Skip to main content

Directional Data Analysis for Shape Classification

  • Conference paper
  • First Online:
Artificial Neural Networks and Machine Learning – ICANN 2018 (ICANN 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11139))

Included in the following conference series:

  • 7109 Accesses

Abstract

In this work we address the problem of learning from images to perform grouping and classification of shapes. The key idea is to encode the instances available for learning in the form of directional data. In two dimensions, the figure to be categorized is characterized by the distribution of the directions of the normal unit vectors along the contour of the object. This directional characterization is used to extract characteristics based on metrics defined in the space of circular distributions. These characteristics can then be used to categorize the encoded shapes. The usefulness of the representation proposed is illustrated in the problem of clustering and classification of otolith shapes.

The authors acknowledge financial support from the Spanish Ministry of Economy, Industry and Competitiveness, project TIN2016-76406-P.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Institutional subscriptions

References

  1. Berrendero, J.R., Cuevas, A., Pateiro-Lpez, B.: Shape classification based on interpoint distance distributions. J. Multivariate Anal. 146, 237–247 (2016). Special Issue on Statistical Models and Methods for High or Infinite Dimensional Spaces

    Article  MathSciNet  Google Scholar 

  2. Chaubey, Y.P.: Smooth kernel estimation of a circular density function: a connection to orthogonal polynomials on the unit circle. J. Probab. Stat. 2018, 4 p. (2018). https://doi.org/10.1155/2018/5372803. Article ID 5372803

    Article  MathSciNet  Google Scholar 

  3. Di Marzio, M., Panzera, A., Taylor, C.: A note on density estimation for circular data (2012)

    Google Scholar 

  4. Fisher, R.: Dispersion on a sphere. Proc. Roy. Soc. Lond. Ser. A: Math. Phys. Sci. 217(1130), 295–305 (1953)

    Article  MathSciNet  Google Scholar 

  5. García-Portugués, E.: Exact risk improvement of bandwidth selectors for kernel density estimation with directional data. Electron. J. Statist. 7, 1655–1685 (2013). https://doi.org/10.1214/13-EJS821

    Article  MathSciNet  MATH  Google Scholar 

  6. Giménez, J., Manjabacas, A., Tuset, V.M., Lombarte, A.: Relationships between otolith and fish size from Mediterranean and Northeastern Atlantic species to be used in predator-prey studies. J. Fish Biol. 89(4), 2195–2202 (2016)

    Article  Google Scholar 

  7. Grogan, M., Dahyot, R.: Shape registration with directional data. Pattern Recogn. 79, 452–466 (2018)

    Article  Google Scholar 

  8. Kendall, D.G.: A survey of the statistical theory of shape. Statist. Sci. 4(2), 87–99 (1989). https://doi.org/10.1214/ss/1177012582

    Article  MathSciNet  MATH  Google Scholar 

  9. Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. Comput. Graph. 21(4), 163–169 (1987)

    Article  Google Scholar 

  10. MacLeod, N.: Geometric morphometrics and geological shape-classification systems. Earth-Sci. Rev. 59(1), 27–47 (2002)

    Article  MathSciNet  Google Scholar 

  11. Mardia, K.V., Jupp, P.: Directional Statistics. Wiley Series in Probability and Statistics. Wiley, New York (2009)

    MATH  Google Scholar 

  12. Gavrielides, M.A., Kallergi, M., Clarke, L.P.: Automatic shape analysis and classification of mammographic calcifications (1997). https://doi.org/10.1117/12.274175

  13. Montero-Manso, P., Vilar, J.: Shape classification through functional data reparametrization and distribution-based comparison (2017)

    Google Scholar 

  14. Moyou, M., Ihou, K.E., Peter, A.M.: LBO-Shape densities: a unified framework for 2D and 3D shape classification on the hypersphere of wavelet densities. Comput. Vis. Image Underst. 152, 142–154 (2016)

    Article  Google Scholar 

  15. Mu, T., Nandi, A.K., Rangayyan, R.M.: Classification of breast masses using selected shape, edge-sharpness, and texture features with linear and kernel-based classifiers. J. Digit. Imaging 21(2), 153–169 (2008)

    Article  Google Scholar 

  16. Pizer, S.M., Thall, A.L., Chen, D.T.: M-Reps: a new object representation for graphics. Technical report, ACM Transactions on Graphics (2000)

    Google Scholar 

  17. Ramsay, J., Silverman, B.: Functional data analysis (1997)

    Google Scholar 

  18. Taylor, C.C.: Automatic bandwidth selection for circular density estimation. Comput. Stat. Data Anal. 52(7), 3493–3500 (2008)

    Article  MathSciNet  Google Scholar 

  19. Tuset, V., Lombarte, A., Assis, C.: Otolith atlas for the Western Mediterranean, North and Central Eastern Atlantic. Scientia Marina 72(Suppl. 1), 7–198 (2008)

    Google Scholar 

  20. Yushkevich, P., Pizer, S.M., Joshi, S., Marron, J.S.: Intuitive, localized analysis of shape variability. In: Insana, M.F., Leahy, R.M. (eds.) IPMI 2001. LNCS, vol. 2082, pp. 402–408. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45729-1_41

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Adrián Muñoz .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Muñoz, A., Suárez, A. (2018). Directional Data Analysis for Shape Classification. In: Kůrková, V., Manolopoulos, Y., Hammer, B., Iliadis, L., Maglogiannis, I. (eds) Artificial Neural Networks and Machine Learning – ICANN 2018. ICANN 2018. Lecture Notes in Computer Science(), vol 11139. Springer, Cham. https://doi.org/10.1007/978-3-030-01418-6_59

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-01418-6_59

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-01417-9

  • Online ISBN: 978-3-030-01418-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics