The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.12 - December (2011 vol.33)
pp: 2538-2544
Yu-Shen Liu , Tsinghua University, Beijing
Karthik Ramani , Purdue University, West Lafayette
Min Liu , Tsinghua University, Beijing
ABSTRACT
A new visibility graph-based algorithm is presented for computing the inner distances of a 3D shape represented by a volumetric model. The inner distance is defined as the length of the shortest path between landmark points within the shape. The inner distance is robust to articulation and can reflect the deformation of a shape structure well without an explicit decomposition. Our method is based on the visibility graph approach. To check the visibility between pairwise points, we propose a novel, fast, and robust visibility checking algorithm based on a clustering technique which operates directly on the volumetric model without any surface reconstruction procedure, where an octree is used for accelerating the computation. The inner distance can be used as a replacement for other distance measures to build a more accurate description for complex shapes, especially for those with articulated parts. The binary executable program for the Windows platform is available from https://engineering.purdue.edu/PRECISE/VMID.
INDEX TERMS
Inner distance, visibility graph, articulated shape descriptor, volumetric models.
CITATION
Yu-Shen Liu, Karthik Ramani, Min Liu, "Computing the Inner Distances of Volumetric Models for Articulated Shape Description with a Visibility Graph", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.33, no. 12, pp. 2538-2544, December 2011, doi:10.1109/TPAMI.2011.116
REFERENCES
[1] H. Ling and D. Jacobs, "Shape Classification Using the Inner-Distance," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 2, pp. 286-299, Feb. 2007.
[2] R. Gal, A. Shamir, and D. Cohen-Or, "Pose-Oblivious Shape Signature," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 2, pp. 261-271, Mar./Apr. 2007.
[3] A.M. Bronstein, M.M. Bronstein, and R. Kimmel, "Topology-Invariant Similarity of Nonrigid Shapes," Int'l J. Computer Vision, vol. 81, no. 3, pp. 281-301, 2009.
[4] A. Elad and R. Kimmel, "On Bending Invariant Signatures for Surfaces," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 10, pp. 1285-1295, Oct. 2003.
[5] T. Funkhouser, P. Min, M. Kazhdan, J. Chen, A. Halderman, D. Dobkin, and D. Jacobs, "A Search Engine for 3D Models," ACM Trans. Graphics, vol. 22, no. 1, pp. 83-105, 2003.
[6] N. Iyer, S. Jayanti, K. Lou, Y. Kalyanaraman, and K. Ramani, "Three Dimensional Shape Searching: State-of-the-Art Review and Future Trends," Computer-Aided Design, vol. 37, pp. 509-530, 2005.
[7] R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin, "Shape Distributions," ACM Trans. Graphics, vol. 21, no. 4, pp. 807-832, 2002.
[8] L. Sael, B. Li, D. La, Y. Fang, K. Ramani, R. Rustamov, and D. Kihara, "Fast Protein Tertiary Structure Retrieval Based on Global Surface Shape Similarity," Proteins, vol. 72, no. 4, pp. 1259-1273, 2008.
[9] A.M. Bronstein, M.M. Bronstein, A.M. Bruckstein, and R. Kimmel, "Analysis of 2D Non-Rigid Shapes," Int'l J. Computer Vision, vol. 78, no. 1, pp. 67-88, 2008.
[10] A.M. Bronstein, M.M. Bronstein, R. Kimmel, M. Mahmoudi, and G. Sapiro, "A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-Rigid Shape Matching," Int'l J. Computer Vision, 2009.
[11] 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.
[12] V. Jain and H. Zhang, "A Spectral Approach to Shape-Based Retrieval of Articulated 3D Models," Computer-Aided Design, vol. 39, no. 5, pp. 398-407, 2007.
[13] R. Rustamov, "Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation," Proc. Fifth Eurographics Symp. Geometry Processing, 2007.
[14] R. Rustamov, Y. Lipman, and T. Funkhouser, "Interior Distance Using Barycentric Coordinates," Computer Graphics Forum, vol. 28, no. 5, pp. 1279-1288, 2009.
[15] K. Siddiqi, J. Zhang, D. Macrini, A. Shokoufandeh, S. Bouix, and S. Dickinson, "Retrieving Articulated 3D Models using Medial Surfaces," Machine Vision and Applications, vol. 19, no. 4, pp. 261-275, 2008.
[16] J. Sun, M. Ovsjanikov, and L. Guibas, "A Concise and Provably Informative Multi-Scale Signature Based on Heat Diffusion," Computer Graphics Forum, vol. 28, no. 5, pp. 1383-1392, 2009.
[17] M. Ovsjanikov, A.M. Bronstein, M.M. Bronstein, and L.J. Guibas, "Shape Google: A Computer Vision Approach for Invariant Shape Retrieval," Proc. NORDIA, 2009.
[18] 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.
[19] T. Funkhouser and P. Shilane, "Partial Matching of 3D Shapes with Priority-Driven Search," Proc. Fourth Eurographics Symp. Geometry Processing, 2006.
[20] A.M. Bronstein, M. Bronstein, and R. Kimmel, "Generalized Multidimensional Scaling: A Framework for Isometry-Invariant Partial Surface Matching," Proc. Nat'l Academy of Sciences USA, vol. 103, no. 5, pp. 1168-1172, 2006.
[21] M.R. Ruggeri and D. Saupe, "Isometry-Invariant Matching of Point Set Surfaces," Proc. Eurographics Workshop 3D Object Retreivel, 2008.
[22] A.B. Hamza and H. Krim, "Geodesic Object Representation and Recognition," Proc. Discrete Geometry for Computer Imagery, pp. 378-387, 2003.
[23] H. Ling and D. Jacobs, "Using the Inner-Distance for Classification of Articulated Shapes," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 286-299, 2005.
[24] S. Biswas, G. Aggarwal, and R. Chellappa, "Efficient Indexing for Articulation Invariant Shape Matching and Retrieval," Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2007.
[25] R. Liu and H. Zhang, "Mesh Segmentation via Spectral Embedding and Contour Analysis," Computer Graphics Forum, vol. 26, no. 3, pp. 385-394, 2007.
[26] Y.-S. Liu, Y. Fang, and K. Ramani, "IDSS: Deformation Invariant Signatures for Molecular Shape Comparison," BMC Bioinformatics, vol. 10, p. 157, 2009.
[27] M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, third ed. Springer, 2008.
[28] J. Tangelder and R. Veltkamp, "A Survey of Content Based 3D Shape Retrieval Methods," Proc. Int'l Conf. Shape Modeling and Applications, pp. 145-156, 2004.
[29] A. Kaufman, D. Cohen, and R. Yagel, "Volume Graphics," Computer, vol. 26, no. 7, pp. 51-64, July 1993.
[30] B. Li, S. Turuvekere, M. Agrawal, D. La, K. Ramani, and D. Kihara, "Characterization of Local Geometry of Protein Surfaces with the Visibility Criterion," Proteins, vol. 71, no. 2, pp. 670-683, 2008.
[31] D. Raviv, M. Bronstein, A.M. Bronstein, and R. Kimmel, "Volumetric Heat Kernel Signatures," Proc. ACM Workshop 3D Object Retrieval, 2010.
[32] R. Rustamov, "Robust Volumetric Shape Descriptor," Proc. Eurographics Workshop 3D Object Retrieval, 2010.
[33] T. Ju, M. Baker, and W. Chiu, "Computing a Family of Skeletons of Volumetric Models for Shape Description," Computer-Aided Design, vol. 39, no. 5, pp. 352-360, 2007.
[34] T. Ju, "Robust Repair of Polygonal Models," ACM Trans. Graphics, vol. 23, no. 3, pp. 888-895, 2004.
[35] P. Soille, Morphological Image Analysis. Springer, 1999.
[36] D. Coeurjolly, S. Miguet, and L. Tougne, "2D and 3D Visibility in Discrete Geometry: An Application to Discrete Geodesic Paths," Pattern Recognition Letters, vol. 25, no. 5, pp. 561-570, 2004.
[37] T. Kanungo, D. Mount, N. Netanyahu, C. Piatko, R. Silverman, and A. Wu, "An Efficient k-Means Clustering Algorithm: Analysis and Implementation," IEEE Trans. Pattern Analysis Machine Intelligence, vol. 24, no. 7, pp. 881-892, July 2002.
[38] M. Pauly, M. Gross, and L. Kobbelt, "Efficient Simplification of Point-Sampled Surfaces," Proc. IEEE Visualization, pp. 163-170, 2002.
[39] G. Schaufler and H. Jensen, "Ray Tracing Point Sampled Geometry," Proc. 11th Eurographics Workshop Rendering, pp. 319-328, 2000.
[40] A. Adamson and M. Alexa, "Ray Tracing Point Set Surfaces," Proc. Shape Modeling Int'l, pp. 272-279, 2003.
[41] Y.-S. Liu, J.-H. Yong, H. Zhang, D.-M. Yan, and J.-G. Sun, "A Quasi-Monte Carlo Method for Computing Areas of Point-Sampled Surfaces," Computer-Aided Design, vol. 38, no. 1, pp. 55-68, 2006.
[42] B. Adams and P. Dutré, "Interactive Boolean Operations on Surfel-Bounded Solids," Proc. ACM SIGGRAPH, pp. 651-656, 2003.
[43] J.B. Tenenbaum, V. de Silva, and J.C. Langford, "A Global Geometric Framework for Nonlinear Dimensionality Reduction," Science, vol. 290, no. 5500, pp. 2319-2323, 2000.
[44] P. Daras, D. Zarpalas, A. Axenopoulos, D. Tzovaras, and M. Strintzis, "3D Shape-Structure Comparison Method for Protein Classification," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 3, no. 3, pp. 193-207, July-Sept. 2006.
[45] S. Jayanti, Y. Kalyanaraman, N. Iyer, and K. Ramani, "Developing an Engineering Shape Benchmark for CAD Models," Computer-Aided Design, vol. 38, no. 9, pp. 939-953, 2006.
[46] R. Coifman and S. Lafon, "Diffusion Maps," Applied and Computational Harmonic Analysis, vol. 21, pp. 5-30, 2006.
[47] M. Mahmoudi and G. Sapiro, "3D Point Cloud Recognition via Distributions of Geometric Distances," Graphical Models, vol. 71, no. 1, pp. 22-31, 2009.
23 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool