Guaranteed quality tetrahedral Delaunay meshing for medical images

In this paper, we present a Delaunay refinement algorithm for meshing 3D medical images. Given that the surface of the represented object is a smooth 2-manifold without boundary, we prove that (a) all the tetrahedra of the output mesh have radius–edge ratio less than 3+2(≈1.93), (b) all the boundary facets have planar angles larger than 30 degrees, (c) the symmetric (2-sided) Hausdorff distance between the object surface and mesh boundary is bounded from above by a user-specified parameter, and (d) the mesh boundary is ambient isotopic to the object surface. The first two guarantees assure that our algorithm produces elements of bounded radius–edge ratio. The last two guarantees assure that the mesh boundary is a good geometric and topological approximation of the object surface. Our method also offers control over the size of tetrahedra in the final mesh. Experimental evaluation of our algorithm on synthetic and real medical data illustrates the theory and shows the effectiveness of our method.