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Regularized implicit surface reconstruction from points and normals
Journal of the Brazilian Computer Society volume 13, pages 7–15 (2007)
We consider the problem of surface reconstruction of a geometric object from a finite set of sample points with normals. Our contribution is to present a new scheme for implicit surface reconstruction. Similarly to the multilevel partition of unity (MPU) method we hierarchically divide the domain obtaining local approximation for the object on each part, and then patch all together obtaining a global description of the object. Our new scheme uses ridge regression and weighted gradient one fitting techniques to get better stability on local approximations. The method behaves reasonably on sparse set of points and data with holes as those which comes from 3D scanning of real objects.
I. Babuska and J. Melenk. The partition of unity method.International Journal of Numerical Methods in Engineering, 40:727–758, 1997.
M. M. Blane, Z. Lei, H. Çivi, and D. Cooper. The 3L algorithm for fitting implicit polynomial curves and surfaces to data.Transactions on Pattern Analalysis and Machine Intelligence, 22(3):298–313, 2000.
Y.-L. Chen and S.-H. Lai. A partition-of-unity based algorithm for implicit surface reconstruction using belief propagation. InShape Modeling and Applications, pages 147–155. IEEE, 2007.
R. Franke and G. Nielson. Smooth interpolation of large sets of scattered data.International Journal of Numerical Methods in Engineering, 15:1691–1704, 1980.
J. P. Gois, V. Polizelli, T. Etiene, E. Tejada, A. Castelo, T. Ertl, and L. G. Nonato. Robust and adaptive surface reconstruction using partition of unity implicits. InSibgrapi, pages 95–104. IEEE, 2007.
M. Levoy, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira, M. Ginzton, S. Anderson, J. Davis, J. Ginsberg, J. Shade, and D. Fulk. The digital Michelangelo project: 3D scanning of large statues. InSiggraph, pages 131–144. ACM, 2000.
G. Taubin. Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation.Pattern Analysis and Machine Intelligence, 13(11):1115–1138, 1991.
J. Carr, R. Beatson, J. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans. Reconstruction and representation of 3D objects with radial basis functions. InSiggraph, pages 67–76. ACM, 2001.
T. Lewiner, H. Lopes, A. W. Vieira, and G. Tavares. Efficient implementation of Marching Cubes’ cases with topological guarantees.Journal of Graphics Tools, 8(2):1–15, 2003.
M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and C. Silva. Point set surfaces. InVisualization, pages 21–28. IEEE, 2001.
M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and C. Silva. Computing and rendering point set surfaces.Transactions on Visualization and Computer Graphics, 9(1):3–15, 2003.
T. K. Dey and S. Goswami. Provable surface reconstruction from noisy samples.Computational Geometry: Theory and Applications, 35(1–2):124–141, 2006.
N. Amenta and M. Bern. Surface reconstruction by voronoi filtering.Discrete and Computational Geometry, 22(4):481–504, 1999.
N. Amenta, S. Choi, T. Dey, and N. Leekha. A simple algorithm for homeomorphic surface reconstruction. InSymposium on Computational Geometry, pages 213–222. ACM, 2000.
N. Amenta, S. Choi, and R. Kolluri. The Power Crust, unions of balls, and the medial axis transform.Computational Geometry: Theory and Applications, 19(2–3):127–153, 2001.
Y. Ohtake, A. Belyaev, and M. Alexa. Sparse lowdegree implicit surfaces with applications to high quality rendering, feature extraction, and smoothing. InSymposium on Geometry processing, page 149. Eurographics, 2005.
Y. Ohtake, A. Belyaev, M. Alexa, G. Turk, and H.-P. Seidel. Multi-level partition of unity implicits. InSiggraph, volume 22, pages 463–470. ACM, 2003.
T. Tasdizen, J. P. Tarel, and D. B. Cooper. Algebraic curves that work better. InComputer Vision and Pattern Recognition, volume II, pages 35–41. IEEE, 1999.
M. Lage, F. Petronetto, A. Paiva, H. Lopes, T. Lewiner, and G. Tavares. Vector field reconstruction from sparse samples. InSibgrapi, pages 297–304. IEEE, 2006.
D. Levin.Mesh-independent surface interpolation, pages 37–49. Springer, 2003.
B. Mederos, N. Amenta, L. Velho, and L. de Figueiredo. Surface reconstruction for noisy point clouds. InSymposium on Geometry Processing, pages 53–62, 2005.
V. V. Savchenko, A. Pasko, O. Okunev, and T. Kuni. Function representation of solid reconstructed from scattered surface points and contours.Computer Graphics Forum, 14:181–188, 2002.
A. Sharf, T. Lewiner, G. Shklarski, S. Toledo, and D. Cohen-Or. Interactive topology-aware surface reconstruction. InSiggraph, pages 43.1–43.9, 2007.
I. Tobor, P. Reuter, and C. Schlick. Reconstructing multi-scale variational partition of unity implicit surfaces with attributes.Graphical Models, 68(1):25–41, 2006.
G. Turk and J. O’Brien. Modeling with implicit surfaces that interpolates.Transaction on Graphics, 21:855–873, 2002.
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Mederos, B., Lage, M., Arouca, S. et al. Regularized implicit surface reconstruction from points and normals. J Braz Comp Soc 13, 7–15 (2007). https://doi.org/10.1007/BF03194253
- Computer graphics
- Implicit modeling
- Surface reconstruction
- Partition of unity
- Ridge regression