Skip to main content

Shape Learning with Function-Described Graphs

  • Conference paper
  • 1594 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5112))

Abstract

A new method for shape learning is presented in this paper. This method incorporates abilities from both statistical and structural pattern recognition approaches to shape analysis. It borrows from statistical pattern recognition the capability of modelling sets of point coordinates, and from structural pattern recognition the ability of dealing with highly irregular patterns, such as those generated by points missingness. To that end we use a novel adaptation of Procrustes analysis, designed by us to align sets of points with missing elements. We use this information to generate sets of attributed graphs (AGs). From each set of AGs we synthesize a function-described graph (FDG), which is a type of compact representation that has the capability of probabilistic modelling of both structural and attribute information. Multivariate normal probability density estimation is used in FDGs instead of the originally used histograms. Comparative results of classification performance are presented of structural vs. attributes + structural information.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Srivastava, A., Joshi, S.H., Mio, W., Liu, X.: Statistical Shape Analysis: Clustering, Learning, and Testing. IEEE Transactions on PAMI 27(4) (April 2005)

    Google Scholar 

  2. Huang, X., Paragios, N., Metaxas, D.N.: Shape Registration in Implicit Spaces Using Information Theory and Free Form Deformations. IEEE Transactions on PAMI 28(8) (August 2006)

    Google Scholar 

  3. Belongie, S., Malik, J., Puzicha, J.: Shape Matching and Object Recognition Using Shape Contexts. IEEE Transactions on PAMI 24(24) (April 2002)

    Google Scholar 

  4. Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active shape models - their training and application. Computer Vision and Image Understanding, 38–59 (January 1995)

    Google Scholar 

  5. Davies, R.H., Twining, C.J., Allen, P.D., Cootes, T.F., Taylor, C.J.: Building optimal 2D statistical shape models. Image and Vision Computing 21, 1171–1182 (2003)

    Article  Google Scholar 

  6. Hill, A., Taylor, C.J., Brett, A.D.: A Framework for Automatic Landmark Identification Using a New Method of Nonrigid Correspondence. IEEE Transactions on PAMI 22(3) (March 2000)

    Google Scholar 

  7. Zhao, H., Kong, M., Luo, B.: Shape Representation Based on Polar-Graph Spectra. In: ICIC 2006. LNCIS, vol. 345, pp. 900–905 (2006)

    Google Scholar 

  8. Goodall, C.: Procrustes methods in the statistical-analysis of shape. Journal of the Royal Statistical Society Series B-Methodological, 285–339 (1991)

    Google Scholar 

  9. Kim, D.H., Yun II, D., Lee, S.U.: A new shape decomposition scheme for graph-based representation. Pattern Recognition 38, 673–689 (2005)

    Article  Google Scholar 

  10. Siddiqi, K., Shokoufandeh, A., Dickinson, S.J., Zucker, S.W.: Shock Graphs and Shape Matching. International Journal of Computer Vision 35(1), 13–32 (1999)

    Article  Google Scholar 

  11. Luo, B., Robles-Kelly, A., Torsello, A., Wilson, R.C., Hancock, E.R.: Discovering Shape Categories by Clustering Shock Trees. In: Skarbek, W. (ed.) CAIP 2001. LNCS, vol. 2124, pp. 152–160. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  12. Serratosa, F., Alquézar, R., Sanfeliu, A.: Function-described graphs for modelling objects represented by sets of attributed graphs. Pattern Recognition 36, 781–798 (2003)

    Article  Google Scholar 

  13. Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. IEEE Transactions on PAMI 18(4) (April 1996)

    Google Scholar 

  14. ten Berge, J.M.F., Kiers, H.A.L., Commandeur, J.J.F.: Orthogonal Procrustes rotation for matrices with missing values. British Journal of Mathematical and Statistical Psychology 46, 119–134 (1993)

    MATH  MathSciNet  Google Scholar 

  15. Serratosa, F., Alquézar, R., Sanfeliu, A.: Synthesis of Function-Described Graphs and Clustering of Attributed Graphs. International Journal of Pattern Recognition and Artificial Intelligence 16(6), 621–655 (2002)

    Article  Google Scholar 

  16. Sanfeliu, A., Serratosa, F., Alquézar, R.: Second-order Random Graphs for Modelling Sets of Attributed Graphs and their Application to Object Learning and Recognition. International Journal of Pattern Recognition and Artificial Intelligence 18(3), 375–396 (2004)

    Article  Google Scholar 

  17. Luo, B., Hancock, E.R.: A unified framework for alignment and correspondence. Computer Vision and Image Understanding 92, 26–55 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Aurélio Campilho Mohamed Kamel

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sanromà, G., Serratosa, F., Alquézar, R. (2008). Shape Learning with Function-Described Graphs. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2008. Lecture Notes in Computer Science, vol 5112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69812-8_47

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-69812-8_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69811-1

  • Online ISBN: 978-3-540-69812-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics