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 to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aptoula, E., Lefèvre, S.: A comparative study on multivariate mathematical morphology. Pattern Recogn. 40(11), 2914–2929 (2007)
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)
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)
Soille, P., Pesaresi, M.: Advances in mathematical morphology applied to geoscience and remote sensing. IEEE Trans. Geosci. Remote Sens. 40(9), 2042–2055 (2002)
Chanussot, J., Lambert, P.: Total ordering based on space filling curves for multivalued morphology (1998)
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)
Bauer, H.U., Pawelzik, K.: Quantifying the neighborhood preservation of self-organizing feature maps. IEEE Trans. Neural Netw. 3(4), 570–579 (1992)
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)
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)
Bauer, H.U., Herrmann, M., Villmann, T.: Neural maps and topographic vector quantization. Neural Netw. 12(45), 659–676 (1999)
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)
Rose, N.: Hilbert-type space-filling curves (2001). http://www4.ncsu.edu/njrose/pdfFiles/HilbertCurve.pdf
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
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)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights 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)