Treffer: 3-D image modeling based on data dependent tetrahedrization

3-D image modeling of volumetric data can be useful to biomedical research, medical therapy, surgery planning, and simulation of critical surgery (i.e. cranio-facial). This paper proposes a algorithm which is based on a tetrahedral domain instead of cubes. The initial tetrahedral domain is constructed by using Delaunay tetrahedrization algorithm. In the case of ambiguity, asymptotic decider is used instead of sphere criterion. In sphere criterion, only positional information is considered, but asymptotic decider allows to count the functional information In other words, the construction of the tetrahedral domain is based on whether or not connecting vertices are joined by a component of the hyperbolic arc. Linear trivariate interpolation is performed through the tetraheral domain. We call this new algorithm Marching Tetrahedra for the purpose of comparing it to Marching Cubes algorithm. The main difference between two algorithms is that tetrahedra are used, instead of cubes, in the process. Marching Tetrahedra algorithm allows the scattered data which can't be accepted by Marching Cubes algorithm.