Dual marching tetrahedra: contouring in the tetrahedronal environment

Abstract

We discuss the dual marching tetrahedra (DMT) method. The DMT can be viewed as a generalization of the classical cuberille method of Chen et al. to a tetrahedronal. The cuberille method produces a rendering of quadrilaterals comprising a surface that separates voxels deemed to be contained in an object of interest from those voxels not in the object. A cuberille is a region of 3D space partitioned into cubes. A tetrahedronal is a region of 3D space decomposed into tetrahedra. The DMT method generalizes the cubille method from cubes to tetrahedra and corrects a fundamental problem of the original cuberille method where separating surfaces are not necessarily manifolds. For binary segmented data, we propose a method for computing the location of vertices this is based upon the use of a minimal discrete norm curvature criterion. For applications where dependent function values are given at grid points, two alternative methods for computing vertex positions are discussed and compared. Examples are drawn from a variety of applications, including the Yes/No/Don't-Know data sets resulting from inconclusive segmentation processes and Well-Log data sets. © Springer-Verlag Berlin Heidelberg 2008.