Topological investigations of object models

The purpose of this paper is the development of a theoretical basis for the investigation of a 3D model's topological structure which is currently a more or less neglected aspect in the areas of object reconstruction and vision. The knowledge of this structure gives rise to detailed statements on the correspondence between a real world object and a digital model which cannot be made using other methods. We describe a generalization of the snake concept to arbitrary triangulated surfaces. Our aim is the calculation of so-called minimal length loops which may be used for the determination and localization of tunnels. Minimal length loops can be used in practice for applications like the assessment of object reconstruction results, autonomous reconstruction and motion planing.