Das 3d-Puzzle-Problem: effiziente Methoden zum paarweisen Zusammensetzen von dreidimensionalen Fragmenten

The reconstruction of three-dimensional fragmented objects (3d-puzzle-problem) is a highly relevant task with many applications. The field of application comprises archaeology, surgery, bioinformatics and robotics. Examples are the reconstruction of broken archaeological artefacts, human bone fracture reduction in surgery, protein-docking, and the assemblage of industrial components. This work considers the whole processing chain, starting from data acquisition with different sensors, the general registration of surfaces, up to special requirements for matching fragments in different applications. In this context, two novel and efficient pairwise matching approaches will be introduced, which are highly robust against measurement inaccuracies, material deterioration and noise. In their basic configuration, both methods search for a relative pose, where the surface contact between all fragments is as high as possible. The first approach is based on a randomized generation of likely pose hypotheses and an efficient forecasting of the contact area. The second approach is based on a deterministic coarse-to-fine strategy without any random variables. Furthermore, this work discusses how a priori knowledge of the broken objects (like shape priors, mirror symmetries and symmetry axes) can be used to increase the efficiency, accuracy and robustness. Particularly, it shows how to use a priori knowledge to reconstruct broken femurs (thigh bones) and pelvis fractures, which is an important building block for computer-assisted fracture reduction in surgery. In addition to the 3d-puzzle-problem, an automatic matching of surfaces has applications in many other important computer vision related fields. It will be shown that the developed approaches are also applicable for 3d object recognition and pose estimation, as well as for registration of range data.