This Article 
 Bibliographic References 
 Add to: 
A Flexible Similarity Measure for 3D Shapes Recognition
November 2004 (vol. 26 no. 11)
pp. 1507-1520
This paper is devoted to presenting a new strategy for 3D objects recognition using a flexible similarity measure based on the recent Modeling Wave (MW) topology in spherical models. MW topology allows us to establish an n-connectivity relationship in 3D objects modeling meshes. Using the complete object model, a study on considering different partial information of the model has been carried out to recognize an object. For this, we have introduced a new feature called Cone-Curvature (CC), which originates from the MW concept. CC gives an extended geometrical surroundings knowledge for every node of the mesh model and allows us to define a robust and adaptable similarity measure between objects for a specific model database. The defined similarity metric has been successfully tested in our lab using range data of a wide variety of 3D shapes. Finally, we show the applicability of our method presenting experimentation for recognition on noise and occlusion conditions in complex scenes.

[1] S. Santini and R. Jain, “Similarity Measures,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 9, pp. 871-883, Sept. 1999.
[2] S. Antani, R. Kasturi, and R. Jain, A Survey on the Use of Pattern Recognition Methods for Abstraction, Indexing and Retrieval of Images and Video Pattern Recognition, vol. 35, pp. 945-965, 2002.
[3] R. Jain, R. Kasturi, and B.G. Schinck, Machine Vision. McGraw-Hill, 1995.
[4] R.J. Campbell and P.J. Flynn, A Survey of Free-Form Object Representation and Recognition Techniques Computer Vision and Image Understanding, vol. 81, pp. 166-210, 2001.
[5] H.-Y. Shum, M. Hebert, and K. Ikeuchi, On 3D Shape Similarity Proc. IEEE Conf. Compter Vision and Pattern Recognition, pp. 526-531, June 1966.
[6] C. Dorai and A.K. Jain, “Cosmos—A Representation Scheme for 3D Free-Form Objects,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, pp. 1115–1130, Oct. 1997.
[7] A.E. Johnson and M. Hebert, “Recognizing Objects by Matching Oriented Points,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 684-689, 1997.
[8] S.M. Yamany and A.A. Farag, “Free-Form Surface Registration Using Surface Signatures,” Proc. IEEE Int'l Conf. Computer Vision, vol. 2, pp. 1098–1104, Sept. 1999.
[9] S.M. Yamany and A.A. Farag, Surfacing Signatures: An Orientation Independent Free-Form Surface Representation Scheme for the Purpose of Objects Registration and Matching IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 8, pp. 1105-1120, Aug. 2002.
[10] C.S. Chua and R. Jarvis, Point Signatures: A New Representation for 3D Object Recognition Int'l J. Computer Vision, vol. 25, no. 1, pp. 63-85, 1997.
[11] R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin, Matching 3D Models with Shape Distributions Shape Modeling Int'l, May 2001.
[12] J.-P. Vandeborre, V. Couillet, and M. Daoudi, A Practical Approach for 3D Model Indexing by Combining Local and Global Invariants Proc. First Int'l Symp. 3D Data Processing Visualization and Transmission, pp. 644-647, 2002.
[13] A. Adán, C. Cerrada, V. Feliu, Global Shape Invariants: A Solution For 3D Object Discrimination/Identification Problem Pattern Recognition, vol. 34, pp. 1331-1348, 2001.
[14] R.C. Veltkamp, Shape Matching: Similarity Measures and Algorithms Technical Report UU-CS-2001-03, Utrecht Univ., Jan. 2001.
[15] F. Serratosa, R. Alquézar, and A. Sanfeliu, Function-Described for Modeling Objects Represented by Attributed Graphs Pattern Recognition, vol. 36, pp. 781-798, 2003.
[16] A. Sehgal and U.B. Desai, 3D Object Recognition Using Bayesian Geometric Hashing and Pose Clustering Pattern Recognition, vol. 36, pp. 765-780, 2003.
[17] B.J. Super and H. Lu, Evaluation of a Hipothesizer for Silhouette-Based 3D Object Recognition Pattern Recognition, vol. 36, pp. 69-78, 2003.
[18] C.M. Cyr and B.B. Kimia, 3D Object Recognition Using Shape Similarity-Based Aspect Graph Proc. Int'l Conf. Computer Vision, pp. 254-261, 2001.
[19] X. Liu, R. Sun, S.B. Kang, and H.Y. Shum, Directional Histogram Model for Three-Dimensional Shape Similarity Proc. Conf. Vision and Pattern Recognition, vol. 1, pp. 813-820, 2003.
[20] H. Delinguette, Simplex Meshes: A General Representation for 3D Shape Reconstruction Technical Report 2214, INRIA, France, 1994.
[21] J.J. Koenderink and A.J. Van Doorn, Surface Shape and Curvature Scales Image and Vision Computing, vol. 10, no. 8, pp. 557-556, 1992.
[22] N. Dyn, K. Hormann, S.J. Kim, and D. Levin, Optimizing 3D Triangulations Using Discrete Curvature Analysis Math. Methods for Curves and Surfaces, pp. 135-146, 2000.
[23] L. Alboul and R. VanDamme, Polyhedral Metrics in Surface Reconstruction The Mathematics of Surfaces VI, G. Mullineux, ed., pp. 171-200, 1996.
[24] A. Adán, C. Cerrada, and V. Feliú, Modeling Wave Set: Definition and Application of a new Topological Organization for 3D Object Modeling Computer Vision and Image Understanding, vol. 79, pp. 281-307, 2000.
[25] A. Adán, C. Cerrada, and V. Feliú, A Fast Mesh Deformation Method to Build Spherical Representation Model of 3D Objects Lecture Notes in Computer Science, vol. 1351, pp. 482-489, 1998.
[26] M. Hebert, K. Ikeuchi, and H. Delingette, “A Spherical Representation for Recognition of Free-Form Surfaces,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 7, p. 681, July 1995.
[27] K.M. Miettinen, Nonlinear Multiobjective Optimization. Kluwer Academic, 1999.
[28] M. Zeleny, Compromise Programming. Multiple Criteria decision Making, J.L. Cochrane and M. Zeleny, eds. Univ. of South Carolina Press, Columbia, pp. 262-301, 1973.
[29] P.L. Yu, A Class of Solutions for Group Decision Problems Management Science, vol. 19, no. 8, pp. 936-946, 1973.
[30] L. Zadeh, Optimality and Non-Scalar-Valued Performance Criteria IEEE Trans. Automatic Control, vol. 8, pp. 59-60, 1963.
[31] J.C. Bezdek and J.D. Harris, Fuzzy Partitions and Relations: an Axiomatic Basis for Clustering Fuzzy Sets and Systems, vol. 1, pp. 111-127, 1978.
[32] A. Adán, S. Salamanca, and C. Cerrada, Reconstruction of Spherical Models From Multiple Partial Models Proc. First Int'l Symp. 3D Data Processing Visualization and Transmission, pp. 532-536, 2002.
[33] P. Merchán, A. Adán, S. Salamanca, and C. Cerrada, 3D Complex Scenes Segmentation From a Single Range Image Using Virtual Exploration Lecture Notes in Artificial Intelligence, vol. 2527, pp. 923-932, 2002.

Index Terms:
Computer vision, feature measurement, object recognition, similarity measures, pattern recognition.
Antonio Ad?, Miguel Ad?, "A Flexible Similarity Measure for 3D Shapes Recognition," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 11, pp. 1507-1520, Nov. 2004, doi:10.1109/TPAMI.2004.94
Usage of this product signifies your acceptance of the Terms of Use.