Skip to main content

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 220))

Abstract

This chapter provides an overview of fuzzy measures and fuzzy integrals, measures of fuzziness, and their application in image processing in the areas of region based segmentation, thresholding, and color retreieval. This chapter also introduces a fuzzy color image retrieval method using a new type of membership function called beta membership function with Generalized Tversky’s index as a measure of fuzziness. Lastly, the proposed method has been compared with some existing fuzzy and non-fuzzy methods.

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

Access this chapter

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
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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. Sugeno M (1977) Fuzzy measures and fuzzy integrals – A survey. In: Gupta, Saridis and Gaines (eds.) Fuzzy Automata and Decision Processes: 89–102.

    Google Scholar 

  2. Frigui H (2001) Interactive image retrieval using fuzzy sets. Pattern Recognition Letters 22: 1021–1031.

    Article  MATH  Google Scholar 

  3. Murofishi T, Sugeno M (1991) A theory of fuzzy measures: representation, the Choquet integral, and null sets. J. of Mathematical Analysis and Applications 159: 532–549.

    Article  Google Scholar 

  4. Li J, Chi Z, Chen G (2004) Image retrieval using Sugeno integral. Third IEEE Intl. Conferance on Image and Graphics (ICIG04), HongKong, China.

    Google Scholar 

  5. using the Choquet integral. IEEE Conferance on Multimedia ans Expo, 1207–1210.

    Google Scholar 

  6. Pham TD, Yan H (1999) Color image segmentation using fuzzy integral and mountain clustering. Fuzzy Sets and Systems 107: 121–130.

    Article  Google Scholar 

  7. Pham TD, Yan H (1999) Color image segmentation using fuzzy integral and mountain clustering. Fuzzy Sets and Systems 107: 121–130.

    Article  Google Scholar 

  8. L. A. Zadeh, Fuzzy sets and systems, Proc. of Symposiam on systems theory, Polytechnic Institute of Brooklyn, NY, USA, 1965.

    Google Scholar 

  9. Luca De A, Termini S (1979) Entropy and energy measures of fuzzy sets: In Gupta M M, Ragade R K ,and Yager R R (eds) Advances in Fuzzy sets Theory and Applications. North Holland, Amsterdam.

    Google Scholar 

  10. Kaufmann A (1980) Introduction to the theory of fuzzy subsets: Fundamental theoretical elements-1. Academic Press, New York.

    Google Scholar 

  11. Yager R R (1979) On the measure of fuzziness and negation. I. Membership in unit interval. Intl. Journal Gen. Systems 5: 221–229.

    Article  MATH  MathSciNet  Google Scholar 

  12. Pal N R, Pal S K (1989) Entropy, a new definition and its application. IEEE Proc. 36: 284–295.

    Google Scholar 

  13. Rosenfeld A (1984) The fuzzy geometry of image subsets, Pattern Recognition Letters 2: 311–317.

    Google Scholar 

  14. Tolias YK, Panas SM et al. (2001) Generalized fuzzy indices for similarity matching. Fuzzy Sets and Systems 120: 255–270.

    Article  MATH  MathSciNet  Google Scholar 

  15. Tversky A (1977) Features of similarity. Psychological Review 84(4): 327–352.

    Article  Google Scholar 

  16. Chaira T, Ray A K (2005) Fuzzy measures for color image retrieval. Fuzzy Sets and Systems Vol. 150(3): 545–560.

    Article  MATH  MathSciNet  Google Scholar 

  17. Huang L K, Wang M J J (1995) Image thresholding by minimizing the measure of fuzziness. Pattern Recognition 28: 41–51.

    Article  Google Scholar 

  18. Chaira T, Ray A K (2004) Threshold selection using fuzzy set theory. Pattern Recognition Letters Vol. 25: 865–874.

    Article  Google Scholar 

  19. Chaira T, Ray A K (2004) Fuzzy measures for threshold selection. The Journal of Fuzzy Mathematics Vol. 12. No.1 (in press).

    Google Scholar 

  20. Chaira T (2003) Image segmentation and color retrieval: a fuzzy and intuitionistic fuzzy set theoretic approach. PhD theses, Indian Institire of Technology, Kharagpur, India.

    Google Scholar 

  21. Bimbo A D (2001) Visual information Retrieval, Morgan Kaufmann Publishers Inc., San Francisco, USA.

    Google Scholar 

  22. Vertan C, Boujemaa N (2000) Using Fuzzy histograms and distances for color image retrieval. Challenge of image retrieval, Brighton: 1–6.

    Google Scholar 

  23. Swain, M J, Ballard D H (1991) Color indexing. International journal of computer vision 7(1): 11–32.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Chaira, T. (2008). Fuzzy Measures in Image Processing. In: Bustince, H., Herrera, F., Montero, J. (eds) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Studies in Fuzziness and Soft Computing, vol 220. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73723-0_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73723-0_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73722-3

  • Online ISBN: 978-3-540-73723-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics