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# Methods for Surface Reconstruction

Ho, M. (2006) Methods for Surface Reconstruction. Bachelor's Thesis, Industrial Engineering and Management.

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## Abstract

Point sets such as laser range data or data from medical images or stereo measurements are commonly used to represent three-dimensional objects. For many applications such as computer graphics, medical imaging and virtual simulation, a two-dimensional surface needs to be constructed from the point set. The problem of surface reconstruction is an interesting problem that arises in different scientific areas. We consider the following reconstruction problem. Let F be a smooth surface of some solid in R3. Let S be a set of sample points that lie on or near F. With S as input, the desired output is a surface U, such that U is a nice approximation of F. That is, U is a two-dimensional manifold such that the distance from any point p 2 F to its closest point x 2 U and the angle between the surface normals of F and of U in p and x, respectively, are both small (in a sense to be made more precise later on). There exist many different methods for surface reconstruction. This paper describes three methods that address the general problem and do not assume any structure on the sample points (for example, that they lie on equidistant planes, as is the case with MRI data). The first two of these methods are based on the construction of simplicial complexes, namely the crust, which is Delaunay-based, and the flow complex. With both methods, first the simplicial complex is constructed, after which some steps are taken to extract the reconstructed surface from it. The last method is based on a data interpolation technique called moving least squares (MLS). With this method, based on the set of sample points, an implicit function is being constructed. The zero set of this function, which is an approximation for the original surface, can then be obtained using a contouring algorithm. The first and the third method presented require the set of sample points S to satisfy certain conditions and guarantee certain results with respect to the reconstructed surface U. The sampling conditions are based on the local feature size (defined in Section 3.2), which is like a measure for the level of detail of the surface in a certain area.

Item Type: Thesis (Bachelor's Thesis) Industrial Engineering and Management Bachelor's Thesis English 15 Feb 2018 07:28 15 Feb 2018 07:28 http://fse.studenttheses.ub.rug.nl/id/eprint/8376