# Growing Surface Structures

### Hendrik Annuth, Christian-A. Bohn

#### Abstract

Strictly iterative approaches derived from unsupervised artificial neural network (ANN) methods have been surprisingly efficient for the application of surface reconstruction from scattered 3D points. This comes from the facts, that on the one hand, ANN are able to robustly cluster samples of arbitrary dimension, size, and complexity, and on the second hand, ANN algorithms can easily be adjusted to specific applications by inventing simple local learning rules without loosing the robustness and convergence behavior of the basic ANN approach. In this work, we break up the idea of having just an ``adjustment'' of the basic unsupervised ANN algorithm but intrude on the central learning scheme and explicitly use learned topology within the training process. We demonstrate the performance of the novel concept in the area of surface reconstruction. In this work, we break up the idea of having just an “adjustment” of the basic unsupervised ANN algorithm but intrude on the central learning scheme and explicitly use the learned topology within the training process. We demonstrate the performance of the novel concept in the area of surface reconstruction.

#### References

- Amenta, N., Bern, M., and Kamvysselis, M. (1998). A new voronoi-based surface reconstruction algorithm. In Proceedings of the 25th annual conference on Computer graphics and interactive techniques, SIGGRAPH 7898, pages 415-421, New York, NY, USA. ACM.
- Annuth, H. and Bohn, C. A. (2010). Tumble tree: reducing complexity of the growing cells approach. In Proceedings of the 20th international conference on Artificial neural networks: Part III, ICANN'10, pages 228-236, Berlin, Heidelberg. Springer-Verlag.
- Annuth, H. and Bohn, C.-A. (2012). Smart growing cells: Supervising unsupervised learning. In Madani, K., Dourado Correia, A., Rosa, A., and Filipe, J., editors, Computational Intelligence, volume 399 of Studies in Computational Intelligence, pages 405-420. Springer Berlin / Heidelberg. 10.1007/978-3-642-27534-0 27.
- Baader, A. and Hirzinger, G. (1993). Three-dimensional surface reconstruction based on a self-organizing feature map. In In Proc. 6th Int. Conf. Advan. Robotics, pages 273-278.
- Bernardini, F., Mittleman, J., Rushmeier, H., Silva, C., Taubin, G., and Member, S. (1999). The ballpivoting algorithm for surface reconstruction. IEEE Transactions on Visualization and Computer Graphics, 5:349-359.
- Carr, J. C., Beatson, R. K., Cherrie, J. B., Mitchell, T. J., Fright, W. R., McCallum, B. C., and Evans, T. R. (2001). Reconstruction and representation of 3d objects with radial basis functions. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques, SIGGRAPH 7801, pages 67-76, New York, NY, USA. ACM.
- Chang, M.-C., Leymarie, F. F., and Kimia, B. B. (2009). Surface reconstruction from point clouds by transforming the medial scaffold. Comput. Vis. Image Underst., 113(11):1130-1146.
- Curless, B. and Levoy, M. (1996). A volumetric method for building complex models from range images. In Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, SIGGRAPH 7896, pages 303-312, New York, NY, USA. ACM.
- Edelsbrunner, H. and Mücke, E. P. (1992). Threedimensional alpha shapes. In Volume Visualization, pages 75-82.
- Fritzke, B. (1993). Growing cell structures - a selforganizing network for unsupervised and supervised learning. Neural Networks, 7:1441-1460.
- Gal, R., Shamir, A., Hassner, T., Pauly, M., and CohenOr, D. (2007). Surface reconstruction using local shape priors. In Proceedings of the fifth Eurographics symposium on Geometry processing, SGP 7807, pages 253-262, Aire-la-Ville, Switzerland, Switzerland. Eurographics Association.
- Gopi, M. and Krishnan, S. (2002). A fast and efficient projection-based approach for surface reconstruction. In Proceedings of the 15th Brazilian Symposium on Computer Graphics and Image Processing, SIBGRAPI 7802, pages 179-186, Washington, DC, USA. IEEE Computer Society.
- Hoppe, H., DeRose, T., Duchamp, T., McDonald, J. A., and Stuetzle, W. (1992). Surface reconstruction from unorganized points. In Thomas, J. J., editor, SIGGRAPH, pages 71-78. ACM.
- Ivrissimtzis, I., Jeong, W.-K., and Seidel, H.-P. (2003a). Neural meshes: Statistical learning methods in surface reconstruction. Technical Report MPI-I-2003-4-007, Max-Planck-Institut f”ur Informatik, Saarbrücken.
- Ivrissimtzis, I. P., Jeong, W.-K., and Seidel, H.-P. (2003b). Using growing cell structures for surface reconstruction. In SMI 7803: Proceedings of the Shape Modeling International 2003, page 78, Washington, DC, USA. IEEE Computer Society.
- Jeong, W.-K., Ivrissimtzis, I., and Seidel, H.-P. (2003). Neural meshes: Statistical learning based on normals. Computer Graphics and Applications, Pacific Conference on, 0:404.
- Kazhdan, M., Bolitho, M., and Hoppe, H. (2006). Poisson surface reconstruction. In Proceedings of the fourth Eurographics symposium on Geometry processing, SGP 7806, pages 61-70, Aire-la-Ville, Switzerland, Switzerland. Eurographics Association.
- Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biological cybernetics, 43:59-69.
- Kuo, C.-C. and Yau, H.-T. (2005). A delaunay-based region-growing approach to surface reconstruction from unorganized points. Comput. Aided Des., 37(8):825-835.
- MacQueen, J. B. (1967). Some methods for classification and analysis of multivariate observations. pages 281 - 297.
- Mederos, B., Amenta, N., Velho, L., and de Figueiredo, L. H. (2005). Surface reconstruction from noisy point clouds. In Proceedings of the third Eurographics symposium on Geometry processing, SGP 7805, Aire-laVille, Switzerland, Switzerland. Eurographics Association.
- Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., and Seidel, H.-P. (2003). Multi-level partition of unity implicits. In ACM SIGGRAPH 2003 Papers, SIGGRAPH 7803, pages 463-470, New York, NY, USA. ACM.
- Schnabel, R., Degener, P., and Klein, R. (2009). Completion and reconstruction with primitive shapes. Computer Graphics Forum (Proc. of Eurographics), 28(2):503- 512.
- Sharf, A., Lewiner, T., Shamir, A., Kobbelt, L., and CohenOr, D. (2006). Competing fronts for coarse-to-fine surface reconstruction. In Eurographics 2006 (Computer Graphics Forum), volume 25, pages 389-398, Vienna. Eurographics.
- Taubin, G. (1995). A signal processing approach to fair surface design. In Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, SIGGRAPH 7895, pages 351-358, New York, NY, USA. ACM.
- Vrady, L., Hoffmann, M., and Kovcs, E. (1999). Improved free-form modelling of scattered data by dynamic neural networks. Journal for Geometry and Graphics, 3:177-183.
- Yu, Y. (1999). Surface reconstruction from unorganized points using self-organizing neural networks. In In IEEE Visualization 99, Conference Proceedings, pages 61-64.

#### Paper Citation

#### in Harvard Style

Annuth H. and Bohn C. (2013). **Growing Surface Structures** . In *Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2013)* ISBN 978-989-8565-77-8, pages 349-359. DOI: 10.5220/0004529203490359

#### in Bibtex Style

@conference{ncta13,

author={Hendrik Annuth and Christian-A. Bohn},

title={Growing Surface Structures},

booktitle={Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2013)},

year={2013},

pages={349-359},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004529203490359},

isbn={978-989-8565-77-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: NCTA, (IJCCI 2013)

TI - Growing Surface Structures

SN - 978-989-8565-77-8

AU - Annuth H.

AU - Bohn C.

PY - 2013

SP - 349

EP - 359

DO - 10.5220/0004529203490359