Skip to main content
SpringerLink
Log in

Fuzzy Hit-or-Miss Transform Using the Fuzzy Mathematical Morphology Based on T-norms

  • Conference paper
Aggregation Functions in Theory and in Practise

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 228))

  • 1179 Accesses

Abstract

The extension of the Hit-or-Miss transform (HMT) to grey-level images is difficult due to the problem of defining the complement of an image in this context. Thus, several extensions have been proposed in the literature avoiding the use of the complement. However, in the fuzzy framework, the complement is well-established by means of a fuzzy negation and the binary HMT can be extended preserving its geometrical interpretation. In this paper, we extend the binary HMT to a fuzzy HMT (FHMT) using the mathematical morphology based on t-norms. Some properties of this operator are studied and some initial experimental results are presented proving the potential of the FHMT in shape recognition and pattern matching.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Al-Omari, M., Qahwaji, R., Colak, T., Ipson, S.: Morphological-based filtering of noise: Practical study on solar images. In: IEEE International Conference on Signal Processing and Communications, ICSPC 2007, pp. 1075–1078 (2007)

    Google Scholar 

  2. Aptoula, E., Lefèvre, S., Ronse, C.: A hit-or-miss transform for multivariate images. Pattern Recogn. Lett. 30(8), 760–764 (2009), http://dx.doi.org/10.1016/j.patrec.2009.02.007 , doi:10.1016/j.patrec.2009.02.007

    Article  Google Scholar 

  3. Baczyński, M., Jayaram, B. (eds.): Fuzzy Implications. STUDFUZZ, vol. 231. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  4. Barat, C., Ducottet, C., Jourlin, M.: Pattern matching using morphological probing. In: Proc. of Int. Conf. on Image Processing, ICIP 2003, vol. 1, pp. 369–372 (2003), doi:10.1109/ICIP.2003.1246975

    Google Scholar 

  5. Beliakov, G., Pradera, A., Calvo, T. (eds.): Aggregation Functions: A Guide for Practitioners. STUDFUZZ, vol. 221. Springer, Heidelberg (2007)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Bloomberg, D.S., Maragos, P.: Generalized hit-miss operators. Proc SPIE 1350, Image Algebra and Morphological Image Processing 116, 116–128 (1990), http://dx.doi.org/10.1117/12.23580 , doi:10.1117/12.23580

    Article  Google Scholar 

  8. Bouraoui, B., Ronse, C., Baruthio, J., Passat, N., Germain, P.: 3D segmentation of coronary arteries based on advanced mathematical morphology techniques. Computerized Medical Imaging and Graphics 34(5), 377–387 (2010), http://www.sciencedirect.com/science/article/pii/S0895611110000121 , doi:10.1016/j.compmedimag.2010.01.001

    Article  Google Scholar 

  9. De Baets, B.: Fuzzy morphology: A logical approach. In: Ayyub, B.M., Gupta, M.M. (eds.) Uncertainty Analysis in Engineering and Science: Fuzzy Logic, Statistics, and Neural Network Approach, pp. 53–68. Kluwer Academic Publishers, Norwell (1997)

    Google Scholar 

  10. Deng, T.Q.: Fuzzy logic and mathematical morphology. Tech. rep., Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands (2000)

    Google Scholar 

  11. Dimitrova, D., Popov, A.: Finding face features in color images using fuzzy hit-or-miss transform. In: Proceedings of the 9th WSEAS International Conference on Fuzzy Systems, FS 2008, pp. 79–84. World Scientific and Engineering Academy and Society (WSEAS), Stevens Point (2008), http://dl.acm.org/citation.cfm?id=1416056.1416069

    Google Scholar 

  12. González, M., Ruiz-Aguilera, D., Torrens, J.: Algebraic properties of fuzzy morphological operators based on uninorms. In: Artificial Intelligence Research and Development. Frontiers in Artificial Intelligence and Applications, vol. 100, pp. 27–38. IOS Press, Amsterdam (2003)

    Google Scholar 

  13. González-Hidalgo, M., Mir-Torres, A., Ruiz-Aguilera, D., Torrens, J.: Fuzzy morphology based on uninorms: Image edge-detection. opening and closing. In: Tavares, J., Jorge, N. (eds.) Computational Vision and Medical Image Processing, pp. 127–133. Taylor & Francis Group, London (2008)

    Google Scholar 

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

    Google Scholar 

  15. Heijmaans, H.: Morphological Image Operators. Academic Press, Boston (1994)

    Google Scholar 

  16. Intajag, S., Paithoonwatanakij, K.: Automated boundary extraction by gradient fuzzy gray-scale hit-or-miss transformation. In: The 2000 IEEE Asia-Pacific Conference on Circuits and Systems, IEEE APCCAS 2000, pp. 465–468 (2000), doi:10.1109/APCCAS.2000.913537

    Google Scholar 

  17. Intajag, S., Paithoonwatanakij, K., Cracknell, A.: Iterative satellite image segmentation by fuzzy hit-or-miss and homogeneity index. IEEE Proceedings on Vision, Image and Signal Processing 153(2), 206–214 (2006), doi:10.1049/ip-vis:20045211

    Article  Google Scholar 

  18. Jin, X., Davis, C.: Vector-guided vehicle detection from high-resolution satellite imagery. In: Proceedings of IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2004, vol. 2, pp. 1095–1098 (2004), doi:10.1109/IGARSS.2004.1368603

    Google Scholar 

  19. Khosravi, M., Schafer, R.W.: Template matching based on a grayscale hit-or-miss transform. IEEE Trans. Image Processing 5(6), 1060–1066 (1996)

    Article  Google Scholar 

  20. Klement, E., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  21. Lefèvre, S., Weber, J.: Automatic building extraction in VHR images using advanced morphological operators. In: Urban Remote Sensing Joint Event, pp. 1–5 (2007), 10.1109/URS.2007.371825

    Google Scholar 

  22. Mansoor, A.B., Mian, A.S., Khan, A., Khan, S.A.: Fuzzy morphology for edge detection and segmentation. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Paragios, N., Tanveer, S.-M., Ju, T., Liu, Z., Coquillart, S., Cruz-Neira, C., Müller, T., Malzbender, T. (eds.) ISVC 2007, Part II. LNCS, vol. 4842, pp. 811–821. Springer, Heidelberg (2007), http://dl.acm.org/citation.cfm?id=1779090.1779177

    Chapter  Google Scholar 

  23. Matheron, G.: Random Sets and Integral Geometry. Wiley (1975)

    Google Scholar 

  24. Murray, P., Marshall, S.: A new design tool for feature extraction in noisy images based on grayscale hit-or-miss transforms. IEEE T. Image Process. 20(7), 1938–1948 (2011), doi:10.1109/TIP.2010.2103952

    Article  MathSciNet  Google Scholar 

  25. Nachtegael, M., Kerre, E.E.: Classical and fuzzy approaches towards mathematical morphology. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing. STUDFUZZ, vol. 52, ch. 1, Physica-Verlag, New York (2000)

    Google Scholar 

  26. Naegel, B., Passat, N., Ronse, C.: a) Grey-level hit-or-miss transforms-Part I: Unified theory. Pattern Recognition 40, 635–647 (2007)

    Article  MATH  Google Scholar 

  27. Naegel, B., Passat, N., Ronse, C.: b) Grey-level hit-or-miss transforms-Part II: Application to angiographic image processing. Pattern Recognition 40, 648–658 (2007)

    Article  MATH  Google Scholar 

  28. Ouyang, Y.: On fuzzy implications determined by aggregation operators. Inform. Sci. 193, 153–162 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  29. Perret, B., Lefèvre, S., Collet, C.: A robust hit-or-miss transform for template matching applied to very noisy astronomical images. Pattern Recognition 42, 2470–2480 (2009)

    Article  MATH  Google Scholar 

  30. Popov, A.T.: General approach for fuzzy mathematical morphology. In: Proc. of 8th International Symposium on Mathematical Morphology (ISMM), pp. 39–48 (2007)

    Google Scholar 

  31. Raducanu, B., Graña, M.: A grayscale hit-or-miss transform based on level sets. In: Proc. IEEE Intl. Conf. Image Processing, Vancouver, BC, Canada, pp. 931–933 (2000)

    Google Scholar 

  32. Raducanu, B., Graña, M., Albizuri, X., d’Anjou, A.: A probabilistic hit-and-miss transform for face localization. Pattern Anal. Appl. 7(2), 117–127 (2004), http://dx.doi.org/10.1007/s10044-004-0207-4 , doi:10.1007/s10044-004-0207-4

    Article  MathSciNet  Google Scholar 

  33. Ronse, C.: A lattice-theoretical morphological view on template extraction in images. Journal of Visual Communication and Image Representation 7(3), 273–295 (1996), http://www.sciencedirect.com/science/article/pii/S1047320396900243 , doi:10.1006/jvci.1996.0024

    Article  Google Scholar 

  34. Schaefer, R., Casasent, D.: Nonlinear optical hit—miss transform for detection. Appl. Opt. 34(20), 3869–3882 (1995), http://ao.osa.org/abstract.cfm?URI=ao-34-20-3869 , doi:10.1364/AO.34.003869

    Article  Google Scholar 

  35. Serra, J.: Image analysis and mathematical morphology, vol. 1. Academic Press, London (1982)

    MATH  Google Scholar 

  36. Sinha, D., Sinha, P., Douherty, E., Batman, S.: Design and analysis of fuzzy morphological algorithms for image processing. IEEE Trans on Fuzzy Systems 5(4) (1997)

    Google Scholar 

  37. Soille, P.: Morphological Image Analysis, 2nd edn. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  38. Stankov, K., He, D.C.: Building detection in very high spatial resolution multispectral images using the hit-or-miss transform. IEEE Geosci. Remote S. 10(1), 86–90 (2013)

    Article  Google Scholar 

  39. Velasco-Forero, S., Angulo, J.: Hit-or-miss transform in multivariate images. In: Blanc-Talon, J., Bone, D., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2010, Part I. LNCS, vol. 6474, pp. 452–463. Springer, Heidelberg (2010), http://dx.doi.org/10.1007/978-3-642-17688-342

    Chapter  Google Scholar 

  40. Wang, M., Leung, Y., Zhou, C., Pei, T., Luo, J.: A mathematical morphology based scale space method for the mining of linear features in geographic data. Data Min. Knowl. Disc. 12, 97–118 (2006), http://dx.doi.org/10.1007/s10618-005-0021-7 , doi:10.1007/s10618-005-0021-7

    Article  MathSciNet  Google Scholar 

  41. Weber, J., Lefèvre, S.: Spatial and spectral morphological template matching. Image and Vision Computing 30, 934–945 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    M. González-Hidalgo, S. Massanet, A. Mir & D. Ruiz-Aguilera

Authors
  1. M. González-Hidalgo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Massanet
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Mir
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Ruiz-Aguilera
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. González-Hidalgo .

Editor information

Editors and Affiliations

  1. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Humberto Bustince

  2. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Javier Fernandez

  3. Department of Mathematics and, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  4. Department of Computer Science, Universidad de Alcalá de Henares, Madrid, Spain

    Tomasa Calvo

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

González-Hidalgo, M., Massanet, S., Mir, A., Ruiz-Aguilera, D. (2013). Fuzzy Hit-or-Miss Transform Using the Fuzzy Mathematical Morphology Based on T-norms. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39165-1_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation