This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A New 3D-Matching Method of Nonrigid and Partially Similar Models Using Curve Analysis
April 2011 (vol. 33 no. 4)
pp. 852-858
Hedi Tabia, LAGIS FRE CNRS University Lille 1, Villeneuve d'Ascq
Mohamed Daoudi, TELECOM Lille 1; Institut TELECOM University Lille 1, Villeneuve d'Ascq
Jean-Philippe Vandeborre, TELECOM Lille 1; Institut TELECOM University Lille 1, Villeneuve d'Ascq
Olivier Colot, LAGIS FRE CNRS University Lille 1, Villeneuve d'Ascq
The 3D-shape matching problem plays a crucial role in many applications, such as indexing or modeling, by example. Here, we present a novel approach to matching 3D objects in the presence of nonrigid transformation and partially similar models. In this paper, we use the representation of surfaces by 3D curves extracted around feature points. Indeed, surfaces are represented with a collection of closed curves, and tools from shape analysis of curves are applied to analyze and to compare curves. The belief functions are used to define a global distance between 3D objects. The experimental results obtained on the TOSCA and the SHREC07 data sets show that the system performs efficiently in retrieving similar 3D models.

[1] G. Antini, S. Berretti, A. Del Bimbo, and P. Pala, "Retrieval of 3D Objects Using Curvature Correlograms," Proc. IEEE Int'l Conf. Multimedia and Expo, 2005.
[2] T. Filali Ansary, M. Daoudi, and J.-P. Vandeborre, "A Bayesian 3D Search Engine Using Adaptive Views Clustering," IEEE Trans. Multimedia, vol. 9, no. 1, pp. 78-88, Jan. 2007.
[3] 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.
[4] 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.
[5] D. Aouada, D.-W. Dreisigmeyer, and H. Krim, "Geometric Modeling of Rigid and Non-Rigid 3D Shapes Using the Global Geodesic Function," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition Workshops, 2008.
[6] J. Tierny, J.-P. Vandeborre, and M. Daoudi, "Partial 3D Shape Retrieval by Reeb Pattern Unfolding," Computer Graphics Forum, vol. 28, pp. 41-55, 2009.
[7] Y. Liu, H. Zha, and H. Qin, "Shape Topics: A Compact Representation and New Algorithms for 3D Partial Shape Retrieval," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2006.
[8] A. Bronstein, M. Bronstein, A. Bruckstein, and R. Kimmel, "Partial Similarity of Objects, or How to Compare a Centaur to a Horse," Int'l J. Computer Vision, vol. 84, no. 2, pp. 163-183, 2008.
[9] S. Jahanbin, H. Choi, Y. Liu, and A.-C. Bovik, "Three Dimensional Face Recognition Using Iso-Geodesic and Iso-Depth Curves," Proc. Second IEEE Int'l Conf. Biometrics: Theory, Applications and Systems, 2008.
[10] C. Samir, A. Srivastava, M. Daoudi, and E. Klassen, "An Intrinsic Framework for Analysis of Facial Surfaces," Int'l J. Computer Vision, vol. 82, pp. 80-95, 2009.
[11] M. Mortara and G. Patanè, "Affine-Invariant Skeleton of 3D Shapes," Proc. Int'l Conf. Shape Modeling and Applications, pp. 245-252, 2002.
[12] S. Katz, G. Leifman, and A. Tal, "Mesh Segmentation Using Feature Point and Core Extraction," The Visual Computer, vol. 25, pp. 865-875, 2005.
[13] K. Cole-McLaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci, "Loops in Reeb Graphs of 2-Manifolds," Proc. 19th Ann. Symp. Computational Geometry, pp. 344-350, 2003.
[14] X. Li, Y. He, X. Gu, and H. Qin, "Curves-On-Surface: A General Shape Comparison Framework," Proc. IEEE Int'l Conf. Shape Modeling and Applications, 2006.
[15] Y. Laurent, "Computable Elastic Distance between Shapes," SIAM J. Applied Math., vol. 58, pp. 565-586, 1998.
[16] P.W. Michor and D. Mumford, "Riemannian Geometries on Spaces of Plane Curves," J. European Math. Soc., vol. 8, pp. 1-48, 2006.
[17] S. Joshi, E. Klassen, A. Srivastava, and I. Jermyn, "Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves," Proc. Sixth Int'l Conf. Energy Minimization Methods in Computer Vision and Pattern Recognition, pp. 387-398, 2007.
[18] A.-J. Yezzi and A. Mennucci, "Conformal Metrics and True "Gradient Flows" for Curves," Proc. 10th IEEE Int'l Conf. Computer Vision, vol. 1, pp. 913-919, 2005.
[19] E. Klassen, A. Srivastava, "Geodesics between 3D Closed Curves Using Path-Straightening," Proc. Ninth European Conf. Computer Vision, pp. 95-106, 2006.
[20] P. Smets and R. Kennes, "The Transferable Belief Model," Artificial Intelligence, vol. 66, pp. 191-234, 1994.
[21] G. Shafer, A Mathematical Theory of Evidence. Princeton Univ. Press, 1976.
[22] A. Bronstein, M. Bronstein, and R. Kimmel, "Efficient Computation of Isometry-Invariant Distances between Surfaces," SIAM J. Scientific Computing , vol. 28, pp. 1812-1836, 2006.
[23] S. Marini, L. Paraboschi, and S. Biasotti, "Shape Retrieval Contest 2007: Partial Matching Track," Proc. SHREC in Conjunction with Proc. Int'l Conf. Shape Modeling and Applications, pp. 13-16, 2007.
[24] D. Saupe and D. Vranic, "3D Model Retrieval with Spherical Harmonics and Moments," Pattern Recognition, Springer, pp. 392-397, 2001.
[25] D. Vranic, "3D Model Retrieval," PhD dissertation, Univ. of Leipzig, May 2004.
[26] R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin, "Shape Distributions," ACM Trans. Graphics, vol. 21, no. 4, pp. 807-832, 2002.
[27] A. Bronstein, M. Bronstein, M. Mahmoudi, R. Kimmel, and G. Sapiro, "A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching," Int'l J. Computer Vision, vol. 89, pp. 266-286, 2010.
[28] A. Gil, O.M. Mozos, M. Ballesta, and O. Reinoso, "A Comparative Evaluation of Interest Point Detectors and Local Descriptors for Visual Slam," Machine Vision and Applications, vol. 21, pp. 905-920, 2009.

Index Terms:
3D-shape matching, curves analysis, belief functions, feature points.
Citation:
Hedi Tabia, Mohamed Daoudi, Jean-Philippe Vandeborre, Olivier Colot, "A New 3D-Matching Method of Nonrigid and Partially Similar Models Using Curve Analysis," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 33, no. 4, pp. 852-858, April 2011, doi:10.1109/TPAMI.2010.202
Usage of this product signifies your acceptance of the Terms of Use.