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, address clearly a new formation of the deformation problem for moving domains, and we apply it in natural images, face images and MRI brain images. And we use a new method to construct diffeomorphisms through a completely different approach. The idea is to control directly the Jacobian determinant and the curl vector of a transformation and use them as one CNN channel with other modalities(T1-weighted, T1-IR and T2-FLAIR) to get more accurate results of brain segmentation. More importantly, we discuss the influence of some optimization parameters to precision analysis of MRI brain segmentation by both numerical experiments and theoretical analysis. We test this method on the IBSR dataset and MRBrainS18 dataset based on VoxResNet and prove the influence of three parameters on the accuracy of MRI brain segmentation.Finally, we also compare the segmentation performance of our method in two networks, VoxResNet and 3D U-Net network. We believe the proposed method can advance the performance in brain segmentation and clinical diagnosis.
The success of the deformation method of grid generation actually relies on the div-curl system, which shows the great importance of the curl vector ( @math ). Hence, in the paper of 2016 @cite_15 , Xi Chen proposed another completely new approach by directly applying JD(the Jacobian determinant @math ) and CV(the curl vector @math ).They used calculus of variation to formulate a new variational method with prescribed JD and CV of constructing transformations @cite_15 . A recovering experiment was designed by the new variational method with the same JD and CV.
@cite_15
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Adaptive grid generation is an active research topic for numer- ical solution of differential equations. In this paper, we propose a variational method which generates transformations with prescribed Jacobian determinant and curl. Then we use this transformation to achieve adaptive grid generation task, and show the importance of curl in a transformation.