Image-based unstructured 3D mesh generation for medical applications.
In P. Neittaanmäki, T. Rossi, K. Majava
and O. Pironneau, editors,
European Congress on Computational Methods in
Applied Sciences and Engineering
We present a dimension-independent algorithm for non-uniform meshing of voxel geometries, e.g. stemming from segmented medical images.
The basic algorithms uses spacetrees (generalized octrees for arbitrary dimension) to build a hierarchical representation of the image information. The resolution of the spacetree can depend on several parameters, such as homogeneity of the material, or application dependent criteria. Arbitrary Cartesian refinement rules can be used, in addition to the usual isotropic binary refinement. This is particularly important for images with anisotropic voxel sizes. Also, the balancing level can be freely chosen.
In a second stage, a non-uniform simplicial or hybrid mesh is generated with guaranteed element quality. Again, this part is completely dimension independent.
In order to achieve smooth material boundaries, we introduce the marching simplices algorithm for 2D and 3D. Marching simplices generalize the Cartesian volumetric marching tetrahedra method to general simplicial meshes. Our algorithm also handles cases where the separating surface passes through mesh vertices. This avoids degeneracies and allows one to shift vertices to the surface where appropriate, thus significantly reducing the number of cut simplices.
The implementation of the algorithmic components makes use of generic programming to maximize reuse, flexibility and composability. We strive for maximal independence of algorithmic components, thus paving the way toward a meshing toolbox which allows to build mesh generators adapted to particular applications. For example, in the context of maxillo-facial surgery simulation special mesh generation options can be applied to the vincinity of cuts.
Mesh generation for large models can require large computational resources. The algorithms described here lend themselves to parallelization, which is planned for the near future. Meshing of large geometries is a good candidate for a Grid service, which is currently under development.