“Shape matching and anisotropy” by Kazhdan, Funkhouser and Rusinkiewicz

With recent improvements in methods for the acquisition and rendering of 3D models, the need for retrieval of models has gained prominence in the graphics and vision communities. A variety of methods have been proposed that enable the efficient querying of model repositories for a desired 3D shape. Many of these methods use a 3D model as a query and attempt to retrieve models from the database that have a similar shape.In this paper we consider the implications of anisotropy on the shape matching paradigm. In particular, we propose a novel method for matching 3D models that factors the shape matching equation as the disjoint outer product of anisotropy and geometric comparisons. We provide a general method for computing the factored similarity metric and show how this approach can be applied to improve the matching performance of many existing shape matching methods.

1. ALT, H., AND GUIBAS, L. J. 1996. Discrete geometric shapes: Matching, interpolation, and approximation: A survey. Tech. Rep. B 96-11, EVL-1996-142, Institute of Computer Science, Freie Universität Berlin.]]Google Scholar
2. ANKERST, M., KASTENMÜLLER, G., KRIEGEL, H., AND SEIDL, T. 1999. 3D shape histograms for similarity search and classification in spatial databases. In Advances in Spatial Databases, 6th International Symposium, 207–226.]] Google ScholarDigital Library
3. BESL, P., AND MCKAY, N. 1992. A method for registration of 3-d shapes. IEEE PAMI 14, 239–256.]] Google ScholarDigital Library
4. BUREL, G., AND HENOCQ, H. 1995. Three-dimensional invariants and their application to object recognition. Signal Processing 45, 1, 1–22.]] Google ScholarDigital Library
5. CCCC. http://merkur01.inf.uni-konstanz.de/.]]Google Scholar
6. FUNKHOUSER, T., MIN, P., KAZHDAN, M., CHEN, J., HALDERMAN, A., DOBKIN, D., AND JACOBS, D. 2003. A search engine for 3D models. ACM Transactions on Graphics, 83–105.]] Google ScholarDigital Library
7. HILAGA, M., SHINAGAWA, Y., KOHMURA, T., AND KUNII, T. 2001. Topology matching for fully automatic similarity estimation of 3D shapes. Computer Graphics (Proceedings of SIGGRAPH 01), 203–212.]] Google ScholarDigital Library
8. HORN, B., HILDEN, H., AND NEGAHDARIPOUR, S. 1988. Closed form solutions of absolute orientation using orthonormal matrices. J. of the Optical Society 5, 1127–1135.]]Google ScholarCross Ref
9. HORN, B. 1984. Extended Gaussian images. In Proceedings of the IEEE, vol. 72, 1656–1678.]]Google ScholarCross Ref
10. HORN, B. 1987. Closed form solutions of absolute orientation using unit quaternions. J. of the Optical Society 4, 629–642.]]Google ScholarCross Ref
11. KANG, S., AND IKEUCHI, K. 1991. Determining 3-d object pose using the complex extended Gaussian image. CVPR, 580–585.]]Google Scholar
12. KAZHDAN, M., FUNKHOUSER, T., AND RUSINKIEWICZ, S. 2003. Rotation invariant spherical harmonic representation of 3D shape descriptors, SGP, 167–175.]]Google Scholar
13. LONCARIC, S. 1998. A survey of shape analysis techniques. Pattern Recognition 31, 8, 983–1001.]]Google ScholarCross Ref
14. OSADA, R., FUNKHOUSER, T., CHAZELLE, B., AND DOBKIN, D. 2001. Matching 3D models with shape distributions. In Shape Modeling International, 154–166.]] Google ScholarDigital Library
15. POPE, A. R. 1994. Model-based object recognition: A survey of recent research. Tech. Rep. TR-94-04, University of British Columbia, January.]] Google ScholarDigital Library
16. PRINCETON 3D MODEL SEARCH ENGINE. http://shape.cs.princeton.edu.]]Google Scholar
17. PRINCETON SHAPE BENCHMARK. http://shape.cs.princeton.edu/benchmark.]]Google Scholar
18. PROTEIN DATA BANK. http://www.rcsb.org.]]Google Scholar
19. SHAPE SIFTER. http://www.shapesearch.net/.]]Google Scholar
20. SIDDIQI, K., SHOKOUFANDEH, A., DICKINSON, S., AND ZUCKER, S. 1998. Shock graphs and shape matching. Sixth International Conference on Computer Vision, 222–229.]] Google ScholarDigital Library
21. TANGELDER, J. W., AND VELTKAMP, R. C. 2004. A survey of content based 3D shape retrieval methods. In Shape Modeling International.]]Google Scholar
22. VRANIC, D., AND SAUPE, D. 2001. 3D model retrieval with spherical harmonics and moments. Proceedings of the DAGM, 392–397.]] Google ScholarDigital Library