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.
This is known as the deformation method. A series of applications were made including adaptive moving grid @cite_7 , and steady euler flow calculations @cite_5 .In addition,the dynamic version of the deformation method on fixed domains was developed in @cite_7 based on solving Poisson's equations. In 2004,The Least-Squares Finite Element Method was first applied to solve the div-curl system in @cite_0 which extends the deformation method of grid deneration to moving domains.This version constructs a diffeomorphism @math , for @math
@cite_0 @cite_5 @cite_7
2028949045 1969724971
An adaptive remeshing procedure based on a cell volume deformation method is presented. Starting with an initial grid, this method offers direct cell volume control through the specification of the transformation Jacobian. Grid points are moved with appropriate grid velocities so that the specified cell volume distribution can be achieved at the end of the grid movement without adding or removing grid points. The grid velocities are determined by solving a scalar Poisson equation. This method is applied to solving the compressible Euler equations. Computational test cases of transonic flow over an airfoil are presented and demonstrate the desired control of grid sizes across shock waves. A new method for generating adaptive moving grids is formulated based on physical quantities. Level set functions are used to construct the adaptive grids, which are solutions of the standard level set evolution equation with the Cartesian coordinates as initial values. The intersection points of the level sets of the evolving functions form a new grid at each time. The velocity vector in the evolution equation is chosen according to a monitor function and is equal to the node velocity. A uniform grid is then deformed to a moving grid with desired cell volume distribution at each time. The method achieves precise control over the Jacobian determinant of the grid mapping as the traditional deformation method does. The new method is consistent with the level set approach to dynamic moving interface problems.