oligometastatic disease, which has poor outcomes with standard therapies due to the local lesion heterogeneity. Personalized image-guided therapies that consider tumor heterogeneity have shown potential in improving survival rates [9; 10]. Typically, CT imaging is used for these interventions, while MRI is utilized to characterize tumor heterogeneity, which is often invisible in CT scans [11]. Differences in patient positioning in the two scanners, as well as the patient's respiration, result in the organs being deformed differently in the corresponding CT and MR images. Therefore, prior to fusion, the registration of CT and MR images is inevitable. Traditionally, medical image registration is performed using conventional methods that involve iteratively updating the transformation parameters to optimize the similarity metrics. However, this approach is often time-consuming as each new image must be re-registered iteratively. To solve this problem, deep learning-based registration methods have been developed to speed up the registration process. In these methods, the network is trained once and subsequent registrations can be performed by passing the new images through the network, eliminating the need for time-consuming iterative methods [12]. In recent years, several neural networks for medical image registration have been published with a wide variety of architectures. These include, e.g., the use of multistage networks, in which different subnetworks are used [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28].