Abstract
We consider the use of medial surfaces to represent symmetries of 3-D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation and deformation of parts. We demonstrate the use of this representation for both indexing and matching 3-D object models. Our formulation uses the geometric information associated with each node along with an eigenvalue labeling of the adjacency matrix of the subgraph rooted at that node. We present comparative results against the techniques of shape distributions [17] and harmonic spheres [12] on a database of 320 models representing 13 object classes. The results demonstrate that medial surface based graph matching significantly outperforms these techniques for objects with articulating parts.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alt, H., Aichholzer, O., Rote, G.: Matching Shapes With a Reference Point. In: Proceedings of the Tenth Annual Symposiusm on Computational Geometry, pp. 85–92 (1994)
Amenta, N., Choi, S., Kolluri, R.: The Power Crust, Unions of Balls, and the Medial Axis Transform. Computational Geometry: Theory and Applications 19(2), 127–153 (2001)
Ankerst, M., Kastenmüller, G., Kriegel, H., Seidl, T.: 3-D Shape Histograms for Similarity Search and Classification in Spatial Databases. In: Advances in Spatial Databases, 6th International Symposium, vol. 18, pp. 700–711 (1999)
Biederman, I.: Recognition–By–Components: A Theory of Human Image Understanding. Psychological Review 94(2), 115–147 (1987)
Binford, T.O.: Visual Perception by Computer. In: IEEE Conference on Systems and Control (December 1971)
Blum, H.: Biological Shape and Visual Science. Journal of Theoretical Biology 38, 205–287 (1973)
Elad, M., Tal, A., Ar, S.: Content Based Retrieval of VRML Objects- An Iterative and Interactive Approach. In: 6th Europgraphics Workshop on Multimedia, Manchester, UK, pp. 107–118 (2001)
Giblin, P.J., Kimia, B.B.: A formal Classification of 3D Medial Axis Points and Their Local Geometry. IEEE Transactions on Pattern Analysis and Machine Intelligence 26(2), 238–251 (2004)
Hamza, A.B., Krim, H.: Geodesic Object Representation and Recognition. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 378–387. Springer, Heidelberg (2003)
Hilaga, M., Shinagawa, Y., Kohmura, T., Kunii, T.L.: Topology Matching for Fully Automatic Similarity Estimation of 3D Shapes. In: Proceedings of ACM SIGGRAPH, pp. 203–212 (2001)
Kazhdan, M., Chazelle, B., Dobkin, D., Funkhouser, T., Rusinkiewicz, S.: A Reflective Symmetry Descriptor for 3-D Models. Algorithmica 38(1), 201–225 (2003)
Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors. In: Symposium on Geometry Processing (June 2003)
Leymarie, F.F., Kimia, B.B.: Computation of the Shock Scaffold for Unorganized Point Clouds in 3D. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Madison, Wisconsin, pp. 821–827 (2003)
Macrini, D.: Indexing and Matching for View-Based 3-D Object Recognition Using Shock Graphs. PhD thesis, University of Toronto (2003)
Malandain, G., Bertrand, G., Ayache, N.: Topological Segmentation of Discrete Surfaces. International Journal of Computer Vision 10(2), 183–197 (1993)
Marr, D., Nishihara, K.H.: Representation and Recognition of the Spatial Organization of Three Dimensional Structure. Proceedings of the Royal Society of London, B 200, 269–294 (1978)
Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Shape Distributions. ACM Transactions on Graphics 21(4), 807–832 (2002)
Pellilo, M., Siddiqi, K., Zucker, S.W.: Matching Hierarchical Structures Using Association Graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(11), 1105–1120 (1999)
Pentland, A.: Perceptual organization and the representation of natural form. Artificial Intelligence 28, 293–331 (1986)
Reyner, S.W.: An Analysis of a Good Algorithm for the Subtree Problem. SIAM J. Comput. 6, 730–732 (1977)
Rosch, E.: Principles of Categorization. In: Cognition and Categorization. L. Erlbaum Associates, Mahwah (1978)
Sebastian, T., Klein, P., Kimia, B.: Recognition of shapes by editing their shock graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence 26, 551–571 (2004)
Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The Princeton Shape Benchmark. In: Shape Modeling International, Genova, Italy (June 2004)
Shinagawa, Y., Kunii, T.L., Kergosien, Y.L.: Surface Coding Based on Morse Theory. IEEE Transactions on Computer Graphics and Applications 11(5), 66–78 (1991)
Shokoufandeh, A., Dickinson, S.J., Siddiqi, K., Zucker, S.W.: Indexing Using a Spectral Encoding of Topological Structure. In: IEEE Conference on Computer Vision and Pattern Recognition, Fort Collins, CO, June 1999, pp. 491–497 (1999)
Shokoufandeh, A., Macrini, D., Dickinson, S., Siddiqi, K., Zucker, S.: Indexing Hierarchical Structures Using Graph Spectra. IEEE Transactions on Pattern Analysis and Machine Intelligence 27(7) (2005)
Siddiqi, K., Bouix, S., Tannenbaum, A., Zucker, S.W.: Hamilton-Jacobi Skeletons. International Journal of Computer Vision 48(3), 215–231 (2002)
Siddiqi, K., Shokoufandeh, A., Dickinson, S.J., Zucker, S.W.: Shock Graphs and Shape Matching. International Journal of Computer Vision 35(1), 13–32 (1999)
Sundar, H., Silver, D., Gagvani, N., Dickinson, S.: Skeleton Based Shape Matching and Retrieval. In: International Conference on Shape Modeling International and Applications, Seoul, Korea, May 2003, pp. 130–142 (2003)
Vranic, D., Saupe, D.: 3-D Model Retrieval With Spherical Harmonics and Moments. In: Radig, B., Florczyk, S. (eds.) DAGM 2001. LNCS, vol. 2191, pp. 392–397. Springer, Heidelberg (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, J., Siddiqi, K., Macrini, D., Shokoufandeh, A., Dickinson, S. (2005). Retrieving Articulated 3-D Models Using Medial Surfaces and Their Graph Spectra. In: Rangarajan, A., Vemuri, B., Yuille, A.L. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2005. Lecture Notes in Computer Science, vol 3757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11585978_19
Download citation
DOI: https://doi.org/10.1007/11585978_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30287-2
Online ISBN: 978-3-540-32098-2
eBook Packages: Computer ScienceComputer Science (R0)