Skip to main content
SpringerLink
Log in
Book cover

European Conference on the Applications of Evolutionary Computation

EvoApplications 2015: Applications of Evolutionary Computation pp 517–528Cite as

Topology-Preserving Ordering of the RGB Space with an Evolutionary Algorithm

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9028))

Abstract

Mathematical morphology (MM) is broadly used in image processing. MM operators require to establish an order between the values of a set of pixels. This is why MM is basically used with binary and grayscale images. Many works have been focused on extending MM to colour images by mapping a multi-dimensional colour space onto a linear ordered space. However, most of them are not validated in terms of topology preservation but in terms of the results once MM operations are applied. This work presents an evolutionary method to obtain total- and P-orderings of a colour space, i.e. RGB, maximising topology preservation. This approach can be used to order a whole colour space as well as to get a specific ordering for the subset of colours appearing in a particular image. These alternatives improve the results obtained with the orderings usually employed, in both topology preservation and noise reduction.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

References

  1. Aptoula, E., Lefèvre, S.: A comparative study on multivariate mathematical morphology. Pattern Recogn. 40(11), 2914–2929 (2007)

    Article  MATH  Google Scholar 

  2. Regazzoni, C., Teschioni, A.: A new approach to vector median filtering based on space filling curves. IEEE Trans. Image Process. 6(7), 1025–1037 (1997)

    Article  Google Scholar 

  3. Stringa, E., Teschioni, A., Regazzoni, C.S.: A classical morphological approach to color image filtering based on space filling curves. In: Proceedings of the IEEE-Eurasip Workshop on Nonlinear Signal and Image Processing, Antalya, Turkey, pp. 351–354 (1999)

    Google Scholar 

  4. Soille, P., Pesaresi, M.: Advances in mathematical morphology applied to geoscience and remote sensing. IEEE Trans. Geosci. Remote Sens. 40(9), 2042–2055 (2002)

    Article  Google Scholar 

  5. Chanussot, J., Lambert, P.: Total ordering based on space filling curves for multivalued morphology (1998)

    Google Scholar 

  6. Angulo, J.: Morphological colour operators in totally ordered lattices based on distances: Application to image filtering, enhancement and analysis. Comput. Vis. Image Underst. 107(1–2), 56–73 (2007)

    Article  Google Scholar 

  7. Bauer, H.U., Pawelzik, K.: Quantifying the neighborhood preservation of self-organizing feature maps. IEEE Trans. Neural Netw. 3(4), 570–579 (1992)

    Article  Google Scholar 

  8. Kaski, S., Lagus, K.: Comparing self-organizing maps. In: Vorbrüggen, J.C., von Seelen, W., Sendhoff, B. (eds.) ICANN 1996. LNCS, vol. 1112, pp. 809–814. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  9. Villmann, T., Der, R., Herrmann, M., Martinetz, T.: Topology preservation in self-organizing feature maps: exact definition and measurement. IEEE Trans. Neural Netw. 8(2), 256–266 (1997)

    Article  Google Scholar 

  10. Bauer, H.U., Herrmann, M., Villmann, T.: Neural maps and topographic vector quantization. Neural Netw. 12(45), 659–676 (1999)

    Article  Google Scholar 

  11. Flórez-Revuelta, F.: Ordering of the RGB space with a growing self-organizing network. application to color mathematical morphology. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3696, pp. 385–390. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Rose, N.: Hilbert-type space-filling curves (2001). http://www4.ncsu.edu/njrose/pdfFiles/HilbertCurve.pdf

  13. Falkenauer, E., Bouffouix, S.: A genetic algorithm for job shop. In: Proceedings of the IEEE International Conference on Robotics and Automation, vol. 1, pp. 824–829, April 1991

    Google Scholar 

  14. Larrañaga, P., Kuijpers, C.M.H., Murga, R.H., Inza, I., Dizdarevic, S.: Genetic algorithms for the travelling salesman problem: A review of representations and operators. Artif. Intell. Rev. 13(2), 129–170 (1999)

    Article  Google Scholar 

  15. Chevalier, E., Angulo, J.: Image adapted total ordering for mathematical morphology on multivariate images. In: Proceedings of the IEEE International Conference on Image Processing, pp. 2943–2947 (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science, Engineering and Computing, Kingston University, Penrhyn Road, Kingston upon Thames, KT1 2EE, UK

    Francisco Flórez-Revuelta

Authors
  1. Francisco Flórez-Revuelta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Francisco Flórez-Revuelta .

Editor information

Editors and Affiliations

  1. Universidad de Granada, Granada, Spain

    Antonio M. Mora

  2. Politecnico di Torino, Turin, Italy

    Giovanni Squillero

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Flórez-Revuelta, F. (2015). Topology-Preserving Ordering of the RGB Space with an Evolutionary Algorithm. In: Mora, A., Squillero, G. (eds) Applications of Evolutionary Computation. EvoApplications 2015. Lecture Notes in Computer Science(), vol 9028. Springer, Cham. https://doi.org/10.1007/978-3-319-16549-3_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-16549-3_42

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16548-6

  • Online ISBN: 978-3-319-16549-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation