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Issue No.11 - Nov. (2012 vol.34)
pp: 2134-2146
G. K. L. Tam , Dept. of Comput. Sci. & Inf., Cardiff Univ., Cardiff, UK
R. W. H. Lau , Dept. of Comput. Sci., City Univ. of Hong Kong, Kowloon, China
Due to the popularity of computer games and animation, research on 3D articulated geometry model retrieval has attracted a lot of attention in recent years. However, most existing works extract high-dimensional features to represent models and suffer from practical limitations. First, misalignment in high-dimensional features may produce unreliable euclidean distances and affect retrieval accuracy. Second, the curse of dimensionality also degrades efficiency. In this paper, we propose an embedding retrieval framework to improve the practicability of these methods. It is based on a manifold learning technique, the Diffusion Map (DM). We project all pairwise distances onto a low-dimensional space. This improves retrieval accuracy because intercluster distances are exaggerated. Then we adapt the Density-Weighted Nyström extension and further propose a novel step to locally align the Nyström embedding to the eigensolver embedding so as to reduce extension error and preserve retrieval accuracy. Finally, we propose a heuristic to handle disconnected manifolds by augmenting the kernel matrix with multiple similarity measures and shortcut edges, and further discuss the choice of DM parameters. We have incorporated two existing matching algorithms for testing. Our experimental results show improvement in precision at high recalls and in speed. Our work provides a robust retrieval framework for the matching of multimedia data that lie on manifolds.
Manifolds, Geometry, Computational modeling, Databases, Delta modulation, Histograms, Feature extraction, geometry recognition, Geometry retrieval, articulated model retrieval, geometry analysis
G. K. L. Tam, R. W. H. Lau, "Embedding Retrieval of Articulated Geometry Models", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.34, no. 11, pp. 2134-2146, Nov. 2012, doi:10.1109/TPAMI.2012.17
[1] M. Hilaga, Y. Shinagawa, T. Kohmura, and T. Kunii, "Topology Matching for Fully Automatic Similarity Estimation of 3d Shapes," Proc. ACM Siggraph, pp. 203-212, 2001.
[2] G. Tam and R. Lau, "Deformable Model Retrieval Based on Topological and Geometric Signatures," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 3, pp. 470-482, May/June 2007.
[3] R. Coifman and S. Lafon, "Diffusion Maps," Applied and Computational Harmonic Analysis, vol. 21, no. 1, pp. 5-30, 2006.
[4] S. Lafon and A. Lee, "Diffusion Maps and Coarse-Graining: A Unified Framework for Dimensionality Reduction, Graph Partitioning, and Data Set Parameterization," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 9, pp. 1393-1403, Sept. 2006.
[5] K. Zhang and J. Kwok, "Density-Weighted Nyström Method for Computing Large Kernel Eigensystems," Neural Computation, vol. 21, no. 1, pp. 121-146, 2009.
[6] M. Kazhdan, T. Funkhouser, and S. Rusinkiewicz, "Rotation Invariant Spherical Harmonic Representation of 3D Shape Descriptors," Proc. Eurographics/ACM Siggraph Symp. Geometry Processing, pp. 156-164, 2003.
[7] R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin, "Matching 3D Models with Shape Distributions," Proc. IEEE Conf. Shape Modeling and Applications, pp. 154-166, 2001.
[8] J. Tangelder and R. Veltkamp, "A Survey of Content Based 3D Shape Retrieval Methods," Proc. IEEE Conf. Shape Modeling and Applications, pp. 145-156, 2004.
[9] A. Ion, N. Artner, G. Peyre, S. Marmol, W. Kropatsch, and L. Cohen, "3D Shape Matching by Geodesic Eccentricity," Proc. IEEE Conf. Computer Vision and Pattern Recognition Workshops, pp. 1-8, 2008.
[10] R. Liu, H. Zhang, A. Shamir, and D. Cohen-Or, "A Part-Aware Surface Metric for Shape Analysis," Computer Graphics Forum, vol. 28, no. 2, pp. 397-406, 2009.
[11] M. Reuter, F. Wolter, and N. Peinecke, "Laplace-Beltrami Spectra as 'Shape-DNA' of Surfaces and Solids," Computer-Aided Design, vol. 38, no. 4, pp. 342-366, 2006.
[12] R. Rustamov, "Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation," Proc. Fifth Eurographics Symp. Geometry Processing, 2007.
[13] R. Ohbuchi and T. Furuya, "Distance Metric Learning and Feature Combination for Shape-Based 3D Model Retrieval," Proc. ACM Workshop 3D Object Retrieval, pp. 63-68, 2010.
[14] M. Ovsjanikov, A. Bronstein, M. Bronstein, and L. Guibas, "Shape Google: A Computer Vision Approach to Isometry Invariant Shape Retrieval," Proc. Workshop Nonrigid Shape Analysis and Deformable Image Alignment, pp. 320-327, 2009.
[15] A. Bronstein, M. Bronstein, M. Ovsjanikov, and L. Guibas, "Shape Google: Geometric Words and Expressions for Invariant Shape Retrieval," ACM Trans. Graphics, vol. 30, pp. 1-20, 2011.
[16] T. Tung and F. Schmitt, "Augmented Reeb Graphs for Content-Based Retrieval of 3D Mesh Models," Proc. IEEE Conf. Shape Modeling and Applications, pp. 157-166, 2004.
[17] S. Biasotti, S. Marini, M. Spagnuolo, and B. Falcidieno, "Sub-Part Correspondence by Structural Descriptors of 3d Shapes," Computer-Aided Design, vol. 38, no. 9, pp. 1002-1019, 2006.
[18] Y. Rubner, C. Tomasi, and L. Guibas, "The Earth Mover's Distance as a Metric for Image Retrieval," Int'l J. Computer Vision, vol. 40, no. 2, pp. 99-121, 2000.
[19] M. Ruggeri and D. Saupe, "Isometry-Invariant Matching of Point Set Surfaces," Proc. EG Workshop 3D Object Retrieval, 2008.
[20] J. Tierny, J. Vandeborre, and M. Daoudi, "Reeb Chart Unfolding Based 3D Shape Signatures," Proc. Eurographics, 2007.
[21] S. Lafon, "Diffusion Maps and Geometric Harmonic," PhD Thesis, Yale Univ., 2004.
[22] M. Demirci, R. van Leuken, and R. Veltkamp, "Indexing through Laplacian Spectra," Computer Vision and Image Understanding, vol. 110, no. 3, pp. 312-325, 2008.
[23] H. Sundar, D. Silver, N. Gagvani, and S. Dickinson, "Skeleton Based Shape Matching and Retrieval," Proc. IEEE Conf. Shape Modeling and Applications, pp. 130-139, 2003.
[24] M. Belkin and P. Niyogi, "Laplacian Eigenmaps for Dimensionality Reduction and Data Representation," J. Neural Computation, vol. 15, no. 6, pp. 1373-1396, 2003.
[25] J. Tenenbaum, V. de Silva, and J. Langford, "A Global Geometric Framework for Nonlinear Dimensionality Reduction," Science, vol. 290, no. 5500, pp. 2319-2323, 2000.
[26] S. Roweis and L. Saul, "Nonlinear Dimensionality Reduction by Locally Linear Embedding," Science, vol. 290, no. 5500, pp. 2323-2326, 2000.
[27] X. He, "Incremental Semi-Supervised Subspace Learning for Image Retrieval," Proc. 12th Ann. ACM Int'l Conf. Multimedia, pp. 2-8, 2004.
[28] T. Cox and M. Cox, Multidimensional Scaling. Chapman & Hall, 1994.
[29] H. Wang, S. Yan, T. Huang, and X. Tang, "Maximum Unfolded Embedding: Formulation, Solution, and Application for Image Clustering," Proc. 14th Ann. ACM Int'l Conf. Multimedia, pp. 45-48, 2006.
[30] H. Sahbi, P. Etyngier, J. Audibert, and R. Keriven, "Manifold Learning Using Robust Graph Laplacian for Interactive Image Search," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 1-8, 2008.
[31] S. Chopra, R. Hadsell, and Y. LeCun, "Learning a Similarity Metric Discriminatively, with Application to Face Verification," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 539-546, 2005.
[32] J. Platt, "Fastmap, Metricmap, and Landmark MDS Are All Nyström Algorithms," Proc. Int'l Workshop Artificial Intelligence and Statistics, pp. 261-268, 2005.
[33] C. Fowlkes, S. Belongie, F. Chung, and J. Malik, "Spectral Grouping Using the Nystrom Method," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 2, pp. 214-225, Feb. 2004.
[34] N. Gershenfeld, The Nature of Mathematical Modeling. Cambridge Univ. Press, 1999.
[35] J. Shi and J. Malik, "Normalized Cuts and Image Segmentation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 8, pp. 888-905, Aug. 2000.
[36] R. Liu and H. Zhang, "Segmentation of 3D Meshes through Spectral Clustering," Proc. 12th Pacific Conf. Computer Graphics and Applications, pp. 298-305, 2004.
[37] H. Zhang, O. van Kaick, and R. Dyer, "Spectral Methods for Mesh Processing and Analysis," Proc. Eurographics State-of-the-Art Report, pp. 1-22, 2007.
[38] V. Jain and H. Zhang, "Robust 3D Shape Correspondence in the Spectral Domain," Proc. IEEE Conf. Shape Modeling and Applications, pp. 118-129, 2006.
[39] F. Bookstein, "Principal Warps: Thin-Plate Splines and the Decomposition of Deformations," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 6, pp. 567-585, June 1989.
[40] S. Belongie, J. Malik, and J. Puzicha, "Shape Matching and Object Recognition Using Shape Contexts," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 4, pp. 509-522, Apr. 2002.
[41] J. Ham, D.D. Lee, and L.K. Saul, "Semisupervised Alignment of Manifolds," Proc. Int'l Workshop Artificial Intelligence and Statistics, 2005.
[42] K. Siddiqi, J. Zhang, D. Macrini, A. Shokoufandeh, S. Bouix, and S. Dickinson, "Retrieving Articulated 3D Models Using Medial Surfaces," J. Machine Vision Applications, vol. 19, no. 4, pp. 261-275, May 2008.
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