THE SELF-ORGANZING APPROACH FOR SURFACE RECONSTRUCTION FROM UNSTRUCTURED POINT CLOUDS

Surface reconstruction from a point cloud is very useful in many different application areas, such as manufacturing (Bernardini et al., 1999), cultural heritage (Bernardini et al., 2002) and medicine (Satava & Jones, 1998). Surface reconstructions methods aim to create digital models to reproduce an object shape given a set of points sampled from its surface using 3D scanning technology. Surface reconstruction starting from a cloud of points is a complex problem which raises a number of challenging issues: Firstly, the connectivity between the vertices must be constructed so that the reconstructed surface has the same topological features as the target surface. However no structural information is available in the input data. Instead the only items of information available are the 3D coordinates of a set of points sampled from the target surface. Secondly, meshes with different resolutions must be generated to fulfil the needs of different applications, otherwise additional processing is required to simplify (or refine) the mesh constructed. Another issue is that the meshes produced must be two dimensional manifolds. Finally, the triangular faces of the mesh should be approximately equilateral. A lot of research effort has been expended to develop surface reconstruction methods. Some of these methods are based on geometric techniques (Amenta et al., 2001), (Hoppe et al., 1992). Another well known approach is that of dynamic methods (Miller et al., 1991), (Qin et al., 1998), based on the evaluation of energy or force functions. A more recent approach to the problem of surface reconstruction is that of learning-based methods. Learning algorithms are able to process very large and/or noisy data, such as point clouds obtained from 3D scanners and have been used to reconstruct surfaces. Following this approach, some studies (Brito et al., 2008), (Hoffmann & Varady, 1998), (Yu, 1999), have employed SelfOrganizing Maps (SOM) and their variants for surface reconstruction. SOM is suitable for the surface reconstruction problem because it can form topological maps to replicate the distribution of input data. In this chapter the authors present two Self-Organizing Maps based on what that they have proposed for surface reconstruction. 11

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