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2D Shape Matching by Contour Flexibility
January 2009 (vol. 31 no. 1)
pp. 180-186
Chunjing Xu, The Chinese University of Hong Kong, Hong Kong
Jianzhuang Liu, The Chinese University of Hong Kong, Hong Kong
Xiaoou Tang, The Chinese University of Hong Kong, Hong Kong
In computer vision, shape matching is a challenging problem, especially when articulation and deformation of parts occur. These variations may be insignificant in terms of human recognition, but often cause a matching algorithm to give results that are inconsistent with our perception. In this paper, we propose a novel shape descriptor of planar contours, called contour flexibility, which represents the deformable potential at each point along a contour. With this descriptor, The local and global features can be obtained from the contour. We then present a shape matching scheme based on the features obtained. Experiments with comparisons to recently published algorithms show that our algorithm performs best.

[1] T. Adamek and N.E. O'Connor, “A Multiscale Representation Method for Nonrigid Shapes with a Single Closed Contour,” IEEE Trans. Circuits and Systems for Video Technology, vol. 14, no. 5, pp. 742-753, 2004.
[2] E. Attalla and P. Siy, “Robust Shape Similarity Retrieval Based on Contour Segmentation Polygonal Multiresolution and Elastic Matching,” Pattern Recognition, vol. 38, no. 12, pp. 2229-2241, 2005.
[3] F. Attneave, “Dimensions of Similarity,” Am. J. Psychology, vol. 63, no. 4, pp.516-556, 1950.
[4] R. Basri, L. Costa, D. Geiger, and D. Jacobs, “Determining the Similarity of Deformable Shapes,” Vision Research, vol. 38, nos. 15-16, pp. 2365-2385, 1998.
[5] 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.
[6] I. Biederman, “Recognition-by-Components: A Theory of Human Image Understanding,” Psychological Rev., vol. 84, pp. 115-147, 1987.
[7] F.L. Bookstein, “Size and Shape Spaces for Landmark Data in Two Dimensions,” Statistical Science, vol. 1, no. 2, pp. 181-222, 1986.
[8] C.C. Chen, “Improved Moment Invariants for Shape Discrimination,” Pattern Recognition, vol. 26, no. 5, pp. 683-686, 1993.
[9] G.C.H. Chuang and C.C.J. Kuo, “Wavelet Descriptor of Planar Curves: Theory and Applications,” IEEE Trans. Image Processing, vol. 5, no. 1, pp. 56-70, 1996.
[10] S.A. Dudani, K.J. Breeding, and R.B. McGhee, “Aircraft Identification by Moment Invariants,” IEEE Trans. Computers, vol. 26, no. 1, pp. 39-46, Jan. 1977.
[11] P.F. Felzenszwalb and J. Schwartz, “Hierarchical Matching of Deformable Shapes,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp.1-8, 2007.
[12] L. Gupta and M.D. Srinath, “Contour Sequence Moments for the Classification of Closed Planar Shapes,” Pattern Recognition, vol. 20, no. 3, pp. 267-272, 1987.
[13] D.D. Hoffman and W.A. Richards, “Parts of Recognition,” Cognition, vol. 18, nos. 1-3, pp. 65-96, 1984.
[14] B.W. Hong, E. Prados, S. Soatto, and L. Vese, “Shape Representation Based on Integral Kernels: Application to Image Matching and Segmentation,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 833-840, 2006.
[15] M.K. Hu, “Visual Pattern Recognition by Moment Invariants,” IEEE Trans. Information Theory, vol. 8, no. 2, pp. 179-187, 1962.
[16] D.G. Kendall, “Shape Manifolds, Procrustean Metrics and Complex Projective Spaces,” Bull. London Math. Soc., vol. 16, pp. 81-121, 1984.
[17] E. Klassen, A. Srivastava, W. Mio, and S.H. Joshi, “Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 3, pp. 372-383, Mar. 2004.
[18] I. Kunttu, L. Lepisto, J. Rauhamaa, and A. Visa, “Multiscale Fourier Descriptor for Shape Classification,” Proc. 12th Int'l Conf. Image Analysis and Processing, vol. 1, pp. 536-541, 2003.
[19] H. Ling and D.W. Jacobs, “Using the Inner-Distance for Classification of Articulated Shapes,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 719-726, 2005.
[20] K.V. Mardia and I.L. Dryden, “Shape Distributions for Landmark Data,” Advances in Applied Probability, vol. 21, no. 4, pp. 742-755, 1989.
[21] J.S. Marques and A.J. Abrantes, “Shape Alignment-Optimal Initial Point and Pose Estimation,” Pattern Recognition Letters, vol. 18, no. 1, pp. 49-53, 1997.
[22] G. McNeill and S. Vijayakumar, “Hierarchical Procrustes Matching for Shape Retrieval,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 885-894, 2006.
[23] E. Milios and E.G.M. Petrakis, “Shape Retrieval Based on Dynamic Programming,” IEEE Trans. Image Processing, vol. 9, no. 1, pp. 141-147, 2000.
[24] F. Mokhtarian, Curvature Scale Space Representation: Theory, Applications, and MPEG-7 Standardization. Springer, 2003.
[25] S.O.O.C. Pei and C.N.A.N. Lin, “Image Normalization for Pattern Recognition,” Image and Vision Computing, vol. 13, no. 10, pp. 711-723, 1995.
[26] M.J.D. Powell, Approximation Theory and Methods. Cambridge Univ. Press, 1981.
[27] L. Rabiner and B.H. Juang, Fundamentals of Speech Recognition. Prentice Hall, 1993.
[28] T.B. Sebastian, P.N. Klein, and B.B. Kimia, “On Aligning Curves,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 1, pp. 116-125, Jan. 2003.
[29] T.B. Sebastian, P.N. Klein, and B.B. Kimia, “Recognition of Shapes by Editing Their Shock Graphs,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 5, pp. 550-571, May 2004.
[30] K. Siddiqi and B.B. Kimia, “Parts of Visual Form: Computational Aspects,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 75-81, 1993.
[31] K. Siddiqi, A. Shokoufandeh, S.J. Dickinson, and S.W. Zucker, “Shock Graphs and Shape Matching,” Int'l J. Computer Vision, vol. 35, no. 1, pp. 13-32, 1999.
[32] B.J. Super, “Learning Chance Probability Functions for Shape Retrieval or Classification,” Proc. IEEE Workshop Learning in Computer Vision and Pattern Recognition, vol. 6, pp. 93-98, 2004.
[33] Z. Tu and A.L. Yuille, “Shape Matching and Recognition—Using Generative Models and Informative Features,” Proc. Eighth European Conf. Computer Vision, pp. 195-209, 2004.
[34] T.P. Wallace and P.A. Wintz, “An Efficient Three-Dimensional Aircraft Recognition Algorithm Using Normalized Fourier Descriptors,” Computer Graphics and Image Processing, vol. 13, no. 2, pp. 99-126, 1980.
[35] L.J. Latecki, R. Lakaemper, and U. Eckhardt, “Shape Descriptors for Non-Rigid Shapes with a Single Close Contour,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 424-429, 2000.

Index Terms:
2D shape, contour flexibility, matching
Citation:
Chunjing Xu, Jianzhuang Liu, Xiaoou Tang, "2D Shape Matching by Contour Flexibility," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 1, pp. 180-186, Jan. 2009, doi:10.1109/TPAMI.2008.199
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