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Persistence Based on LBP Scale Space

  • Ines JanuschEmail author
  • Walter G. Kropatsch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9667)

Abstract

This paper discusses the connection between the texture operator LBP (local binary pattern) and an application of LBPs to persistent homology. A shape representation - the LBP scale space - is defined as a filtration based on the variation of an LBP parameter. A relation between the LBP scale space and a variation of thresholds used in the segmentation of a graylevel image is discussed. Using the LBP scale space a characterization of (parts of) shapes is demonstrated based on simple shape primitives, the observations may also be generalized for smooth curves. The LBP scale space is augmented by associating it with polar coordinates (with the origin located at the LBP center). In this way a procedure of shape reconstruction based on the LBP scale space is defined and its reconstruction accuracy is demonstrated in an experiment. Furthermore, this augmented LBP scale space representation is invariant to translation and rotation of the shape.

Keywords

LBP Persistence Scale space Filtration Shape analysis Shape reconstruction Segmentation 

Notes

Acknowledgments

We thank the anonymous reviewers for their constructive comments.

References

  1. 1.
    Biasotti, S., De Floriani, L., Falcidieno, B., Frosini, P., Giorgi, D., Landi, C., Papaleo, L., Spagnuolo, M.: Describing shapes by geometrical-topological properties of real functions. ACM Comput. Surv. (CSUR) 40(4), 12 (2008)CrossRefGoogle Scholar
  2. 2.
    Verri, A., Uras, C., Frosini, P., Ferri, M.: On the use of size functions for shape analysis. Biol. Cybern. 70(2), 99–107 (1993)CrossRefzbMATHGoogle Scholar
  3. 3.
    Carlsson, G., Zomorodian, A., Collins, A., Guibas, L.J.: Persistence barcodes for shapes. Int. J. Shape Model. 11(02), 149–187 (2005)CrossRefzbMATHGoogle Scholar
  4. 4.
    Cerri, A., Di Fabio, B., Medri, F.: Multi-scale approximation of the matching distance for shape retrieval. In: Ferri, M., Frosini, P., Landi, C., Cerri, A., Di Fabio, B. (eds.) CTIC 2012. LNCS, vol. 7309, pp. 128–138. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  5. 5.
    Ghrist, R.: Barcodes: the persistent topology of data. Bull. Am. Math. Soc. 45(1), 61–75 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Biasotti, S., Giorgi, D., Spagnuolo, M., Falcidieno, B.: Reeb graphs for shape analysis and applications. Theoret. Comput. Sci. 392(13), 5–22 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Ojala, T., Pietikäinen, M., Harwood, D.: A comparative study of texture measures with classification based on featured distributions. Pattern Recogn. 29(1), 51–59 (1996)CrossRefGoogle Scholar
  8. 8.
    Pietikäinen, M., Hadid, A., Zhao, G., Ahonen, T.: Computer vision using local binary patterns. Computational Imaging and Vision. Springer, London (2011)CrossRefGoogle Scholar
  9. 9.
    Chen, J., Kellokumpu, V., Zhao, G., Pietikäinen, M.: RLBP: robust local binary pattern. In: Proceedings of the British Machine Vision Conference (2013)Google Scholar
  10. 10.
    Janusch, I., Kropatsch, W.G.: Shape classification according to LBP persistence of critical points. In: Normand, N., Guédon, J., Autrusseau, F. (eds.) DGCI 2016. LNCS, vol. 9647, pp. 166–177. Springer, Heidelberg (2016). doi: 10.1007/978-3-319-32360-2_13 CrossRefGoogle Scholar
  11. 11.
    Gonzalez-Diaz, R., Kropatsch, W.G., Cerman, M., Lamar, J.: Characterizing configurations of critical points through LBP. In: Computational Topology in Image Context (2014)Google Scholar
  12. 12.
    Edelsbrunner, H.: Persistent homology: theory and practice (2014)Google Scholar
  13. 13.
    Sebastian, T., Klein, P., Kimia, B.: Recognition of shapes by editing shock graphs. In: International Conference on Computer Vision, vol. 1, pp. 755–762. IEEE Computer Society (2001)Google Scholar
  14. 14.
    Kropatsch, W.G., Ion, A., Haxhimusa, Y., Flanitzer, T.: The eccentricity transform (of a digital shape). In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds.) DGCI 2006. LNCS, vol. 4245, pp. 437–448. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Matas, J., Chum, O., Urban, M., Pajdla, T.: Robust wide-baseline stereo from maximally stable extremal regions. Image Vis. Comput. 22(10), 761–767 (2004)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Pattern Recognition and Image Processing Group, Institute of Computer Graphics and AlgorithmsTU WienViennaAustria

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