The dichotomy between full detail representation and the efficient management of data digitization is still a big issue in the context of the acquisition and visualization of 3D objects, especially in the field of the cultural heritage. Modern scanning devices enable very detailed geometry to be acquired, but it is usually quite hard to apply these technologies to large artifacts. In this article we present a project aimed at virtually reconstructing the impressive (7×11 m.) portal of the Ripoll Monastery, Spain. The monument was acquired using triangulation laser scanning technology, producing a dataset of 2212 range maps for a total of more than 1 billion triangles. All the steps of the entire project are described, from the acquisition planning to the final setup for dissemination to the public. We show how time-of-flight laser scanning data can be used to speed-up the alignment process. In addition we show how, after creating a model and repairing imperfections, an interactive and immersive setup enables the public to navigate and display a fully detailed representation of the portal. This article shows that, after careful planning and with the aid of state-of-the-art algorithms, it is now possible to preserve and visualize highly detailed information, even for very large surfaces.

We explore the automatic recovery of solids from their volumetric discretizations. In particular, we propose an approach, called Pressing, for smoothing isosurfaces extracted from binary volumes while recovering their large planar regions ( ats). Pressing yields a surface that is guaranteed to contain the samples of the volume classi ed as interior and exclude those classi ed as exterior. It uses global optimization to identify ats and constrained bilaplacian smoothing to eliminate sharp features and high-frequencies from the rest of the isosurface. It recovers sharp edges between at regions and between at and smooth regions. Hence, the resulting isosurface is usually a much more accurate approximation of the original solid than isosurfaces produced by previously proposed approaches. Furthermore, the segmentation of the isosurface into at and curved faces and the sharp/smooth labelling of their edges may be valuable for shape recognition, simpli cation, compression, and various reverse engineering and manufacturing applications.

The computation of the largest planar region approximating a 3D object is an important problem with wide applications in modeling and rendering. Given a voxelization of the 3D object, we propose an efficient algorithm to solve a discrete version of this problem. The input of the algorithm is the set of grid edges connecting the interior and the exterior of the object (called sticks). Using a voting-based approach, we compute the plane that slices the largest number of sticks and is orientation-compatible with these sticks. The robustness and efficiency of our approach rests on the use of two different parameterizations of the planes with suitable properties. The first of these is exact and is used to retrieve precomputed local solutions of the problem. The second one is discrete and is used in a hierarchical voting scheme to compute the global maximum. This problem has diverse applications that range from finding object signatures to generating simplified models. Here we demonstrate the merits of the algorithm for efficiently computing an optimized set of textured impostors for a given polygonal model.

Since the publication of the original Marching Cubes algorithm, numerous variations have been proposed for guaranteeing water-tight constructions of triangulated approximations of isosurfaces. Most approaches divide the 3D space into cubes that each occupy the space between eight neighboring samples of a regular lattice. The portion of the isosurface inside a cube may be computed independently of what happens in the other cubes, provided that the constructions for each pair of neighboring cubes agree along their common face. The portion of the isosurface associated with a cube may consist of one or more connected components, which we call sheets. The topology and combinatorial complexity of the isosurface is influenced by three types of decisions made during its construction: (1) how to connect the four intersection points on each ambiguous face, (2) how to form interpolating sheets for cubes with more than one loop, and (3) how to triangulate each sheet. To determine topological properties, it is only relevant whether the samples are inside or outside the object, and not their precise value, if there is one. Previously reported techniques make these decisions based on local -per cube-criteria, often using precomputed look-up tables or simple construction rules. Instead, we propose global strategies for optimizing several topological and combinatorial measures of the isosurfaces: triangle count, genus, and number of shells. We describe efficient implementations of these optimizations and the auxiliary data structures developed to support them.