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Symbolic Signatures for Deformable Shapes
January 2006 (vol. 28 no. 1)
pp. 75-90
Recognizing classes of objects from their shape is an unsolved problem in machine vision that entails the ability of a computer system to represent and generalize complex geometrical information on the basis of a finite amount of prior data. A practical approach to this problem is particularly difficult to implement, not only because the shape variability of relevant object classes is generally large, but also because standard sensing devices used to capture the real world only provide a partial view of a scene, so there is partial information pertaining to the objects of interest. In this work, we develop an algorithmic framework for recognizing classes of deformable shapes from range data. The basic idea of our component-based approach is to generalize existing surface representations that have proven effective in recognizing specific 3D objects to the problem of object classes using our newly introduced symbolic-signature representation that is robust to deformations, as opposed to a numeric representation that is often tied to a specific shape. Based on this approach, we present a system that is capable of recognizing and classifying a variety of object shape classes from range data. We demonstrate our system in a series of large-scale experiments that were motivated by specific applications in scene analysis and medical diagnosis.

[1] R. Andersen, F.L. Bookstein, K. Conradsen, B.K. Ersboll, J.L. Marsh, and S. Kreiborg, “Surface-Bounded Growth Modeling Applied to Human Mandibles,” IEEE Trans. Medical Imaging, vol. 19, no. 11, pp. 1053-1063, 2000.
[2] B. Blantz and T. Vetter, “A Morphable Model for the Synthesis of 3-F Faces,” Proc. 1999 ACM SIGGRAPH, pp. 187-194, 1999.
[3] F.L. Bookstein, “Shape and the Information in Medical Images: A Decade of the Morphometric Synthesis,” Computer Vision and Image Understanding, vol. 66, no. 2, pp. 99-118, 1997.
[4] C.J.C. Burges, “A Tutorial on Support Vector Machines for Pattern Recognition,” Data Mining and Knowledge Discovery, vol. 2, no. 2, pp. 121-167, 1998.
[5] S. Capell, S. Green, B. Curless, T. Duchamp, and Z. Popovic, “A Multiresolution Framework for Dynamic Deformations,” Proc. 2002 ACM SIGGRAPH, vol. 2, pp. 42-48, 2002.
[6] T.F. Cootes, D. Cooperand, C.J. Taylor, and J. Graham, “Active Shape Models,” Computer Vision and Image Understanding, vol. 61, no. 1, pp 38-59, 1995.
[7] C. Cortes and V.N. Vapnik, “Support Vector Networks,” Machine Learning, vol. 20, pp. 273-279, 1996.
[8] R.H. Davies, C.J. Twining, T.F. Cootes, J.C. Waterton, and C.J. Taylor, “A Minimum Description Length Approach to Statistical Shape Modeling,” IEEE Trans. Medical Imaging, vol. 21, no. 5, pp. 525-537, 2002.
[9] I. Dryden and K. Mardi, Statistical Shape Analysis. New York: Wiley, 1998.
[10] B. Efron, The Jackknife, the Bootstrap, and Other Resampling Plans. Philadephia: SIAM, 1982.
[11] U.G. Froster-Iskenius and J.E. Allanson, Handbook of Normal Physical Measurements. Oxford Medical Publications, 1989.
[12] 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. 83-115, 2003.
[13] P. Golland, “Discriminative Direction for Kernel Classifiers,” Advances in Neural Information Processing Systems, vol. 13, pp 745-752, 2001.
[14] P. Golland, “Statistical Shape Analysis of Anatomical Structures,” doctoral dissertation, Massachusetts Inst. of Tech nology, 2001.
[15] R. Hebrich and T. Graepel, “Bayes Point Machines,” J. Machine Learning Research, no. 1, pp. 245-279, 2001.
[16] B. Heisele, T. Serre, M. Pontil, T. Vetter, and T. Poggio, “Categorization by Learning and Combining Object Parts,” Advances in Neural Information Processing Systems, vol. 2, pp. 1239-1245, 2001.
[17] T. Jaakkola, M. Meila, and T. Jebara, “Maximum Entropy Discrimination,” Advances in Neural Information Processing Systems, no. 11, pp 640-646, 1999.
[18] A.E. Johnson and M. Hebert, “Control of Polygonal Mesh Resolution for 3D Computer Vision,” Graphics, Modeling, and Computer Vision, 1998.
[19] A.E. Johnson and M. Hebert, “Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes,” IEEE Trans. Pattern Recognition and Machine Intelligence, vol. 21, no. 5, pp. 433-449, May 1999.
[20] K.L. Jones, Smith's Recognizable Patterns of Human Malformation. W.B. Saunders Company, 1999.
[21] M. Kazhdan, B. Chazelle, D. Dobkin, T. Funkhouser, and S. Rusinkiewicz, “A Reflexive Symmetry Descriptor for 3D Models,” Algorithmica, vol. 38, no. 2, pp. 201-225, 2003.
[22] S.R. Lale and J.T. Richtsmeier, An Invariant Approach to Statistical Analysis of Shape. Chapman and Hall/CRC, 2001.
[23] S. Loncaric, “A Survey of Shape Analysis Techniques,” Pattern Recognition, vol. 31, no. 8, pp. 938-1001, 1998.
[24] J. Martin, A. Pentland, S. Sclaroff, and R. Kikinis, “Characterization of Neurophatological Shape Deformations,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 2, Feb. 1998.
[25] R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin, “Matching 3D Models with Shape Distributions,” Proc. Shape Modeling Int'l, pp. 154-166, 2001.
[26] D. Rueckert, A.F. Frangi, and J.A. Schnabel, “Automatic Construction of 3D Statistical Deformation Models of the Brain Using Nonrigid Registration,” IEEE Trans. Medical Imaging, vol. 22, no. 8, pp. 1014-1025, 2003.
[27] S. Ruiz-Correa, L.G. Shapiro, and M. Meila, “A New Signature-based Method for Efficient 3D Object Recognition,” IEEE Soc. Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 769-1776, 2001.
[28] S. Ruiz-Correa, L.G. Shapiro, and M. Meila, “A New Paradigm for Recognizing 3D Object Shapes from Range Data,” Proc. IEEE Int'l Conf. Computer Vision, vol. 2, pp. 1126-1133, 2003.
[29] S. Ruiz-Correa, L.G. Shapiro, M. Meila, and G. Berson, “Discriminating Deformable Shape Classes,” Advances in Neural Information Processing Systems 16, S. Thrun, L. Saul, and B. Schölkopf, eds., Cambridge, Mass.: MIT Press, 2004.
[30] B. Scholköpf, J. Platt, A.J. Smola, J. Shawe-Taylor, and R.C. Williamson, “Estimating the Support of a High-Dimensional Distribution,” Neural Computation, vol. 13, pp. 1443-1471, 2001.
[31] B. Scholköpf and A.J. Smola, Learning with Kernels. Cambridge Univ. Press, 2002.
[32] C.R. Shelton, “Morphable Surface Models,” Int'l J. Computer Vision, vol. 38, no. 1, pp. 75-91, 2000.
[33] G. Taubin, “Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation,” IEEE CS Proc. Fifth Int'l Conf. Computer Vision, p. 902, 1995.
[34] V.V. Vapnik, Statistical Learning Theory. John Wiley and Sons, 1998.

Index Terms:
Index Terms- Three-dimensional object recognition and classification, deformable shapes, range data, numeric and symbolic signatures, Mercer kernel, scene analysis, craniosynostosis, craniofacial malformations.
Salvador Ruiz-Correa, Linda G. Shapiro, Marina Meila, Gabriel Berson, Michael L. Cunningham, Raymond W. Sze, "Symbolic Signatures for Deformable Shapes," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 1, pp. 75-90, Jan. 2006, doi:10.1109/TPAMI.2006.23
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