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Abstract

An attribute opening is an idempotent, anti-extensive and increasing operator that removes, in the case of binary images, all the connected components (CC) which do not fulfil a given criterion. When the increasingness property is dropped, more general algebraic thinnings are obtained. We propose in this paper, to use criteria based on the geodesic diameter to build algebraic thinnings for greyscale images. An application to the extraction of cracks is then given to illustrate the performance of the proposed filters. Finally, we will discuss the advantages of these new operators compared to other methods.

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References

  1. Appleton, B., Talbot, H.: Efficient path openings and closings. Mathematical Morphology: 40 Years On, pp. 33–42 (2005)

    Google Scholar 

  2. Beucher, S., Blosseville, J.M., Lenoir, F.: Traffic spatial measurements using video image processing. In: Intelligent Robots and Computer Vision. Proc. SPIE, vol. 848, pp. 648–655 (1987)

    Google Scholar 

  3. Braga-Neto, U.: Alternating sequential filters by adaptive-neighborhood structuring functions. Mathematical Morphology and its Applications to Image and Signal Processing, 139–146 (1996)

    Google Scholar 

  4. Breen, E.J., Jones, R.: Attribute openings, thinnings, and granulometries. Computer Vision and Image Understanding 64(3), 377–389 (1996)

    Article  Google Scholar 

  5. Lantuéjoul, C., Maisonneuve, F.: Geodesic methods in quantitative image analysis. Pattern Recognition 17(2), 177–187 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  6. Matheron, G.: Random sets and integral geometry, vol. 9. Wiley, New York (1975)

    MATH  Google Scholar 

  7. Salembier, P., Oliveras, A., Garrido, L.: Antiextensive connected operators for image and sequence processing. IEEE Transactions on Image Processing 7, 555–570 (1998)

    Article  Google Scholar 

  8. Salembier, P., Wilkinson, M.H.F.: Connected operators. IEEE Signal Processing Magazine 26(6), 136–157 (2009)

    Article  Google Scholar 

  9. Serra, J.: Image analysis and mathematical morphology. Academic, London (1982)

    MATH  Google Scholar 

  10. Serra, J., Vincent, L.: An overview of morphological filtering. Circuits Syst. Signal Process. 11(1), 47–108 (1992), http://portal.acm.org/citation.cfm?id=150488

    Article  MathSciNet  MATH  Google Scholar 

  11. Talbot, H., Appleton, B.: Efficient complete and incomplete path openings and closings. Image and Vision Computing 25(4), 416–425 (2007)

    Article  Google Scholar 

  12. Urbach, E., Wilkinson, M.: Shape-only granulometries and gray-scale shape filters. In: Mathematical Morphology: Proceedings of the VIth International Symposium, ISMM 2002, p. 305. Csiro (2002)

    Google Scholar 

  13. Vincent, L.: Grayscale area openings and closings, their efficient implementation and applications. In: First Workshop on Mathematical Morphology and its Applications to Signal Processing, pp. 22–27 (1993)

    Google Scholar 

  14. Wilkinson, M.H.F., Westenberg, M.A.: Shape preserving filament enhancement filtering. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 770–777. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

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Morard, V., Decencière, E., Dokladal, P. (2011). Geodesic Attributes Thinnings and Thickenings. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds) Mathematical Morphology and Its Applications to Image and Signal Processing. ISMM 2011. Lecture Notes in Computer Science, vol 6671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21569-8_18

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  • DOI: https://doi.org/10.1007/978-3-642-21569-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21568-1

  • Online ISBN: 978-3-642-21569-8

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