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Survey of Surface Reconstruction Algorithms

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Surface reconstruction is a problem in the field of computational geometry that is concerned with recreating a surface from scattered data points sampled from an unknown surface. To date, the primary application of surface reconstruction algorithms has been in computer graphics, where physical models are digitized in three dimensions with laser range scanners or mechanical digitizing probes (Bernardini et al., 1999 [1]). Surface reconstruction algorithms are used to convert the set of digitized points into a wire frame mesh model, which can be colored, textured, shaded, and placed into a 3D scene (in a movie or television commercial, for example). In this paper, we discuss some computational geometry preliminaries, and then move on to a summary of some different techniques used to address the surface reconstruction problem. The coming sections describe two algorithms: that of Hoppe, et al. (1992 [2]) and Amenta, et al. (1998 [3]). Finally, we present other applications of surface reconstruction and a brief comparison for some algorithms in this filed emphasizing on their advantages and disadvantages.
Cite this paper
Alqudah, A. (2014) Survey of Surface Reconstruction Algorithms. Journal of Signal and Information Processing, 5, 63-79. doi: 10.4236/jsip.2014.53009. 
 

[1] Bernardini, F., Bajaj, C., Chen, J. and Schikore, D. (1999,) Automatic Reconstruction of 3D CAD Models from Digital Scans. International Journal of Computational Geometry Applications, 9, 327-370.
[2] Hoppe, H., DeRose, T. and Duchamp, T. (1992) Surface Reconstruction from Unorganized Points. Proceedings of ACM SIGGRAPH’92, 27-31 July 1992, Chicago, 71-78.
[3] Amenta, N., Bern, M. and Kamvysselis, M. (1998) A New Voronoi-Based Surface Reconstruction Algrorithm. Proceedings of ACM SIGGRAPH’98, 19-24 July 1998, Orlando, 415-422.
[4] O’Rourke, J. (1998) Computational Geometry in C. 2nd Edition, Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511804120
[5] de Berg, M., van Kreveld, M., Overmars, M. and Schwarzkopf, O. (1997) Computational Geometry: Algorithms and Applications. Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-3-662-03427-9
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[7] Boissonnat, J.-D. (1984) Geometric Structures for Three-Dimensional Shape Representation. ACM Transactions on Graphics, 3, 266-286. http://dx.doi.org/10.1145/357346.357349
[8] Bentley, J.L. and Friedman, J.H. (1979) Data Structures for Range Searching. Computing Surveys, 111, 398-409.
[9] Lorensen, W.E. and Cline, H. E. (1987) Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics, 21, 163-169. http://dx.doi.org/10.1145/37402.37422
[10] Boissonnat, J.-D. and Cazals, F. (2000) Smooth Shape Reconstruction via Natural Neighbor Interpolation of Distance Functions. ACM Symposium on Computational Geometry, 12-14 June 2000, Hong Kong, 223-232.
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