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A Novel Edge Detector Based on Discrete t-norms for Noisy Images

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Topics in Medical Image Processing and Computational Vision

Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 8))

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Abstract

Image edge detection is one of the more fashionable topics in image processing and it is an important preprocessing step in many image processing techniques since its performance is crucial for the results obtained by subsequent higher-level processes. In this paper, an edge detection algorithm for noisy images, corrupted with salt and pepper noise, using a fuzzy morphology based on discrete t-norms is proposed. It is shown that this algorithm is robust when it is applied to different types of noisy images. The obtained results are objectively compared with other well-known morphological algorithms such as the ones based on the Łukasiewicz t-norm, representable and idempotent uninorms and the classical umbra approach. This comparison is addressed using some different objective measures for edge detection, such as Pratt’s figure of merit, the \(\rho \)-coefficient, and noise removal like the structural similarity index and the fuzzy \(DI\)-subsethood measure. The filtered results and the edge images obtained with our approach improve the values obtained by the other approaches.

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References

  1. Bloch I, Maître H (1995) Fuzzy mathematical morphologies: a comparative study. Pattern Recogn 28:1341–1387

    Article  Google Scholar 

  2. Bowyer K, Kranenburg C, Dougherty S (1999) Edge detector evaluation using empirical ROC curves. Comput Vis Pattern Recogn 1:354–359

    Google Scholar 

  3. Bustince H, Barrenechea E, Pagola M, Fernandez J (2009) Interval-valued fuzzy sets constructed from matrices: application to edge detection. Fuzzy Sets Syst 160(13):1819–1840

    Article  MathSciNet  MATH  Google Scholar 

  4. Bustince H, Pagola M, Barrenechea E (2007) Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images. Inform Sci 177:906–929

    Article  MathSciNet  MATH  Google Scholar 

  5. Canny J (1986) A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell 8(6):679–698

    Article  Google Scholar 

  6. González-Hidalgo M, Massanet S (2011) Towards an objective edge detection algorithm based on discrete t-norms. In: Galichet S, Montero J, Mauris G (eds) Proceedings of the 7th conference of the european society for fuzzy logic and technology (EUSFLAT-2011) and LFA-2011, Advances in Intelligent Systems Research, pp 319–326

    Google Scholar 

  7. González-Hidalgo M, Massanet S, Torrens J (2010) Discrete t-norms in a fuzzy mathematical morphology: algebraic properties and experimental results. In: Proceedings of WCCI-FUZZ-IEEE, Barcelona, Spain, pp 1194–1201

    Google Scholar 

  8. González-Hidalgo M, Massanet S, Mir A (2011) Closing and opening based on discrete t-norms. Applications to natural image analysis. In: Galichet S, Montero J, Mauris G (eds) Proceedings of the 7th conference of the European society for fuzzy logic and technology (EUSFLAT-2011) and LFA-2011, Advances in intelligent systems research, pp 358–365

    Google Scholar 

  9. M. González-Hidalgo, A. Mir-Torres, and D. Ruiz-Aguilera. A robust edge detection algorithm based on a fuzzy mathematical morphology using uninorms (\(\phi \text{ MM}\text{-U}\) morphology). In J. M. R. Tavares and R. M. N. Jorge, editors, Computational Vision and Medical Image Processing: VIPIMAGE 2009, pages 630–635, Bristol, PA, USA, 2009. CRC Press, Taylor & Francis, Inc.

    Google Scholar 

  10. González-Hidalgo M, Mir-Torres A, Ruiz-Aguilera D, Torrens J (2009) Edge-images using a uninorm-based fuzzy mathematical morphology: Opening and closing. In: Tavares J, Jorge N (eds) Advances in computational vision and medical image processing, number 13 in computational methods in applied sciences, Chap. 8, Springer, Netherlands, pp 137–157

    Google Scholar 

  11. González-Hidalgo M, Mir-Torres A, Ruiz-Aguilera D, Torrens J (2009) Image analysis applications of morphological operators based on uninorms. In: Proceedings of the IFSA-EUSFLAT 2009 Conference, Lisbon, Portugal, pp 630–635

    Google Scholar 

  12. Grigorescu C, Petkov N, Westenberg MA (2003) Contour detection based on nonclassical receptive field inhibition. IEEE Trans Image Process 12(7):729–739

    Article  Google Scholar 

  13. Jiang J-A, Chuang C-L, Lu Y-L, Fahn C-S (2007) Mathematical-morphology-based edge detectors for detection of thin edges in low-contrast regions. IET Image Process 1(3):269–277

    Google Scholar 

  14. Kovesi PD MATLAB and Octave functions for computer vision and image processing. Centre for exploration targeting, school of earth and environment, the university of western australia. http://www.csse.uwa.edu.au/~pk/research/matlabfns/

  15. Mayor G, Torrens J (2005) Triangular norms in discrete settings. In: Klement E, Mesiar R (eds) Logical, Algebraic, Analytic, and Probabilistic aspects of triangular norms, Chap. 7, Elsevier, Amsterdam, pp 189–230

    Google Scholar 

  16. Nachtegael M, Kerre E (2000) Classical and fuzzy approaches towards mathematical morphology. In: Kerre EE, Nachtegael M (eds) Fuzzy techniques in image processing, number 52 in studies in fuzziness and soft computing, Chap. 1, Physica, New York, pp 3–57

    Google Scholar 

  17. Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man and Cybern 9:62–66

    Article  Google Scholar 

  18. Pratt WK (2007) Digital image processing. 4 edn. Wiley-Interscience, New York

    Google Scholar 

  19. Serra J (1982,1988) Image analysis and mathematical morphology. vols. 1, 2. Academic Press, London

    Google Scholar 

  20. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: From error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612

    Article  Google Scholar 

  21. Zhang TY, Suen CY (1984) A fast parallel algorithm for thinning digital patterns. Commun ACM 27:236–239

    Article  Google Scholar 

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Acknowledgments

This paper has been partially supported by the Spanish Grant MTM2009-10320 with FEDER support.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of the Balearic Islands, 07122, Palma de Mallorca, Spain

    M. González-Hidalgo, S. Massanet & A. Mir

Authors
  1. M. González-Hidalgo
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  2. S. Massanet
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  3. A. Mir
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Corresponding author

Correspondence to M. González-Hidalgo .

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Editors and Affiliations

  1. Faculdade de Engenharia, Departamento de Engenharia Mecânica, Universidade do Porto, Dr. Roberto Frias, Porto, 4200-465, Portugal

    João Manuel R.S. Tavares

  2. Faculdade de Engenharia, Departamento de Engenharia Mecânica, Universidade do Porto, Porto, Porto, 4200-465, Portugal

    Renato M. Natal Jorge

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González-Hidalgo, M., Massanet, S., Mir, A. (2013). A Novel Edge Detector Based on Discrete t-norms for Noisy Images. In: Tavares, J., Natal Jorge, R. (eds) Topics in Medical Image Processing and Computational Vision. Lecture Notes in Computational Vision and Biomechanics, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0726-9_6

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  • DOI: https://doi.org/10.1007/978-94-007-0726-9_6

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0725-2

  • Online ISBN: 978-94-007-0726-9

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