Advertisement

Colour Image Segmentation by Region Growing Based on Conformal Geometric Algebra

  • Jaroslav HrdinaEmail author
  • Radek Matoušek
  • Radek Tichý
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11542)

Abstract

We apply conformal geometric algebra (CGA) to classical algorithms for colour image segmentation. Particularly, we modify standard Prewitt quaternionic filter for edge detection and region growing segmentation procedure and use them simultaneously, which is only allowed by common CGA language, more precisely by the notion of flat point in normalised and unnormalised form.

Keywords

Conformal geometric algebra Image segmentation Region growing Flat point 

Notes

Acknowledgment

We would like to thank to Aleš Návrat for helpful discussions. We thank the anonymous reviewers whose comments have greatly improved this manuscript.

References

  1. 1.
    Busin, L., Vandenbroucke, N., Macaire, L.: Color spaces and image segmentation. Adv. Imaging Electron Phys. 151, 65–168 (2008)CrossRefGoogle Scholar
  2. 2.
    Dorst, L., Fontijne, D., Mann, S.: Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry, 1st edn. Morgan Kaufmann Publishers Inc., San Francisco (2007)Google Scholar
  3. 3.
    Hildenbrand, D.: Foundations of Geometric Algebra Computing, 1st edn. Springer, Hiedelberg (2013).  https://doi.org/10.1007/978-3-642-31794-1CrossRefzbMATHGoogle Scholar
  4. 4.
    Hildenbrand, D.: Introduction to Geometric Algebra Computing. CRC Press, Taylor & Francis Group, Boca Raton (2019)zbMATHGoogle Scholar
  5. 5.
    Hrdina, J., Návrat, A., Vašík, P., Matoušek, R.: CGA-based robotic snake contol. Adv. Appl. Clifford Algebr. 27(1), 621–632 (2017).  https://doi.org/10.1007/s00006-016-0695-5MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Hrdina, J., Návrat, A., Vašík, P.: Geometric algebra for conics. Adv. Appl. Clifford Algebr. 28, 66 (2018).  https://doi.org/10.1007/s00006-018-0879-2MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Hrdina, J., Návrat, A.: Binocular computer vision based on conformal geometric algebra. Adv. Appl. Clifford Algebr. 27(3), 1945–1959 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hrdina, J., Vašík, P., Matoušek, R., Návrat, A.: Geometric algebras for uniform colour spaces. Math. Methods Appl. Sci. 41(11), 4117–4130 (2018).  https://doi.org/10.1002/mma.4489MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Janku, P., Kominkova Oplatkova, Z., Dulik, T., Snopek, P., Liba, J.: Fire detection in video stream by using simple artificial neural network. MENDEL 24(2), 55–60 (2018)CrossRefGoogle Scholar
  10. 10.
    Ohta, N., Robertson, A.R.: Colorimetry: Fundamentals and Applications, 6th edn. Wiley, New York (2005)CrossRefGoogle Scholar
  11. 11.
    Oleari, C.: Standard Colorimetry: Definitions, Algorithms, and Software, 1st edn. Wiley, Hoboken (2016)Google Scholar
  12. 12.
    Perwass, C.: Geometric Algebra with Applications in Engineering, 1st edn. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-540-89068-3CrossRefzbMATHGoogle Scholar
  13. 13.
    Sangwine, S.J., Hitzer, E.: Clifford multivector toolbox (for MATLAB). Adv. Appl. Clifford Algebr. 27, 539–558 (2017).  https://doi.org/10.1007/s00006-016-0666-xMathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Ell, T.A., Le Bihan, N., Sangwine, S.: Quaternion Fourier Transforms for Signal and Image Processing. FOCUS Series Periodical. Wiley-ISTE, Hoboken (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringBrno University of TechnologyBrnoCzech Republic

Personalised recommendations