Art Tevs
Abstract
In this paper we address the problem of finding correspondences between related shapes of widely varying geometry. We propose a new method based on the observation that symmetry and regularity in shapes is often associated with their function. Hence, they provide cues for matching related geometry even under strong shape variations. Correspondingly, we decomposes shapes into overlapping regions determined by their regularity properties. Afterwards, we form a graph that connects these pieces via pairwise relations that capture geometric relations between rotation axes and reflection planes as well as topological or proximity relations. Finally, we perform graph matching to establish correspondences. The method yields certain more abstract but semantically meaningful correspondences between man-made shapes that are too difficult to recognize by traditional geometric methods.
Supplemental Material
- Allen, B., Curless, B., and Popović, Z. 2003. The space of human body shapes: Reconstruction and parameterization from range scans. ACM Trans. Graph. 22, 3, 587--594. Google Scholar
Digital Library
- Bokeloh, M., Berner, A., Wand, M., Seidel, H.-P., and Schilling, A. 2009. Symmetry detection using line features. Computer Graphics Forum (Proc. Eurographics).Google Scholar
- Bokeloh, M., Wand, M., Seidel, H.-P., and Koltun, V. 2012. An algebraic model for parameterized shape editing. ACM Transactions on Graphics 31, 4. Google ScholarDigital Library
- Cullen, B., and O'Sullivan, C. 2011. Symmetry hybrids. In Proceedings of the International Symposium on Computational Aesthetics in Graphics, Visualization, and Imaging, ACM, New York, NY, USA, CAe '11, 33--38. Google ScholarDigital Library
- Fisher, M., Savva, M., and Hanrahan, P. 2011. Characterizing structural relationships in scenes using graph kernels. ACM Trans. Graph. 30, 4 (July), 34:1--34:12. Google ScholarDigital Library
- Gal, R., Sorkine, O., Mitra, N., and Cohen-Or, D. 2009. iwires: An analyze-and-edit approach to shape manipulation. ACM Trans. Graph. 28, 3. Google ScholarDigital Library
- Gelfand, N., and Guibas, L. J. 2004. Shape segmentation using local slippage analysis. In Proc. SGP, 214--223. Google ScholarDigital Library
- Gelfand, N., Mitra, N. J., Guibas, L. J., and Pottmann, H. 2005. Robust global registration. In Proc. SGP, 197--206. Google ScholarDigital Library
- Hahn, T. 2002. International Tables for Crystallography, Volume A: Space Group Symmetry. Springer Verlag, Berlin.Google Scholar
- Hauagge, D. C., and Snavely, N. 2012. Image matching using local symmetry features. In Proc. CVPR, 206--213. Google ScholarDigital Library
- Henderson, T. C., Cohen, E., Joshi, A., Grant, E., Draelos, M., and Deshpande, N. 2012. Symmetry as a basis for perceptual fusion. In Multisensor Fusion and Integration for Intelligent Systems (MFI), 2012 IEEE Conference on, 101--107.Google Scholar
- Huang, Q., Zhang, G., Gao, L., Hu, S., Bustcher, A., and Guibas, L. 2012. An optimization approach for extracting and encoding consistent maps in a shape collection. ACM Transactions on Graphics 31, 125:1--125:11. Google ScholarDigital Library
- Kalogerakis, E., Hertzmann, A., and Singh, K. 2010. Learning 3d mesh segmentation and labeling. ACM Trans. Graph. 29, 3. Google ScholarDigital Library
- Kazhdan, M., Funkhouser, T., and Rusinkiewicz, S. 2003. Rotation invariant spherical harmonic representation of 3D shape descriptors. In Symposium on Geometry Processing. Google ScholarDigital Library
- Kazhdan, M., Funkhouser, T., and Rusinkiewicz, S. 2004. Symmetry descriptors and 3d shape matching. In Proc. Symposium on Geometry Processing (SGP). Google ScholarDigital Library
- Kim, V. G., Li, W., Mitra, N., DiVerdi, S., and Funkhouser, T. 2012. Exploring collections of 3d models using fuzzy correspondences. In ACM SIGGRAPH 2012 papers. Google ScholarDigital Library
- Leordeanu, M., and Hebert, M. 2006. Efficient map approximation for dense energy functions. ICML '06, 545--552. Google ScholarDigital Library
- Lipman, Y., Chen, X., Daubechies, I., and Funkhouser, T. 2010. Symmetry factored embedding and distance. ACM Trans. Graph. 29 (July), 103:1--103:12. Google ScholarDigital Library
- Liu, T., Kim, V. G., and Funkhouser, T. 2012. Finding surface correspondences using symmetry axis curves. Computer Graphics Forum (Proc. SGP) (July). Google ScholarDigital Library
- Martinet, A. 2007. Structuring 3D Geometry based on Symmetry and Instancing Information. PhD thesis, INP Grenoble.Google Scholar
- Mitra, N. J., Guibas, L. J., and Pauly, M. 2006. Partial and approximate symmetry detection for 3d geometry. ACM Trans. Graph. 25, 3, 560--568. Google ScholarDigital Library
- Mitra, N. J., Yang, Y.-L., Yan, D.-M., Li, W., and Agrawala, M. 2010. Illustrating how mechanical assemblies work. ACM Transactions on Graphics 29, 3. Google ScholarDigital Library
- Nguyen, A., Ben-Chen, M., Welnicka, K., Ye, Y., and Guibas, L. 2011. An optimization approach to improving collections of shape maps. Computer Graphics Forum (Proc. SGP), 1481--1491.Google Scholar
- Ovsjanikov, M., Li, W., Guibas, L., and Mitra, N. 2011. Exploration of continuous variability in collections of 3d shapes. ACM Trans. Graph. (Proc. Siggraph). Google ScholarDigital Library
- Pauly, M., Mitra, N. J., Wallner, J., Pottmann, H., and Guibas, L. 2008. Discovering structural regularity in 3D geometry. ACM Transactions on Graphics 27, 3, #43, 1--11. Google ScholarDigital Library
- Sidi, O., van Kaick, O., Kleiman, Y., Zhang, H., and Cohen-Or, D. 2011. Unsupervised co-segmentation of a set of shapes via descriptor-space spectral clustering. ACM Trans. Graph. 30, 6 (Dec.), 126:1--126:10. Google ScholarDigital Library
- Simari, P., Nowrouzezahrai, D., Kalogerakis, E., and Singh, K. 2009. Multi-objective shape segmentation and labeling. Computer Graphics Forum 28, 5. Google ScholarDigital Library
- Thrun, S., and Wegbreit, B. 2005. Shape from symmetry. In Proc. ICCV'05, 1824--1831. Google ScholarDigital Library
- van Kaick, O., Zhang, H., Hamarneh, G., and Cohen-Or, D. 2011. A survey on shape correspondence. Computer Graphics Forum 30, 6, 1681--1707. Google ScholarDigital Library
- van Kaick, O., Xu, K., Zhang, H., Wang, Y., Sun, S., Shamir, A., and Cohen-Or, D. 2013. Co-hierarchical analysis of shape structures. ACM Trans. Graph. (Proc. Siggraph) 32, 4 (July), 69:1--69:10. Google ScholarDigital Library
- Wang, Y., Xu, K., Li, J., Zhang, H., Shamir, A., Liu, L., Cheng, Z., and Xiong, Y. 2011. Symmetry hierarchy of man-made objects. Computer Graphics Forum (Proc. EUROGRAPHICS) 30, 2.Google ScholarCross Ref
- Wang, Y., Xu, K., Zhang, H., Cohen-Or, D., and Shamir, A. 2012. Structural co-hierarchy of a set of shapes. Tech. rep.Google Scholar
- Xu, K., Zhang, H., Tagliasacchi, A., Liu, L., Li, G., Meng, M., and Xiong, Y. 2009. Partial intrinsic reflectional symmetry of 3d shapes. ACM Transactions on Graphics, (Proceedings SIGGRAPH Asia 2009) 28, 5, 138:1--138:10. Google ScholarDigital Library
Index Terms
- Relating shapes via geometric symmetries and regularities
Recommendations
An algebraic model for parameterized shape editing
We present an approach to high-level shape editing that adapts the structure of the shape while maintaining its global characteristics. Our main contribution is a new algebraic model of shape structure that characterizes shapes in terms of linked ...
Pattern-aware shape deformation using sliding dockers
This paper introduces a new structure-aware shape deformation technique. The key idea is to detect continuous and discrete regular patterns and ensure that these patterns are preserved during free-form deformation. We propose a variational deformation ...
Pattern-aware shape deformation using sliding dockers
SA '11: Proceedings of the 2011 SIGGRAPH Asia ConferenceThis paper introduces a new structure-aware shape deformation technique. The key idea is to detect continuous and discrete regular patterns and ensure that these patterns are preserved during free-form deformation. We propose a variational deformation ...
Comments