Octree skeleton: An efficient tool for shape and topology analysis of digital models

Analyzing the topology and shape of a digital model has wide applications ranging from CAD to bio-medical imaging. For example, identifying shape components, such as tubes and plates, can reveal the structure of a CAD model or a protein molecule. Identifying topological components, such as handles, is the first step in repairing incorrect topology as a result of reconstruction from noisy point clouds or medical images. A classical tool for describing the shape and topology of a solid model is the skeleton, a discrete approximation of the medial axis. However, existing representations and computations of skeletons on digital models have mostly been restricted to uniform grids, making efficient applications to large models difficult. We present algorithms for representing, computing and utilizing skeletons of digital models on adaptive octree grids, allowing efficient topology and shape analysis on large inputs. These algorithms are based on a new representation of octree grids that gives rise to simple criteria for preserving topology and shape during skeleton generation. The resulted octree skeletons can be used in a range of topological and shape operations, including removing topological errors and identifying shape components.