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Corner Detection Using the Affine Morphological Scale Space

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Scale Space and Variational Methods in Computer Vision (SSVM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10302))

Abstract

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.

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References

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  5. Alvarez, L., Morales, F.: Affine morphological multiscale analysis of corners and multiple junctions. Int. J. Comput. Vis. 25(2), 95–107 (1997)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)

    Article  Google Scholar 

  10. Mokhtarian, F., Suomela, R.: Robust image corner detection through curvature scale space. IEEE Trans. Pattern Anal. Mach. Intell. 20(12), 1376–1381 (1998)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sapiro, G., Tannenbaum, A.: On affine plane curve evolution. J. Funct. Anal. 119(1), 79–120 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sapiro, G., Tannenbaum, A.: Affine invariant scale-space. Int. J. Comput. Vis. 11(1), 25–44 (1993)

    Article  MATH  Google Scholar 

  14. Yu, G., Morel, J.M.: ASIFT: an algorithm for fully affine invariant comparison. Image Proces. On Line 1, 11–38 (2011)

    Google Scholar 

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Acknowledgement

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

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Correspondence to Luis Alvarez .

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Alvarez, L. (2017). Corner Detection Using the Affine Morphological Scale Space. In: Lauze, F., Dong, Y., Dahl, A. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2017. Lecture Notes in Computer Science(), vol 10302. Springer, Cham. https://doi.org/10.1007/978-3-319-58771-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-58771-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58770-7

  • Online ISBN: 978-3-319-58771-4

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