We present a fully automatic technique which converts an inconsistent input mesh into an output mesh that is guaranteed to be a clean and consistent mesh representing the closed manifold surface of a solid object. The algorithm removes all typical mesh artifacts such as degenerate triangles, incompatible face orientation, non-manifold vertices and edges, overlapping and penetrating polygons, internal redundant geometry, as well as gaps and holes up to a user-defined maximum size ρ. Moreover, the output mesh always stays within a prescribed tolerance ε to the input mesh. Due to the effective use of a hierarchical octree data structure, the algorithm achieves high voxel resolution (up to 4096 3 on a 2GB PC) and processing times of just a few minutes for moderately complex objects. We demonstrate our technique on various architectural CAD models to show its robustness and reliability.

Active contour models are an efficient, accurate, and robust tool for the segmentation of 2D and 3D image data.In particular, geometric deformable models (GDM) that represent an active contour as the level set of an implicitfunction have proven to be very effective. GDMs, however, do not provide any topology control, i.e. contours maymerge or split arbitrarily and hence change the genus of the reconstructed surface. This behavior is inadequate insettings like the segmentation of organic tissue or other objects whose genus is known beforehand. In this paperwe describe a novel method to overcome this limitation while still preserving the favorable properties of the GDMsetup. We achieve this by adding (sparse) topological information to the volume representation at locations whereit is necessary to locally resolve topological ambiguities. Since the sparse topology information is attached to theedges of the voxel grid, we can reconstruct the interfaces where the deformable surface touches itself at sub‐voxelaccuracy. We also demonstrate the efficiency and robustness of our method.

In this paper we propose a progressive 3D geometry transmission technique that is robust with respect to data loss. In a preprocessing step we decompose a given polygon mesh model into a set of overlapping ellipsoids, representing the coarse shape of the model, and a stream of sample points, representing its fine detail. On the client-side, we derive a coarse approximation of the model from the ellipsoid decomposition and then re-insert the sample points to reconstruct the fine detail. The overlapping ellipsoids as well as the sample points represent independent pieces of geometric information, hence partial data loss can be tolerated by our reconstruction algorithm and will only lead to a gradual degradation of the reconstruction quality. We present a transmission scheme that is especially well-suited for geometry broadcasting where we exploit the fact that the order of the sample points can be arbitrarily permuted.

Extracting isosurfaces from volumetric datasets is an essential step for indirect volume rendering algorithms. For physically measured data, e.g. in medical imaging applications, one often introduces topological errors such as small handles that stem from measurement inaccuracy and cavities that are generated by tight folds of an organ. During isosurface extraction these measurement errors result in a surface whose genus is much higher than that of the actual surface. In many cases, however, the topological type of the object under consideration is known beforehand, e.g., the cortex of a human brain is always homeomorphic to a sphere. By using topology preserving morphological operators we can exploit this knowledge to gradually dilate an initial set of voxels with correct topology until it fits the target isosurface. This approach avoids the formation of handles and cavities and guarantees a topologically correct reconstruction of the object's surface.