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Transitions of a Multi-scale Image Hierarchy Tree

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Scale Space and Variational Methods in Computer Vision (SSVM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5567))

Abstract

In this work we describe the possible transitions for the hierarchical structure that describes an image in Gaussian scale space. Until now, this tree structure has only been used for topological segmentation. In order to perform image matching and retrieval tasks based on this structure, one needs to know which transitions are allowed when the structure is changed under influence of one control parameter. We present a list of such transitions, enabling tree edit distance operations.

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References

  1. Koenderink, J.J.: The structure of images. Biological Cybernetics 50, 363–370 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  2. Kuijper, A., Florack, L.M.J.: Hierarchical pre-segmentation without prior knowledge. In: Proceedings of the 8th ICCV, pp. 487–493 (2001)

    Google Scholar 

  3. Kuijper, A.: Exploring and exploiting the structure of saddle points in Gaussian scale space. Computer Vision and Image Understanding 112(3), 337–349 (2008)

    Article  Google Scholar 

  4. Kanters, F., Platel, B., Florack, L.M.J., ter Haar Romeny, B.: Content based image retrieval using multiscale top points. In: Griffin, L.D., Lillholm, M. (eds.) Scale-Space 2003. LNCS, vol. 2695, pp. 33–43. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Kanters, F., Lillholm, M., Duits, R., Janssen, B., Platel, B., Florack, L.M.J., ter Haar Romeny, B.: On image reconstruction from multiscale top points. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds.) Scale-Space 2005. LNCS, vol. 3459, pp. 431–442. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Platel, B., Balmachnova, E., Florack, L.M.J., Kanters, F., ter Haar Romeny, B.: Using Top-Points as Interest Points for Image Matching. In: Fogh Olsen, O., Florack, L.M.J., Kuijper, A. (eds.) DSSCV 2005. LNCS, vol. 3753, pp. 211–222. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Fogh Olsen, O.: Tree edit distances from singularity theory. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds.) Scale-Space 2005. LNCS, vol. 3459, pp. 316–326. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Lindeberg, T.: Scale-Space Theory in Computer Vision. The Kluwer International Series in Engineering and Computer Science. Kluwer Academic Publishers, Dordrecht (1994)

    Book  MATH  Google Scholar 

  9. Damon, J.: Local Morse theory for solutions to the heat equation and Gaussian blurring. Journal of Differential Equations 115(2), 386–401 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Arnold, V.I.: Catastrophe Theory. Springer, Berlin (1984)

    Book  MATH  Google Scholar 

  11. Koenderink, J.J.: A hitherto unnoticed singularity of scale-space. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(11), 1222–1224 (1989)

    Article  Google Scholar 

  12. Kuijper, A., Florack, L.M.J.: The relevance of non-generic events in scale space models. International Journal of Computer Vision 57(1), 67–84 (2004)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Fraunhofer Institute for Computer Graphics Research & TU Darmstadt, Germany

    Arjan Kuijper

Authors
  1. Arjan Kuijper
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Oslo, Norway

    Knut Mørken

  3. Simula Research Laboratory, M. Linges v 17, Fornebu, P.O.Box 134, N-1325, Lysaker, Norway

    Marius Lysaker

  4. SINTEF ICT, Oslo, Norway

    Knut-Andreas Lie

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© 2009 Springer-Verlag Berlin Heidelberg

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Kuijper, A. (2009). Transitions of a Multi-scale Image Hierarchy Tree. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_70

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  • DOI: https://doi.org/10.1007/978-3-642-02256-2_70

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02255-5

  • Online ISBN: 978-3-642-02256-2

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