Generation of Myocardial Wall Surface Meshes from Segmented MRI
Figure 2
Mesh generation summary. The input image (a) is segmented into the object and background, resulting in a binary image (b). A sphere enclosing the object is centered at the object barycenter (c). The sphere is uniformly sampled with the number of points equal to the number of singularities. The binary image is resampled with isotropic voxels and the Laplace equation is numerically solved between the sphere (boundary condition of 0) and the object (boundary condition of 1). The solution of the Laplace equation is encoded in the gray levels in (c) and (d). The binary object is eroded, and the points are propagated from the sphere to the eroded object in the direction of the gradient of the Laplace equation solution to define the singularity locations, shown as red squares in (d) and (e). Boundary points, specified as midpoints for each pair of neighboring voxel, where one voxel is in the object and the other is in the background, are shown as red dots in (e). The singularity locations as well as the boundary points are used to specify the analytic solution of the Laplace equation. The boundary points are propagated in the negative gradient direction of the solution of the Laplace equation from the object boundary to the sphere (f). Their values of the underlying solution of the Laplace equation are interpolated at the sphere to the define the stopping function. The number of degrees of freedom of the stopping function is defined by the number of control points, which are shown as blue circles in (g). An approximately uniform mesh is generated on the sphere. The vertices of the mesh on the sphere, shown as black crosses in (g), are propagated from the sphere in the direction of the gradient of the solution of the Laplace equation until the value of the underlying solution of the Laplace equation is equal to the corresponding value of the stopping function. The propagated mesh nodes define the final mesh, shown in (h). Figures (a)–(h) are two dimensional for illustration purposes, while the method is three dimensional.
