Effects of Differential Geometry Parameters on Grid Generation and Segmentation of MRI Brain Image

Accurate segmentation of brain tissue in magnetic resonance images (MRI) is a difficult task due to different types of brain abnormalities. In this paper, we review the deformation method focus on the construction of diffeomorphisms to generate the 2D MRI image grids and extend it to the 3D MRI images, address clearly a new formation of the deformation problem for moving domains and construction of diffeomorphisms through a completely different approach. The idea is to control directly the first order differential operators including the Jacobian determinant (JD), divergence (DIV), and curl vector (CV) generated by the 2D and 3D MRI image grids and use them as CNN channels with other modalities (T1-weighted, T1-IR, and T2-FLAIR) or single T1-weighted modality to improve the performance of brain segmentation. More importantly, we discuss the influence of three optimization parameters to the generation of the 2D and 3D MRI image grids by both theoretical analysis and the numerical experiments. We test this method on the IBSR dataset and MRBrainS18 dataset based on VoxResNet and verify the influence of three parameters on the accuracy of MRI brain segmentation. Finally, we also compare the segmentation performance of our method in three networks, including 2D U-Net, 3D U-Net, and VoxResNet. We believe the proposed method can advance the performance in brain segmentation and clinical diagnosis.