Corner Detection Using the Affine Morphological Scale Space

  • Luis AlvarezEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)


We introduce a method for corner estimation based on the affine morphological scale space (AMSS). Using some explicit known formula about corner evolution across AMSS, proven by Alvarez and Morales in 1997, we define a morphological cornerness measure based on the expected evolution of an ideal corner across AMSS. We define a new procedure to track the corner motion across AMSS. To evaluate the accuracy of the method we study in details the results for a collection of synthetic corners with angles from 15 to 160\(^\circ \). We also present experiments in real images and we show that the proposed method can also automatically handle the case of multiple junctions.


Affine scale space Corner detection Morphology 



This research has partially been supported by the MINECO project reference MTM2016-75339-P (AEI/FEDER, UE) (Ministerio de Economía y Competitividad, Spain).


  1. 1.
    Alvarez, L., Cuenca, C., Esclarín, J., Mazorra, L., Morel, J.M.: Affine invariant distance using multiscale analysis. J. Math. Imaging Vis. 55(2), 199–209 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Alvarez, L., Guichard, F., Lions, P.L., Morel, J.M.: Axiomatisation et nouveaux opérateurs de la morphologie mathématique. Comptes rendus de l’Académie des sciences. Série 1, Mathématique 315(3), 265–268 (1992)Google Scholar
  3. 3.
    Alvarez, L., Guichard, F., Lions, P.L., Morel, J.M.: Axiomes et équations fondamentales du traitement d’images. (analyse multiéchelle et edp). Comptes rendus de l’Académie des sciences. Série 1, Mathématique 315(2), 135–138 (1992)Google Scholar
  4. 4.
    Alvarez, L., Guichard, F., Lions, P.L., Morel, J.M.: Axioms and fundamental equations of image processing. Arch. Ration. Mech. Anal. 123(3), 199–257 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Alvarez, L., Morales, F.: Affine morphological multiscale analysis of corners and multiple junctions. Int. J. Comput. Vis. 25(2), 95–107 (1997)CrossRefGoogle Scholar
  6. 6.
    Angenent, S., Sapiro, G., Tannenbaum, A.: On the affine heat equation for non-convex curves. J. Am. Math. Soc. 11(3), 601–634 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Demetz, O., Hafner, D., Weickert, J.: Morphologically invariant matching of structures with the complete rank transform. Int. J. Comput. Vis. 113(3), 220–232 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Harris, C., Stephens, M.: A combined corner and edge detector. In: Proceedings of Fourth Alvey Vision Conference, pp. 147–151 (1988)Google Scholar
  9. 9.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)CrossRefGoogle Scholar
  10. 10.
    Mokhtarian, F., Suomela, R.: Robust image corner detection through curvature scale space. IEEE Trans. Pattern Anal. Mach. Intell. 20(12), 1376–1381 (1998)CrossRefGoogle Scholar
  11. 11.
    Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79(1), 12–49 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Sapiro, G., Tannenbaum, A.: On affine plane curve evolution. J. Funct. Anal. 119(1), 79–120 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Sapiro, G., Tannenbaum, A.: Affine invariant scale-space. Int. J. Comput. Vis. 11(1), 25–44 (1993)CrossRefzbMATHGoogle Scholar
  14. 14.
    Yu, G., Morel, J.M.: ASIFT: an algorithm for fully affine invariant comparison. Image Proces. On Line 1, 11–38 (2011)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Departamento de Informática y SistemasUniversidad de Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain

Personalised recommendations