GAC Application to Corner Detection Based on Eccentricity

  • Jaroslav Hrdina
  • Aleš Návrat
  • Petr VašíkEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11542)


The geometric algebra GAC offers the same efficiency for calculations with arbitrary conic sections as provided by CGA for spheres. We shall exploit these properties in image processing, particularly in corner detection. Indeed, the point cluster will be approximated by a conic section and, consequently, classified as points with ellipse–like or hyperbola–like neighbourhood. Then, by means of eccentricity, we decide whether the points form a corner.


Geometric algebras GAC Corner detection 


  1. 1.
    Dorst, L., Fontijne, D., Mann, S.: Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry, 1st edn. Morgan Kaufmann Publishers Inc., Burlington (2007)Google Scholar
  2. 2.
    Easter, R.B., Hitzer E.: Double conformal geometric algebra for quadrics and darboux cyclides. In: Proceedings of the 33rd Computer Graphics International (CGI 2016), pp. 93–96. ACM, New York (2016)Google Scholar
  3. 3.
    Hrdina, J., Návrat, A., Vašík, P.: Geometric algebra for conics. Adv. Appl. Cliord Algebras 28, 66 (2018). Scholar
  4. 4.
    Hrdina, J., Návrat, A., Vašík, P.: Conic fitting in geometric algebra setting. Adv. Appl. Clifford Algebras (2019, to appear)Google Scholar
  5. 5.
    Perwass, C.: Junction and Corner detection through the extraction and analysis of line segments. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 568–582. Springer, Heidelberg (2004). Scholar
  6. 6.
    Perwass, C.: Geometric Algebra with Applications in Engineering, 1st edn. Springer, Heidelberg (2009). Scholar
  7. 7.
    Zamora-Esquivel, J.: \(\mathbb{G}_{6,3}\) Geometric algebra; description and implementation. Adv. Appl. Cliord Algebras 24, 493 (2014). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mathematics, Faculty of Mechanical EngineeringBrno University of TechnologyBrnoCzech Republic

Personalised recommendations