Resumen de Extracting shapes from binary grids
Antonio Chica Calaf 
This work explores the retrieval of shape information from binary discretizations of solids, In particular, we study binary regular grids and the associated isosurface extraction using Marching Cubes. Binary grids are chosen instead of scalar fields because they are the most basic result of segmentation methods. Furthermore, any technique designed to obtain shape information from binary grids may be easily extended to scalar grids.
First, the problem is stated and the contributions made by this thesis are introduced. Then its relation to relevant previous work is presented. This includes isosurface extraction, topology disambiguation, feature extraction, smoothing, simplification and reverse engineering. Some basic concepts are also introduced. Most of them are related to the problem of isosurface extraction. An algorithm to identify and globally solve topology ambiguity problems is proposed. Ambiguous cubes and faces provide different extraction options during Marching Cubes. Thus, applying different criteria to them offers the possibility of optimizing some topological properties, like the resulting number of handles or the number of shells.
Once ambiguity has been figured out, a second voting-based algorithm is used to identify large planar regions. Every edge separating a black node from a white one, which we call a stick, votes for the planes that stab it. The entire vote is tracked using a discretization of an special plane parameterization called Connected-Cubes parameterization, which is described in detail. As a result, a plane that approximates a large region of the model is generated, and this process is repeated to obtain a set of approximating planes. These computed planar approximations are used in combination with a smoothing algorithm to obtain a shape from a binary grid, which closely resembles the original one. In this method, the planar regions are kept fixed while a constrained bilaplacian smoothing algorithm, specifically designed to deal with
