Balancing Deformability and Discriminability for Shape Matching

  • Haibin Ling
  • Xingwei Yang
  • Longin Jan Latecki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6313)


We propose a novel framework, aspect space, to balance deformability and discriminability, which are often two competing factors in shape and image representations. In this framework, an object is embedded as a surface in a higher dimensional space with a parameter named aspect weight, which controls the importance of intensity in the embedding. We show that this framework naturally unifies existing important shape and image representations by adjusting the aspect weight and the embedding. More importantly, we find that the aspect weight implicitly controls the degree to which a representation handles deformation. Based on this idea, we present the aspect shape context, which extends shape context-based descriptors and adaptively selects the “best” aspect weight for shape comparison. Another observation we have is the proposed descriptor nicely fits context-sensitive shape retrieval. The proposed methods are evaluated on two public datasets, MPEG7-CE-Shape-1 and Tari 1000, in comparison to state-of-the-art solutions. In the standard shape retrieval experiment using the MPEG7 CE-Shape-1 database, the new descriptor with context information achieves a bull’s eye score of 95.96%, which surpassed all previous results. In the Tari 1000 dataset, our methods significantly outperform previous tested methods as well.


Pattern Anal Geodesic Distance Scale Invariant Feature Transform Shape Descriptor Retrieval Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Adamek, T., O’Connor, N.: A multiscale representation method for nonrigid shapes with a single closed contour. IEEE Tran. Cir. & Sys. for Video Technology 14(5), 742–753 (2004)CrossRefGoogle Scholar
  2. 2.
    Alajlan, N., Kamel, M., Freeman, G.: Geometry-based image retrieval in binary image databases. IEEE Trans. Pattern Anal. Mach. Intell. 30(6), 1003–1013 (2008)CrossRefGoogle Scholar
  3. 3.
    Aslan, C., Erdem, A., Erdem, E., Tari, S.: Disconnected skeleton: Shape at its absolute scale. IEEE Trans. Pattern Anal. Mach. Intell. 30(12), 2188–2203 (2008)CrossRefGoogle Scholar
  4. 4.
    Baseski, E., Erdem, A., Tari, S.: Dissimilarity between two skeletal trees in a context. Pattern Recognition 42(3), 370–385 (2009)zbMATHCrossRefGoogle Scholar
  5. 5.
    Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. Pattern Anal. Mach. Intell. 24(4), 509–522 (2002)CrossRefGoogle Scholar
  6. 6.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proc. Nat. Acad. Sci. 103(5), 1168–1172 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Bronstein, A.M., Bronstein, M.M., Bruckstein, A.M., Kimmel, R.: Analysis of two-dimensional non-rigid shapes. Int. Journal of Computer Vision 78(1), 67–88 (2008)CrossRefGoogle Scholar
  8. 8.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching. Int. Journal of Computer Vision 89(2–3), 266–286 (2010)CrossRefGoogle Scholar
  9. 9.
    Cheng, H., Liu, Z., Zheng, N., Yang, J.: A deformable local image descriptor. In: CVPR, pp. 1–8 (2008)Google Scholar
  10. 10.
    Elad, A., Kimmel, R.: On bending invariant signatures for surfaces. IEEE Trans. Pattern Anal. Mach. Intell. 25(10), 1285–1295 (2003)CrossRefGoogle Scholar
  11. 11.
    Felzenszwalb, P., Schwartz, J.: Hierarchical matching of deformable shapes. In: CVPR, pp. 1–8 (2007)Google Scholar
  12. 12.
    Hu, M.: Visual pattern recognition by moment invariants. IRE Tran. Information Theory 8, 179–187 (1962)Google Scholar
  13. 13.
    Johnson, A.E., Hebert, M.: Using spin images for efficient object recognition in cluttered 3D scenes. IEEE Trans. Pattern Anal. Mach. Intell. 21(5), 433–449 (1999)CrossRefGoogle Scholar
  14. 14.
    Kadir, T., Zisserman, A., Brady, M.: An affine invariant salient region detector. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3021, pp. 228–241. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Kontschieder, P., Donoser, M., Bischof, H.: Beyond pairwise shape similarity analysis. In: Zha, H., Taniguchi, R.-i., Maybank, S. (eds.) Computer Vision – ACCV 2009. LNCS, vol. 5996, pp. 655–666. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Latecki, L.J., Lakämper, R.: Shape similarity measure based on correspondence of visual parts. IEEE Trans. Pattern Anal. Mach. Intell. 22(10), 1185–1190 (2000)CrossRefGoogle Scholar
  17. 17.
    Latecki, L.J., Lakamper, R., Eckhardt, U.: Shape descriptors for non-rigid shapes with a single closed contour. In: CVPR, vol. 1, pp. 424–429 (2000)Google Scholar
  18. 18.
    Lazebnik, S., Schmid, C., Ponce, J.: A sparse texture representation using affine-invariant regions. IEEE Trans. Pattern Anal. Mach. Intell. 27(8), 1265–1278 (2005)CrossRefGoogle Scholar
  19. 19.
    Lin, L., Zeng, K., Liu, X.B., Zhu, S.C.: Layered Graph Matching by Composite Cluster Sampling with Collaborative and Competitive Interactions. In: CVPR (2009)Google Scholar
  20. 20.
    Lindeberg, T.: Feature detection with automatic scale selection. Int. Journal of Computer Vision 30(2), 79–116 (1998)CrossRefGoogle Scholar
  21. 21.
    Ling, H., Jacobs, D.W.: Deformation invariant image matching. In: ICCV, pp. 1466–1473 (2005)Google Scholar
  22. 22.
    H. Ling and D. W. Jacobs. Shape classification using the inner-distance. IEEE Trans. Pattern Anal. Mach. Intell., 29(2):286–299, 2007.CrossRefGoogle Scholar
  23. 23.
    Ling, H., Okada, K.: EMD-L1: An Efficient and Robust Algorithm for Comparing Histogram-Based Descriptors. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3953, pp. 330–343. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  24. 24.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. Journal of Computer Vision 60(2), 91–110 (2004)CrossRefGoogle Scholar
  25. 25.
    Matas, J., Chum, O., Urban, M., Pajdla, T.: Robust wide baseline stereo from maximally stable extremal regions. In: BMVC (2002)Google Scholar
  26. 26.
    McNeill, G., Vijayakumar, S.: Hierarchical procrustes matching for shape retrieval. In: CVPR, pp. 885–894 (2006)Google Scholar
  27. 27.
    Mikolajczyk, K., Schmid, C.: Scale & affine invariant interest point detectors. Int. Journal of Computer Vision 60(1), 63–86 (2004)CrossRefGoogle Scholar
  28. 28.
    Mokhtarian, F., Abbasi, S., Kittler, J.: Efficient and robust retrieval by shape content through curvature scale space. In: Wkshp on Image DataBases and MultiMedia Search (1996)Google Scholar
  29. 29.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1-4), 259–268 (1992)zbMATHCrossRefGoogle Scholar
  30. 30.
    Rustamov, R., Lipman, Y., Funkhouser, T.: Interior Distance Using Barycentric Coordinates. In: Symposium on Geometry Processing (2009)Google Scholar
  31. 31.
    Sebastian, T.B., Klein, P.N., Kimia, B.B.: Recognition of shapes by editing their shock graphs. IEEE Trans. Pattern Anal. Mach. Intell. 26(5), 550–571 (2004)CrossRefGoogle Scholar
  32. 32.
    Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Nat. Acad. Sci. 93(4), 1591–1595 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Sivic, J., Zisserman, A.: Video Google: Efficient visual search of videos. In: Ponce, J., Hebert, M., Schmid, C., Zisserman, A. (eds.) Toward Category-Level Object Recognition, pp. 127–144 (2006)Google Scholar
  34. 34.
    Sochen, N., Kimmel, R., Malladi, R.: A general framework for low level vision. IEEE Trans. Image Processing 7(3), 310–318 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  35. 35.
    Thompson, D.W.: On Growth and Form. Cambridge University Press, Cambridge (1917)Google Scholar
  36. 36.
    Torralba, A., Murphy, K., Freeman, W., Rubin, M.: Context-based vision system for place and object recognition. In: ICCV, pp. 273–280 (2003)Google Scholar
  37. 37.
    Vedaldi, A., Soatto, S.: Features for recognition: Viewpoint invariance for non-planar scenes. In: ICCV, vol. 2, pp. 1474–1481 (2005)Google Scholar
  38. 38.
    Xu, C., Liu, J., Tang, X.: 2d shape matching by contour flexibility. IEEE Trans. Pattern Anal. Mach. Intell. 31(1), 180–186 (2009)CrossRefGoogle Scholar
  39. 39.
    Xu, Y., Ji, H., Fermüller, C.: A projective invariant for textures. In: CVPR, pp. 1932–1939 (2006)Google Scholar
  40. 40.
    Yang, X., Bai, X., Latecki, L.J., Tu, Z.: Improving shape retrieval by learning graph transduction. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part IV. LNCS, vol. 5305, pp. 788–801. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  41. 41.
    Yang, X., Köknar-Tezel, S., Latecki, L.J.: Locally constrained diffusion process on locally densified distance spaces with applications to shape retrieval. In: CVPR (2009)Google Scholar
  42. 42.
    Zhang, J., Marszalek, M., Lazebnik, S., Schmid, C.: Local features and kernels for classification of texture and object categories: A comprehensive study. Int. Journal of Computer Vision 73(2), 213–238 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Haibin Ling
    • 1
  • Xingwei Yang
    • 1
  • Longin Jan Latecki
    • 1
  1. 1.Center for Information Science and Technology, Dept. of Computer and Information ScienceTemple UniversityPhiladelphiaUSA

Personalised recommendations