Skip to main content
SpringerLink
Log in

Variable Precision Fuzzy Hit-or-Miss Transformation Models to Object Identification in Grey-Scale Images

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

Morphological image operators are important geometry-based image transformations, whereas fuzzy set theory and fuzzy logic, favoured for their ability to describe and cope with imprecise and uncertain natures of objects, are successfully applied to image processing and pattern recognition. In this paper, generalizations of hit-or-miss transformation (HMT) for grey-scale images are investigated in the framework of fuzzy set theory and fuzzy logic. To address the problem of robust object identification, a notion of fuzzy vertical translation is proposed and two variable precision fuzzy HMT models are developed for grey-scale images to cater for flexible selection of structuring elements in the fuzzy setting. Their extensions to the rank case are designed to adapt the HMT to noisy images and images with inhomogeneous intensities. Superior performance of the proposed models over the state-of-the-art HMT models in objection extraction is verified by a series of experiments on synthetic images and real images.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Agam, G., Dinstein, I.: Regulated morphological operators. Pattern Recogn. 32(6), 947–971 (1999)

    Article  Google Scholar 

  2. Andreopoulos, A., Tsotsos, J.K.: 50 years of object recognition: Directions forward. Comput. Vis. Image Underst. 117, 827–891 (2013)

    Article  Google Scholar 

  3. Barat, C., Ducottet, C., Jourlin M.: Pattern matching using morphological probing. In: Proc. International Conference on Image Process. pp. 369–372 (2003)

  4. Bloch, I., Maître, H.: Fuzzy mathematical morphologies: a comparative study. Pattern Recogn. 28(9), 1341–1387 (1995)

    Article  Google Scholar 

  5. Bloch, I.: Lattice fuzzy sets and bipolar fuzzy sets, and mathematical morphology. Inform. Sci. 181(10), 2002–2015 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bloomberg, D.S., Vincent, L.M.: Pattern matching using the blur hit-or-miss transform. J. Electron. Imaging 9, 140–150 (2000)

    Article  Google Scholar 

  7. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  8. De Baets, B., Kerre, E., Gupta, M.: The fundamentals of fuzzy mathematical morphology, part I: basic concepts. Int. J. Gen. Syst. 23, 155–171 (1994)

    Article  Google Scholar 

  9. De Baets, B., Kerre, E., Gupta, M.: The fundamentals of fuzzy mathematical morphology, part II: idempotence, convexity and decomposition. Int. J. Gen. Syst. 23, 307–322 (1995)

    Article  MATH  Google Scholar 

  10. Deng, T., Chen, Y.: Generalized fuzzy morphological operators. Fuzzy Systems and Knowledge Discovery. LNCS, vol. 3614, pp. 275–284 (2005)

  11. Deng, T., Heijmans, H.: Grey-scale morphology based on fuzzy logic. J. Math. Imaging Vis. 16(2), 155–171 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Gasterators, A., Andreadis, I., Tsalides, Ph: Fuzzy soft mathematical morphology. IEE Proc. Vis. Image Signal Process. 145(1), 41–49 (1998)

    Article  Google Scholar 

  13. Harvey N., Porter R., Theiler J.: Ship detection in satellite imagery using rank-order grey-scale hit-or-miss transforms. http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-10-01553 (2010)

  14. Heijmans, H.: Theoretical aspects of gray-level morphology. IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 568–582 (1991)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  16. Heygster, G.: Rank filters in digital image processing. Comput. Graph. Image Process. 19(2), 148–164 (1982)

    Article  Google Scholar 

  17. Jan, J.: Medical Image Processing, Reconstruction and Restoration: Concepts and Methods. CRC Press, Boca Raton (2006)

    Google Scholar 

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

    Article  Google Scholar 

  19. Koskinen, L., Astola, J.: Soft morphological filters: A robust morphological filtering method. J. Electron. Imag. 3(1), 60–70 (1994)

    Article  Google Scholar 

  20. Kuosmanen, P., Astola, J.: Soft morphological filtering. J. Math. Imag. Vis. 5(3), 231–262 (1995)

    Article  MATH  Google Scholar 

  21. Maragos P.: Optimal morphological approaches to image matching and object detection. In: Proceedings of Second International Conference on Computing and Visualization. pp. 655–699 (1988)

  22. Maragos, P.: Lattice image processing: a unification of morphological and fuzzy algebraic systems. J. Math. Imaging Vis. 22(2–3), 333–353 (2005)

    Article  MathSciNet  Google Scholar 

  23. Maragos, P., Schafer, R.: Morphological filters, part II: their relations to median, order-statistic, and stack filters. IEEE. Trans. Acoustics Speech Signal Process. 35(8), 1170–1184 (1987)

    Article  MathSciNet  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 Trans. Image Process. 20(7), 1938–1948 (2011)

    Article  MathSciNet  Google Scholar 

  25. Murray P., Marshall S.: Selectively filtering image features using a Percentage Occupancy Hit-or-Miss Transform. In: IET Conference on Image Process. pp. 1–6 (2012)

  26. Naegel, B., Passat, N., Ronse, C.: Grey-level hit-or-miss transforms, part I: unified theory. Pattern Recogn. 40(2), 635–647 (2007)

    Article  MATH  Google Scholar 

  27. Naegel, B., Passat, N., Ronse, C.: Grey-level hit-or-miss transforms, part II: application to angiographic image processing. Pattern Recogn. 40(2), 648–658 (2007)

    Article  MATH  Google Scholar 

  28. Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic, 2nd edn. Chapman & HALL/CRC, New York (1999)

    Google Scholar 

  29. Perret, B., Lefèvre, S., Collet, Ch.: A robust hit-or-miss transform for template matching applied to very noisy astronomical images. Pattern Recogn. 42(11), 2470–2480 (2009)

    Article  MATH  Google Scholar 

  30. Raducanu, B., Grana, M.: A grayscale hit-or-miss transform based on level sets. In: Proceedings of International Conference on Image Process. vol. 2, pp. 931–933 (2000)

  31. Ronse, C.: Why mathematical morphology needs complete lattices. Signal Process. 21(1), 129–154 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  32. Ronse, C.: A lattice-theoretical morphological view on template extraction in images. J. Vis. Commun. Image R. 7(3), 273–295 (1996)

    Article  Google Scholar 

  33. Schnofeld, D.: On the relation of order-statistics filters and template matching: optimal morphological pattern recognition. IEEE Trans. Image Process. 9(5), 945–949 (2000)

    Article  Google Scholar 

  34. Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982)

    MATH  Google Scholar 

  35. Sinha, D., Dougherty, E.R.: Fuzzy methematical morpholgy. J. Vis. Commun. Image R. 3(3), 286–302 (1992)

    Article  Google Scholar 

  36. Skoneczny, S., Cieslik, D.: Weighted order statistic filters for pattern detection. ICANNGA 2007, Part II. LNCS 4432, 624–632 (2007)

    Google Scholar 

  37. Soille, P.: On morphological operators based on rank filters. Pattern Recogn. 35(2), 527–535 (2002)

    Article  MATH  Google Scholar 

  38. Soille, P.: Morphological Image Analysis: Principles and Applications. Springer, New York (2003)

    Google Scholar 

  39. 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 

  40. Sternberg, S.R.: Grayscale morphology. Comput Vis. Graph. Image Process 35(3), 333–355 (1986)

    Article  MathSciNet  Google Scholar 

  41. Sussner, P., Nachtegael, M., Melange, T., Deschrijver, G., Esmi, E., Kerre, E.: Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology. J. Math. Imaging Vis. 43, 50–71 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  42. Sussner, P., Ritter, G.X.: Decomposition of gray-scale morphological templates using the rank method. IEEE Trans. Pattern Anal. Mach. Intell. 19(6), 649–658 (1997)

    Article  Google Scholar 

  43. Sussner, P., Valle, M.E.: Classification of fuzzy mathematical morphologies based on concepts of inclusion measure and duality. J. Math. Imaging Vis. 32(2), 139–159 (2008)

    Article  MathSciNet  Google Scholar 

  44. Wilson, S.: Vector morphology and iconic neural networks. IEEE Trans. Systems Man Cybernet. 19(6), 1636–1644 (1989)

    Article  Google Scholar 

  45. Wu, C., Agam, G., Roy, A.S., Armato III, S.G.: Regulated morphology approach to fuzzy shape analysis with application to blood vessel extraction in thoracic CT scans. In: Proceedings of SPIE. vol. 5370, 1262–1268 (2004)

  46. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the editor-in-chief and anonymous reviewers for constructive comments and suggestions for improving the quality and readability of this paper. This paper is partly supported by the National Natural Science Foundation of China under Grants 10771043 and 11471001.

Author information

Authors and Affiliations

  1. Harbin Engineering University, Harbin, People’s Republic of China

    Wei Xie, Tingquan Deng, Qiang Li & Minghua Ma

  2. Harbin University of Science and Technology, Harbin, People’s Republic of China

    Wei Xie

Authors
  1. Wei Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tingquan Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Minghua Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tingquan Deng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xie, W., Deng, T., Li, Q. et al. Variable Precision Fuzzy Hit-or-Miss Transformation Models to Object Identification in Grey-Scale Images. J Math Imaging Vis 53, 112–129 (2015). https://doi.org/10.1007/s10851-014-0552-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-014-0552-x

Keywords

Search

Navigation