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.
The first two authors were supported by a grant of the Czech Science Foundation (GAČR) number 17–21360S, “Advances in Snake-like Robot Control” the last author was supported by Grant No. FSI–S–17–4464.
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References
Busin, L., Vandenbroucke, N., Macaire, L.: Color spaces and image segmentation. Adv. Imaging Electron Phys. 151, 65–168 (2008)
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)
Hildenbrand, D.: Foundations of Geometric Algebra Computing, 1st edn. Springer, Hiedelberg (2013). https://doi.org/10.1007/978-3-642-31794-1
Hildenbrand, D.: Introduction to Geometric Algebra Computing. CRC Press, Taylor & Francis Group, Boca Raton (2019)
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/s00006-016-0695-5
Hrdina, J., Návrat, A., Vašík, P.: Geometric algebra for conics. Adv. Appl. Clifford Algebr. 28, 66 (2018). https://doi.org/10.1007/s00006-018-0879-2
Hrdina, J., Návrat, A.: Binocular computer vision based on conformal geometric algebra. Adv. Appl. Clifford Algebr. 27(3), 1945–1959 (2017)
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.4489
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)
Ohta, N., Robertson, A.R.: Colorimetry: Fundamentals and Applications, 6th edn. Wiley, New York (2005)
Oleari, C.: Standard Colorimetry: Definitions, Algorithms, and Software, 1st edn. Wiley, Hoboken (2016)
Perwass, C.: Geometric Algebra with Applications in Engineering, 1st edn. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-540-89068-3
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-x
Ell, T.A., Le Bihan, N., Sangwine, S.: Quaternion Fourier Transforms for Signal and Image Processing. FOCUS Series Periodical. Wiley-ISTE, Hoboken (2014)
Acknowledgment
We would like to thank to Aleš Návrat for helpful discussions. We thank the anonymous reviewers whose comments have greatly improved this manuscript.
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Hrdina, J., Matoušek, R., Tichý, R. (2019). Colour Image Segmentation by Region Growing Based on Conformal Geometric Algebra. In: Gavrilova, M., Chang, J., Thalmann, N., Hitzer, E., Ishikawa, H. (eds) Advances in Computer Graphics. CGI 2019. Lecture Notes in Computer Science(), vol 11542. Springer, Cham. https://doi.org/10.1007/978-3-030-22514-8_56
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