Topographic Arrangement of 3D Design Components on 2D Maps by Unsupervised Feature Extraction

As a result of the daily workflow in the design development departments of companies, databases containing huge numbers of 3D geometric models are generated. According to the given problem engineers create CAD drawings based on their design ideas and evaluate the performance of the resulting design, e.g. by computational simulations. Usually, new geometries are built either by utilizing and modifying sets of existing components or by adding single newly designed parts to a more complex design. The present paper addresses the two facets of acquiring components from large design databases automatically and providing a reasonable overview of the parts to the engineer. A unified framework based on the topographic non-negative matrix factorization (TNMF) is proposed which solves both aspects simultaneously. First, on a given database meaningful components are extracted into a parts-based representation in an unsupervised manner. Second, the extracted components are organized and visualized on square-lattice 2D maps. It is shown on the example of turbine-like geometries that these maps efficiently provide a wellstructured overview on the database content and, at the same time, define a measure for spatial similarity allowing an easy access and reuse of components in the process of design development.

Authors:

• Stefan Menzel

Keywords:

• Design decomposition
• topographic non-negative matrix factorization
• parts-based representation
• self-organization
• unsupervised feature extraction.

References:

[1] J. W. H. Tangelder, and R. C. Veltkamp, "A survey of content based 3D
shape retrieval methods," Multimedia Tools and Applications, vol. 39,
Springer Netherlands, pp. 441-471, Sep. 2008.
[2] Z. Bozakov, L. Graening, S. Hasler, H. Wersing, and S. Menzel,
"Unsupervised extraction of design components for a 3D parts-based
representation," IJCNN, pp. 2009-2016, IEEE, Hongkong, 2008.
[3] K. Hosoda, M. Watanabe, H. Wersing, E. Koerner, H. Tsujino,
H. Tamura, and I. Fujita, "A model for learning topographically
organized parts-based representations of objects in visual cortex:
topographic non-negative matrix factorization, " Neural Computation,
2009, in press.
[4] D. D. Lee and S. H. Seung, "Learning the parts of objects by
non-negative matrix factorization," Nature, vol. 401, no. 6755,
pp. 788-791, 1999.
[5] I.T. Jolliffe, "Principle Component Analysis," Series: Springer Series in
Statistics, 2nd ed., Springer, New York, 2002.
[6] J. B. MacQueen, "Some Methods for classification and Analysis of
Multivariate Observations," Proceedings of 5-th Berkeley Symposium
on Mathematical Statistics and Probability, Berkeley, University of
California Press, 1:281-297, 1967.
[7] T. Kohonen, "Self-Organizing Maps," Springer-Verlag, Berlin 1995,
ISBN 3-540-58600-8.
[8] Z. Bozakov, "Unsupervised Component Extraction for Design
Optimisation using Feature Analysis," Master Thesis, Control Theory
and Robotics Lab, Institute for Automatic Control, TU Darmstadt, 2007.
[9] B. M. Chazelle, "Convex decomposition of polyhedra," in STOC -81:
Proceedings of the thirteenth annual ACM symposium on Theory of
computing. New York, NY, USA: ACM Press, pp. 70-79, 1981.
[10] J.-M. Lien and N. M. Amato, "Approximate convex decomposition of
polygons," in SCG -04: Proceedings of the 20th annual symposium on
Computational geometry, NY, USA: ACM Press, pp. 17-26, 2004.
[11] J.-M. Lien and N. M. Amato, "Approximate convex decomposition," in
SCG -04: Proceedings of the 20th annual symposium on Computational
geometry. NY, USA: ACM Press, pp. 457-458, 2004.
[12] H. Sundar, D. Silver, N. Gagvani, and S. Dickenson. Skeleton based
shape matching and retrieval. In SMI 2003, pages 130-139, 2003.
[13] S. Katz and A. Tal, "Hierarchical mesh decomposition using fuzzy
clustering and cuts," in SIGGRAPH -03: ACM SIGGRAPH 2003 Papers.
NY, USA: ACM Press, pp. 954-961, 2003.
[14] T. Funkhouser, M. Kazhdan, P. Min and P. Shilane, "Shape-based
Retrieval and Analysis of 3D Models," in Communications of the ACM,
Vol. 48, No.6, pp. 58-64, June 2005.