Commenced in January 2007
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Paper Count: 30172
Topographic Arrangement of 3D Design Components on 2D Maps by Unsupervised Feature Extraction

Authors: Stefan Menzel

Abstract:

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.

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079752

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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.