Publication Details
Panagiotis Foteinos, Andrey Chernikov and Nikos Chrisochoides.
Published in Computational Geometry: Theory and Applications, Publisher Elsevier, Volume 47, No. 4, pages 539 -- 562, 2014
Abstract
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 \ratio less than sqrt(sqrt(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. 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.
