Tetrahedral mesh generation for medical images with multiple regions using active surfaces

In this paper, we present a method for automatically generating tetrahedral meshes from 3D images with multiple region labels. The first step consists of constructing an adaptively sized tetrahedral mesh that conforms exactly to the voxelized regions in the image. Active surfaces (active contours in 2D) are then employed to smooth the region boundaries and remove the voxelization. Specifically, an energy with three terms is minimized: a smoothing term to remove the voxelization, a fidelity term to keep the mesh from moving too far away from the image data, and an elasticity term to keep the tetrahedra from becoming flattened or inverted as the mesh deforms. The algorithm for tetrahedral mesh generation is applied to an MRI image that has been automatically segmented using an existing method. The resulting mesh has a number of desirable properties such as tetrahedra with all dihedral angles away from 0 and 180 degrees, smoothness, and a high level of detail for the number of tetrahedra used.