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Processing Multispectral Images via Mathematical Morphology

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Visualization and Processing of Higher Order Descriptors for Multi-Valued Data

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

In this chapter, we illustrate how to process multispectral and hyperspectral images via mathematical morphology. First, according to the number of channels the data are embeded into a sufficiently high dimensional space. This transformation utilizes a special geometric structure, namely double hypersimplices, for further processing the data. For example, RGB-color images are transformed into points within a specific double hypersimplex. It is explained in detail how to calculate the supremum and infimum of samples of those transformed data to allow for the meaningful definition of morphological operations such as dilation and erosion and in a second step top hats, gradients, and morphological Laplacian. Finally, numerical results are presented to explore the advantages and shortcomings of the new proposed approach.

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Notes

  1. 1.

    https://engineering.purdue.edu/~biehl/MultiSpec/hyperspectral.html.

References

  1. Angula, J., Lefèvre, S., Lezoray, O.: Color representation and processing in polar color spaces. In: Fernandez-Maloigne, C., Robert-Inacio, F., Macaire, L. (eds.) Digital Color Imaging, pp. 1–40. Wiley-ISTE, Hoboken, New Jersey (2013)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  3. Banon, G.J.F., Barrera, J., Braga-Neto, U.d.M., Hirata, N.S.T. (eds.): Proceedings of the 8th International Symposium on Mathematical Morphology: Volume 1 - Full Papers. Computational Imaging and Vision, vol. 1. Instituto Nacional de Pesquisas Espaciais (INPE), São José dos Campos (2007)

    Google Scholar 

  4. Braun, K.M., Balasubramanian, R., Eschbach, R.: Development and evaluation of six gamut-mapping algorithms for pictorial images. In: Color Imaging Conference, pp. 144–148. IS&T - The Society for Imaging Science and Technology, Springfield (1999)

    Google Scholar 

  5. Burgeth, B., Kleefeld, A.: Morphology for color images via Loewner order for matrix fields. In: Luengo Hendriks, C.L., Borgefors, G., Strand, R. (eds.) Mathematical Morphology and Its Applications to Signal and Image Processing (Proceedings of the 11th International Symposium on Mathematical Morphology, Uppsala, 27–29 May). Lecture Notes in Computer Science, vol. 7883, pp. 243–254. Springer, Berlin (2013)

    Chapter  Google Scholar 

  6. Burgeth, B., Kleefeld, A.: An approach to color-morphology based on einstein addition and loewner order. Pattern Recognit. Lett. 47, 29–39 (2014)

    Article  Google Scholar 

  7. Burgeth, B., Papenberg, N., Bruhn, A., Welk, M., Feddern, C., Weickert, J.: Mathematical morphology based on the loewner ordering for tensor data. In: Ronse, C., Najman, L., Decencière, E. (eds.) Mathematical Morphology: 40 Years On, Computational Imaging and Vision, vol. 30, pp. 407–418. Springer, Dordrecht (2005)

    Chapter  Google Scholar 

  8. Burgeth, B., Welk, M., Feddern, C., Weickert, J.: Mathematical morphology on tensor data using the loewner ordering. In: Weickert, H.H.J. (ed.) Visualization and Processing of Tensor Fields. Springer, Berlin (2006)

    Google Scholar 

  9. Comer, M.L., Delp, E.J.: Morphological operations for color image processing. J. Electron. Imaging 8(3), 279–289 (1999)

    Article  Google Scholar 

  10. Heijmans, H.J.A.M.: Morphological Image Operators. Academic, Boston (1994)

    MATH  Google Scholar 

  11. Luengo Hendriks, C.L., Borgefors, G., Strand, R. (eds.): Mathematical morphology and its applications to image and signal processing. In: Proceedings of the 11th International Symposium on Mathematical Morphology. Lecture Notes in Computer Science, vol. 7883. Springer, Berlin (2013)

    Google Scholar 

  12. Matheron, G.: Eléments pour une théorie des milieux poreux. Masson, Paris (1967)

    Google Scholar 

  13. Matheron, G.: Random Sets and Integral Geometry. Wiley, New York (1975)

    MATH  Google Scholar 

  14. Ostwald, W.: Die Farbenfibel. Unesma, Leipzig (1916)

    Google Scholar 

  15. Ronse, C., Serra, J.: Algebraic foundations of morphology. In: Najman, L., Talbot, H. (eds.) Mathematical Morphology: From Theory to Applications, Chap. 2, pp. 35–80. ISTE/Wiley, London (2010)

    Google Scholar 

  16. Ronse, C., Najman, L., Decencière, E. (eds.): Mathematical Morphology: 40 Years On, Computational Imaging and Vision, vol. 30. Springer, Dordrecht (2005)

    Google Scholar 

  17. Serra, J.: Echantillonnage et estimation des phénomènes de transition minier. Ph.D. thesis, University of Nancy, France (1967)

    Google Scholar 

  18. Serra, J.: Image Analysis and Mathematical Morphology, vol. 1. Academic, London (1982)

    Google Scholar 

  19. Serra, J.: The false colour problem. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.) Mathematical Morphology and Its Application to Signal and Image Processing. Proceedings of the 9th International Symposium on Mathematical Morphology. Lecture Notes in Computer Science, vol. 5720, Chap. 2, pp. 13–23. Springer, Heidelberg (2009)

    Google Scholar 

  20. Serra, J., Soille, P. (eds.): Mathematical Morphology and Its Applications to Image Processing. Computational Imaging and Vision, vol. 2. Kluwer, Dordrecht (1994)

    Google Scholar 

  21. Soille, P.: Morphological Image Analysis, 2nd edn. Springer, Berlin (2003)

    MATH  Google Scholar 

  22. Soille, P., Pesaresi, M., Ouzounis, G. (eds.): Mathematical Morphology and Its Applications to Image and Signal Processing. Proceedings of the 10th International Symposium on Mathematical Morphology. Lecture Notes in Computer Science, vol. 6671. Springer, Berlin (2011)

    Google Scholar 

  23. Ungar, A.A.: Einstein’s special relativity: the hyperbolic geometric viewpoint. In: Conference on Mathematics, Physics and Philosophy on the Interpretations of Relativity, II. Budapest (2009)

    Google Scholar 

  24. van de Gronde, J.J., Roerdink, J.B.T.M.: Group-invariant frames for colour morphology. In: Luengo Hendriks, C.L., Borgefors, G., Strand, R. (eds.) Mathematical Morphology and Its Applications to Signal and Image Processing (Proceedings of the 11th International Symposium on Mathematical Morphology, Uppsala, 27–29 May). Lecture Notes in Computer Science, vol. 7883, pp. 267–278. Springer, Berlin (2013)

    Chapter  Google Scholar 

  25. Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds.): Mathematical Morphology and Its Application to Signal and Image Processing. Proceedings of the 9th International Symposium on Mathematical Morphology. Lecture Notes in Computer Science, vol. 5720. Springer, Heidelberg (2009)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Natural Sciences and Computer Science, Brandenburg University of Technology Cottbus, 03046, Cottbus, Germany

    Andreas Kleefeld

  2. Faculty of Mathematics and Computer Science, Saarland University, 66041, Saarbrücken, Germany

    Bernhard Burgeth

Authors
  1. Andreas Kleefeld
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  2. Bernhard Burgeth
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Corresponding author

Correspondence to Andreas Kleefeld .

Editor information

Editors and Affiliations

  1. Linköping University, Norrköping, Sweden

    Ingrid Hotz

  2. Visualization and Medical Image Analysis, University of Bonn, Bonn, Germany

    Thomas Schultz

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Kleefeld, A., Burgeth, B. (2015). Processing Multispectral Images via Mathematical Morphology. In: Hotz, I., Schultz, T. (eds) Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-15090-1_7

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