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Issue No.12 - December (2008 vol.30)
pp: 2188-2203
ABSTRACT
We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale. Our motivation is to rely on stable properties the shape instead of inaccurately measured secondary details. The new representation does not suffer from the common instability problems of the traditional connected skeletons, and the matching process gives quite successful results on a diverse database of 2D shapes. An important difference of our approach from the conventional use of skeleton is that we replace the local coordinate frame with a global Euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations. As a result, we can produce descriptions that are sensitive to any combination of changes in scale, position, orientation and articulation, as well as invariant ones.
INDEX TERMS
Shape, Representations
CITATION
Cagri Aslan, Aykut Erdem, Erkut Erdem, Sibel Tari, "Disconnected Skeleton: Shape at Its Absolute Scale", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.30, no. 12, pp. 2188-2203, December 2008, doi:10.1109/TPAMI.2007.70842
REFERENCES
[1] L. Ambrosio and V. Tortorelli, “On the Approximation of Functionals Depending on Jumps by Elliptic Functionals via $\Gamma$ -Convergence,” Comm. Pure and Applied Math., vol. 43, no. 8, pp.999-1036, 1990.
[2] C. Aslan, “Disconnected Skeletons for Shape Recognition,” master's thesis, Dept. of Computer Eng., Middle East Technical Univ., May 2005.
[3] C. Aslan, A. Erdem, E. Erdem, and S. Tari, supplemental material, http://doi.ieeecomputersociety.org/10.1109/TPAMI.2007.70842, 2008.
[4] C. Aslan, and S. Tari, “An Axis-Based Representation for Recognition,” Proc. IEEE Int'l Conf. Computer Vision, pp. 1339-1346, 2005.
[5] J. August, K. Siddiqi, and S.W. Zucker, “Ligature Instabilities in the Perceptual Organization of Shape,” Computer Vision and Image Understanding, vol. 76, no. 3, pp. 231-243, 1999.
[6] X. Bai, L.J. Latecki, and W.-Y. Liu, “Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 3, pp. 449-462, Mar. 2007.
[7] E. Baseski, “Context-Sensitive Matching of Two Shapes,” master's thesis, Dept. of Computer Eng., Middle East Technical Univ., July 2006.
[8] R. Basri, “Recognition by Prototypes,” Proc. Computer Vision and Pattern Recognition, pp. 161-167, 1993.
[9] 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.
[10] H. Blum, “Biological Shape and Visual Science,” J. Theoretical Biology, vol. 38, pp. 205-287, 1973.
[11] F.L. Bookstein, Morphometric Tools for Landmark Data—Geometry and Biology. Cambridge Univ. Press, 1991.
[12] M. Brady and H. Asada, “Smoothed Local Symmetries and Their Implementation,” Int'l J. Robotics Research, vol. 3, no. 3, pp. 36-61, 1984.
[13] J.W. Bruce, P.J. Giblin, and C.G. Gibson, “Symmetry Sets,” Proc. Royal Soc. Edinburgh, vol. 101, pp. 163-186, 1985.
[14] M.C. Burl and P. Perona, “Recognition of Planar Object Classes,” Proc. Computer Vision and Pattern Recognition, pp. 223-230, 1996.
[15] V. Camion and L. Younes, “Geodesic Interpolating Splines,” Proc. Fourth Int'l Workshop Energy Minimization Methods in Computer Vision and Pattern Recognition, pp. 513-527, 2001.
[16] H. Chui and A. Rangarajan, “A New Point Matching Algorithm for Non-Rigid Registration,” Computer Vision and Image Understanding, vol. 89, nos. 2-3, pp. 114-141, 2003.
[17] A.R. Dill, M.D. Levine, and P.B. Noble, “Multiple Resolution Skeletons,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 4, pp. 495-504, Apr. 1987.
[18] S. Edelman, “Representation Is Representation of Similarities,” Behavioral and Brain Sciences, vol. 21, no. 4, pp. 449-498, 1998.
[19] A. Erdem, E. Erdem, and S. Tari, “Articulation Prior in an Axial Representation,” Proc. Int'l Workshop Representation and Use of Prior Knowledge in Vision, pp. 1-14, 2006.
[20] D. Geiger, T.L. Liu, and R.V. Kohn, “Representation and Self-Similarity of Shapes,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 1, pp. 86-99, Jan. 2003.
[21] J. Glaunes, A. Trouve, and L. Younes, “Diffeomorphic Matching of Distributions: A New Approach for Unlabelled Point-Sets and Sub-Manifolds Matching,” Proc. Computer Vision and Pattern Recognition, pp. 712-718, 2004.
[22] L. Gorelick, M. Galun, E. Sharon, R. Basri, and A. Brandt, “Shape Representation and Classification Using the Poisson Equation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 12, pp. 1991-2005, Dec. 2006.
[23] J. Goutsias and D. Schonfeld, “Morphological Representation of Discrete and Binary Images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 39, no. 6, pp. 1369-1379, June 1991.
[24] D.G. Kendall, D. Barden, T.K. Carne, and H. Le, Shape and Shape Theory. John Wiley & Sons, 1999.
[25] B.B. Kimia, A.R. Tannenbaum, and S.W. Zucker, “Shapes, Shocks, and Deformations I: The Components of Two-Dimensional Shape and the Reaction-Diffusion Space,” Int'l J. Computer Vision, vol. 15, no. 3, pp. 189-224, 1995.
[26] R. Kresch, “Morphological Image Representation for Coding Applications,” PhD dissertation, Technion-Israel Inst. of Tech nology, 1995.
[27] R. Kresch and D. Malah, “Morphological Reduction of Skeleton Redundancy,” Signal Processing, vol. 38, pp. 143-151, 1994.
[28] C. Lantuejoul, “La Squelettisation et Son Application aux Mesures Topologiques des Mosaïques Polycristallines,” PhD dissertation, Ecole des Mines de Paris, 1978.
[29] L.J. Latecki and R. Lakamper, “Shape Similarity Measure Based on Correspondence of Visual Parts,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 10, pp. 1185-1190, Oct. 2000.
[30] K. Leonard, “Classification of 2D Shapes via Efficiency Measures,” unpublished work, 2006.
[31] G. Levi and U. Montanari, “A Grey-Weighted Skeleton,” Information and Control, vol. 17, no. 1, pp. 62-91, 1970.
[32] M. Leyton, “A Process-Grammar for Shape,” Artificial Intelligence, vol. 34, no. 2, pp. 213-247, 1988.
[33] H. Ling and D.W. Jacobs, “Using the Inner-Distance for Classification of Articulated Shapes,” Proc. Computer Vision and Pattern Recognition), pp. 719-726, 2005.
[34] P. Maragos, “Pattern Spectrum and Multiscale Shape Representation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 701-716, July 1989.
[35] P. Maragos and R.W. Schafer, “Morphological Skeleton Representation and Coding of Binary Images,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 34, no. 5, pp. 1228-1244, 1986.
[36] G. Matheron, Random Sets and Integral Geometry. John Wiley & Sons, 1975.
[37] W. Mio, A. Srivastava, and S. Joshi, “On Shape of Plane Elastic Curves,” Int'l J. Computer Vision, vol. 73, no. 3, pp. 307-324, 2007.
[38] D. Mumford and J. Shah, “Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems,” Comm. Pure and Applied Math., vol. 42, no. 5, pp. 577-685, 1989.
[39] R. Ogniewicz and O. Kubler, “Hierarchic Voronoi Skeletons,” Pattern Recognition, vol. 28, no. 3, pp. 343-359, 1995.
[40] O.C. Ozcanli, A. Tamrakar, B.B. Kimia, and J.L. Mundy, “Augmenting Shape with Appearance in Vehicle Category Recognition,” Proc. Computer Vision and Pattern Recognition, pp.935-942, 2006.
[41] M. Pelillo, K. Siddiqi, and S.W. Zucker, “Matching Hierarchical Structures Using Association Graphs,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 11, pp. 1105-1120, Nov. 1999.
[42] A. Peter and A. Rangarajan, “Shape Matching Using the Fisher-Rao Riemannian Metric: Unifying Shape Representation and Deformation,” Proc. IEEE Int'l Symp. Biomedical Imaging: From Nano to Macro, pp. 1164-1167, 2006.
[43] S.M. Pizer, W.R. Oliver, and S.H. Bloomberg, “Hierarchical Shape Description via the Multiresolution Symmetric Axis Transform,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 4, pp. 505-511, Apr. 1987.
[44] S.M. Pizer, K. Siddiqi, G. Székely, J.N. Damon, and S.W. Zucker, “Multiscale Medial Loci and Their Properties,” Int'l J. Computer Vision, vol. 55, no. 2-3, pp. 155-179, 2003.
[45] 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.
[46] J. Serra, Image Analysis and Mathematical Morphology. London Academic Press, 1982.
[47] J. Shah, “Segmentation by Nonlinear Diffusion II,” Proc. Computer Vision and Pattern Recognition, pp. 644-647, 1992.
[48] J. Shah, “A Common Framework for Curve Evolution, Segmentation and Anisotropic Diffusion,” Proc. Computer Vision and Pattern Recognition, pp. 136-142, 1996.
[49] J. Shah, “Grayscale Skeletons and Segmentation of Shapes,” Computer Vision and Image Understanding, vol. 99, no. 1, pp. 96-109, 2005.
[50] J. Shah, “An $H^{2}$ Type Riemannian Metric on the Space of Planar Curves,” Proc. Workshop Math. Foundations of Computational Anatomy, pp. 40-46, 2006.
[51] D. Shaked and A.M. Bruckstein, “Pruning Medial Axes,” Computer Vision and Image Understanding, vol. 69, no. 2, pp. 156-169, 1998.
[52] K. Siddiqi, S. Bouix, A. Tannenbaum, and S.W. Zucker, “Hamilton-Jacobi Skeletons,” Int'l J. Computer Vision, vol. 48, no. 3, pp.215-231, 2002.
[53] K. Siddiqi and B.B. Kimia, “A Shock Grammar for Recognition,” Proc. Computer Vision and Pattern Recognition, pp. 507-513, 1996.
[54] 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.
[55] C. Small, The Statistical Theory of Shape. Springer, 1996.
[56] S. Tari and J. Shah, “Local Symmetries of Shapes in Arbitrary Dimension,” Proc. IEEE Int'l Conf. Computer Vision, pp. 1123-1128, 1998.
[57] S. Tari, J. Shah, and H. Pien, “A Computationally Efficient Shape Analysis via Level Sets,” Proc. Workshop Math. Methods in Biomedical Image Analysis, pp. 234-243, 1996.
[58] S. Tari, J. Shah, and H. Pien, “Extraction of Shape Skeletons from Grayscale Images,” Computer Vision and Image Understanding, vol. 66, no. 2, pp. 133-146, 1997.
[59] M. van Eede, D. Macrini, A. Telea, C. Sminchisescu, and S. Dickinson, “Canonical Skeletons for Shape Matching,” Proc. Int'l Conf. Pattern Recognition, vol. 2, pp. 64-69, 2006.
[60] S.C. Zhu, “Stochastic Jump-Diffusion Process for Computing Medial Axes in Markov Random Fields,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 11, pp. 1158-1169, Nov. 1999.
[61] S.C. Zhu and A.L. Yuille, “FORMS: A Flexible Object Recognition and Modeling System,” Int'l J. Computer Vision, vol. 20, no. 3, pp.187-212, 1996.
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