Abstract
This paper presents an approach to matching parts of deformable shapes. Multiscale salient parts of the two shapes are first identified. Then, these parts are matched if their immediate properties are similar, the same holds recursively for their subparts, and the same holds for their neighbor parts. The shapes are represented by hierarchical attributed graphs whose node attributes encode the photometric and geometric properties of corresponding parts, and edge attributes capture the strength of neighbor and part-of interactions between the parts. Their matching is formulated as finding the subgraph isomorphism that minimizes a quadratic cost. The dimensionality of the matching space is dramatically reduced by convexifying the cost. Experimental evaluation on the benchmark MPEG-7 and Brown datasets demonstrates that the proposed approach is robust.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Biederman, I.: Recent psychophysical and neural research in shape recognition. In: Osaka, N., Rentschler, I., Biederman, I. (eds.) Object Recognition, Attention, and Action, pp. 71–88. Springer, Heidelberg (2007)
Günther, O., Wong, E.: The arc tree: an approximation scheme to represent arbitrary curved shapes. Comput. Vision Graph. Image Process. 51(3), 313–337 (1990)
Felzenszwalb, P.F., Schwartz, J.D.: Hierarchical matching of deformable shapes. In: CVPR (2007)
Mokhtarian, F., Mackworth, A.K.: A theory of multiscale, curvature-based shape representation for planar curves. IEEE TPAMI 14(8), 789–805 (1992)
Ueda, N., Suzuki, S.: Learning visual models from shape contours using multiscale convex/concave structure matching. IEEE TPAMI 15(4), 337–352 (1993)
Ling, H., Jacobs, D.: Shape classification using the inner-distance. IEEE TPAMI 29(2), 286–299 (2007)
Fan, X., Qi, C., Liang, D., Huang, H.: Probabilistic contour extraction using hierarchical shape representation. In: ICCV, pp. 302–308 (2005)
Mcneill, G., Vijayakumar, S.: Hierarchical procrustes matching for shape retrieval. In: CVPR (2006)
Siddiqi, K., Shokoufandeh, A., Dickinson, S.J., Zucker, S.W.: Shock graphs and shape matching. Int. J. Comput. Vision 35(1), 13–32 (1999)
Shokoufandeh, A., Macrini, D., Dickinson, S., Siddiqi, K., Zucker, S.W.: Indexing hierarchical structures using graph spectra. IEEE TPAMI 27(7), 1125–1140 (2005)
Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Rec. Letters 1(4), 245–253 (1983)
Sebastian, T.B., Klein, P.N., Kimia, B.B.: Recognition of shapes by editing their shock graphs. IEEE Trans. Pattern Anal. Machine Intell. 26(5), 550–571 (2004)
Pelillo, M., Siddiqi, K., Zucker, S.W.: Matching hierarchical structures using association graphs. IEEE TPAMI 21(11), 1105–1120 (1999)
Tu, Z., Yuille, A.: Shape matching and recognition - using generative models and informative features. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3023, pp. 195–209. Springer, Heidelberg (2004)
Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE TPAMI 18(4), 377–388 (1996)
Jiang, H., Drew, M.S., Li, Z.N.: Matching by linear programming and successive convexification. IEEE TPAMI 29(6), 959–975 (2007)
Teh, C.H., Chin, R.T.: On the detection of dominant points on digital curves. IEEE Trans. Pattern Anal. Mach. Intell. 11(8), 859–872 (1989)
Torsello, A., Hancock, E.R.: Computing approximate tree edit distance using relaxation labeling. Pattern Recogn. Lett. 24(8), 1089–1097 (2003)
Pelillo, M., Siddiqi, K., Zucker, S.W.: Many-to-many matching of attributed trees using association graphs and game dynamics. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, pp. 583–593. Springer, Heidelberg (2001)
Demirci, M.F., Shokoufandeh, A., Keselman, Y., Bretzner, L., Dickinson, S.J.: Object recognition as many-to-many feature matching. Int. J. Computer Vision 69(2), 203–222 (2006)
Todorovic, S., Ahuja, N.: Region-based hierarchical image matching. Int. J. of Computer Vision 78(1), 47–66 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Payet, N., Todorovic, S. (2009). Matching Hierarchies of Deformable Shapes. In: Torsello, A., Escolano, F., Brun, L. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2009. Lecture Notes in Computer Science, vol 5534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02124-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-02124-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02123-7
Online ISBN: 978-3-642-02124-4
eBook Packages: Computer ScienceComputer Science (R0)