Tetrahedron topological characterization with application in volumetric reconstruction

One of the challenges of Volume Modelling is the definition of theoretical frameworks to support object manipulation and representation. Opposite to what is seen in the field of surface modelling, few satisfactory tools have been presented that ensure topological robustness to volumetric models. In this paper we offer one such mathematical framework for volumetric model definition based on tetrahedral meshes. From a complete tetrahedron topological characterization, a set of Morse Operators is given, which enable global tolopogical control during tetrahedron addition or removal. A number of applications can be envisaged, from geometrical modelling to volume reconstruction. We show the effectiveness of the tetrahedron characterization framework for volume reconstruction from images, showing that the method is capable of handling certain types of noise topologically without the need for a time consuming preprocessing step, or a post-processing step to detect cavities and holes.