Abstract
Creating models of real objects is a complex task for which the use of traditional modeling techniques has proven to be difficult. To solve some of the problem encountered, laser rangefinders are frequently used to sample an object’s surface from several viewpoints resulting in a set of range images that are registered and integrated into a final triangulated model. In practice, due to surface reflectance properties, occlusions and accessibility limitations, certain areas of the object’s surface are not sampled leaving holes which create undesirable artifacts in the integrated model. In this paper, we present a novel algorithm for the automatic hole-filling of triangulated models. The algorithm starts by locating hole boundary regions. A hole consists of a closed path of edges of boundary triangles that have at least an edge, which is not shared with any other triangle. The edge of the hole is then fitted with a b-spline where the average variation of the torsion of the b-spline approximation is calculated. Using a simple threshold of the average variation of the torsion along the edge, one can automatically classify real holes from man-made holes. Following this classification process, we then use an automated version of a radial basis function interpolator to fill the inside of the hole using neighboring edges. Excellent experimental results are presented.
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References
1. Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., and Silva, C., “Point Set Surfaces”, IEEE Visualization, pp. 21–28, 2001.
2. Amenta, N., Bern, M., and Kamvysselis, M., “A new Voronoi-based surface reconstruction algorithm”, SIGGRAPH'98, pp.415–421, 1998.
3. Bajaj, C., Bernardini, F., and Xu, G., “Automatic Reconstruction of Surfaces and Scalar Fields from 3D Scans”, SIGGRAPH'95, pp.109–118, 1995.
4. Bertalmio, M., Shapiro, G., Caselles, V., and Ballester, C. “Image Inpainting”, SIGGRAPH'00, pp.417–424, 2000.
5. Besl, P., “Advances in Machine Vision”, Advances in Machine Vision, Springer Verlag, Chapter 1 - Active Optical Range Sensors, pp. 1–63, 1989.
6. Besl, P. and McKay, N., “A method for registration of 3D shapes”, IEEE Trans. on PAMI, 14 (2). pp. 239–256, 1992.
7. Carr, J., Beatson, R., Cherrie, J., Mitchell, T. Fright, W., and McCallum, B., “Reconstruction and Representation of 3D Objects with Radial Basis Functions”, SIGGRAPH' 01, pp. 67–76, 2001.
8. Curless, B. and Levoy, M., “A Volumetric Method for Building Complex Models from Range Images”, SIGGRAPH' 96, pp. 303–312, 1996.
9. Davis, J., Marschner, S., Garr, M., and Levoy, M., “Filling Holes in Complex Surfaces Using Volumetric Diffusion” Proc. First International Symposium on 3D Data Processing, Visualization, Transmission, pp. 428–861, 2002.
10. Efros, A. and Freeman, W., “Image Quilting for Texture Synthesis and Transfer”, SIGGRAPH'01, pp. 341–348, 2001.
11. Gopi, M. and Krishnan, S., “A Fast and Efficient Projection Based Approach for Surface Reconstruction”, Intern. Journal of High Performance Computer Graphics, Multimedia and Visualization, 1 (1), pp. 1–12, 2000.
12. Hoppe, H., DeRose, T., Duchamp, McDonald, T. J.A., and Stuetzle, W., “Surface reconstruction from unorganized points”, SIGGRAPH'92, pp. 71–78, 1992.
13. Lancaster, P. and Salkauskas, K., Curve and Surface Fitting: an Introduction. Academic Press. 1986.
14. Lorensen, W. and Cline, H., “Marching cubes: A high resolution 3D surface construction algorithm”, Proc. SIGGRAPH'87, pp. 163–169, 1987.
15. McAllister, D., Nyland, L., Popescu, V., Lastra A. and McCue, C., “Real Time Rendering of Real World Environments”, Proc. Rendering Techniques'99, pp. 145–60, 1999.
16. Nyland, L., et al., “The Impact of Dense Range Data on Computer Graphics”, Proceedings of Multi-View Modeling and Analysis Workshop, pp. 3–10, 1999.
17. Nyland, L., Lastra, A., Mc Allister, D., Popescuand, V., McCue, C., and Fuchs, H., “Capturing, Processing and Rendering Real-World Scenes”, In Videometrics and Optical Methods for 3D Shape Measurement, Electronic Imaging, Photonics West, SPIE Vol. 4309, pp. 107–116, 2001.
18. Oliveira, M., Bowen, B., McKenna, R., and Chang, Y., “Fast Digital Image Inpainting”, International Conference on Visualization, Imaging and Image Processing (VIIP 2001), Marbella, Spain, pp. 261–2665, 2001.
19. Hartigan, J. and Wong, M. A., “A K-Means Clustering Algorithm”, Journal of Applied Statistics, 28 (1), pp. 100–108, 1979.
20. Pulli, K., “Multiview Registration for Large Data Sets”, 3DIM'99, pp. 160–168, 1999.
21. Wang, J. and Oliveira, M., “Improved Scene Reconstruction from Range Images”, Proc. EUROGRAPHICS' 2002, pp. 521–530, 2002.
22. Wei, L.Y. and Levoy, M., “Texture Synthesis over Arbitrary Manifold Surfaces”, SIGGRAPH'01, pp. 355–360, 2001.
23. Ying, L., Hertzmann, A., Biermann, H., and Zorin, D., “Texture and Shape Synthesis on Surfaces”, Eurographics'2001, Rendering Workshop, pp. 301–312, 2001.
24. Yu, Y., Ferencz, A., and Malik, J., “Extracting Objects from Range and Radiance Images”, IEEE Transactions on Visualization and Computer Graphics, 7 (4), pp. 351–364, 2001.
25. Carr, J. C., Beatson, R. K., McCallum, B. C., Fright, W. R., McLennan, T. J., and Mitchell, T. J., “Smooth surface reconstruction from noisy range data”, Proceedings of the 1st international conference on computer graphics and interactive techniques in Australasia and South East Asia, Melbourne, Australia, February 11–14, ACM Press, pp. 119-ff, 2003.
26. Buhmann, M., “Radial Basis Fuction: Theory and Implementations”, Cambridge Monographs on Applied and Computational Mathematics, 2003.
27. Carr, J.C., Beatson, R.K., Cherrie, J. B., Mitchell, T.J., Fright, W. R., McLennan, T.J., and Evans, T.R., “Reconstruction and representation of objects with radial basis function”, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp. 67–76, 2001.
28. C. Montani, R. Scateni, R. Scopigno, A modified look-up table for implicit disambiguation of marching cubes, Visual Comput. 10 (1994) 353–355.
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Branch, J., Prieto, F., Boulanger, P. (2006). A Hole-Filling Algorithm for Triangular Meshes Using Local Radial Basis Function. In: Pébay, P.P. (eds) Proceedings of the 15th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34958-7_24
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DOI: https://doi.org/10.1007/978-3-540-34958-7_24
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