Skip to main content
SpringerLink
Log in

A New Vector Median Filter Based on Fuzzy Metrics

  • Conference paper
Image Analysis and Recognition (ICIAR 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3656))

Included in the following conference series:

Abstract

Vector median filtering is a well known technique for reducing noise in color images. These filters are defined on the basis of a suitable distance or similarity measure, being the most common used the Euclidean and City-Block distances. In this paper, a Fuzzy Metric, in the sense of George and Veeramani (1994), is defined and applied to color image filtering by means of a new Vector Median Filter. It is shown that the standard Vector Median Filter is outperformed when using this Fuzzy Metric instead of the Euclidean and City-Block distances.

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 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. Allende, H., Galbiati, J.: A non-parametric filter for image restoration using cluster analysis. Pattern Recognition Letters 25(8), 841–847 (2004)

    Article  Google Scholar 

  2. Arakawa, K.: Median filter based on fuzzy rules and its application to image restoration. Fuzzy Sets and Systems 77(1), 3–13 (1996)

    Article  Google Scholar 

  3. Astola, J., Haavisto, P., Neuvo, Y.: Vector Median Filters. Proc. IEEE. 78(4), 678–689 (1990)

    Article  Google Scholar 

  4. Barni, M., Buti, F., Bartolini, F., Capellini, V.: A Quasi-Euclidean Norm to Speed Up Vector Median Filtering. IEEE Transactions on Image Processing 9(10), 1704–1709 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Barni, M.: A Fast Algorithm for 1-Norm Vector Median Filtering. IEEE Transactions on Image Processing 6(10), 1452–1455 (1997)

    Article  MathSciNet  Google Scholar 

  6. Bloch, I.: Fuzzy spatial relationships for image processing and interpretation: a review. Image and Vision Computing 23(2), 89–110 (2005)

    Article  Google Scholar 

  7. Bloch, I.: On fuzzy spatial distances. Advances in imaging and electron physics 128 (2003)

    Google Scholar 

  8. Boncelet, C.: Image noise models. In: Bovik, A. (ed.) Handbook of Image and Video Processing. Academic Press, London (2000)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  10. Chaira, T., Ray, A.K.: Fuzzy approach for color region extraction. Pattern Recognition Letters 24(12), 1943–1950 (2003)

    Article  MATH  Google Scholar 

  11. Coillot, O., Tuzikov, A.V., Cesar, R.M., Bloch, I.: Approximate reflectional simmetries of fuzzy objects with an application in model based object recognition. Fuzzy Sets and Systems 147(1), 141–163 (2004)

    Article  MathSciNet  Google Scholar 

  12. George, A., Veeramani, P.: On Some results in fuzzy metric spaces. Fuzzy Sets and Systems 64(3), 395–399 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  13. George, A., Veeramani, P.: Some theorems in fuzzy metric spaces . J. Fuzzy Math. 3, 933–940 (1995)

    MATH  MathSciNet  Google Scholar 

  14. Gregori, V., Romaguera, S.: Some properties of fuzzy metric spaces. Fuzzy Sets and Systems 115(3), 477–483 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Gregori, V., Romaguera, S.: Characterizing completable fuzzy metric spaces. Fuzzy Sets and Systems 144(3), 411–420 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Karakos, D.G., Trahanias, P.E.: Generalized multichannel image-filtering structures . IEEE Transactions on Image Processing 6(7), 1038–1045 (1997)

    Article  Google Scholar 

  17. Khriji, L., Gabbouj, M.: Adaptive fuzzy order statistics-rational hybrid filters for color image processing. Fuzzy Sets and Systems 128(1), 35–46 (2002)

    Article  MATH  Google Scholar 

  18. Kramosil, I., Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetica 11, 326–334 (1975)

    MathSciNet  Google Scholar 

  19. Lukac, R., Smolka, B., Plataniotis, K.N., Venetsanopoulos, A.N.: Selection weighted vector directional filters. Computer Vision and Image Understanding 94, 140–167 (2004)

    Article  Google Scholar 

  20. Lukac, R.: Adaptive vector median filtering. Pattern Recognition Letters 24(12), 1889–1899 (2003)

    Article  Google Scholar 

  21. Lukac, R., Smolka, B., Martin, K., Plataniotis, K.N., Venetsanopoulos, A.N.: Vector Filtering for Color Imaging. IEEE Signal Processing Magazine. Special Issue on Color Image Processing 22(1), 74–86 (2005)

    Google Scholar 

  22. Lukac, R., Plataniotis, K.N., Smolka, B., Venetsanopoulos, A.N.: Generalized Selection Weighted Vector Filters. EURASIP Journal on applied signal processing. Special Issue on Nonlinear signal and image processing 12, 1870–1885 (2004)

    Google Scholar 

  23. Lukac, R., Plataniotis, K.N., Smolka, B., Venetsanopoulos, A.N.: A Multichannel Order-Statistic Technique for cDNA Microarray Image Processing. IEEE Transactions on Nanobioscience 3(4), 272–285 (2004)

    Article  Google Scholar 

  24. Lukac, R., Plataniotis, K.N., Smolka, B., Venetsanopoulos, A.N.: cDNA Microarray Image Processing Using Fuzzy Vector Filtering Framework. Fuzzy Sets and Systems, Special Issue on Fuzzy Sets and Systems on Bioinformatics 152(1), 17–35 (2005)

    MATH  MathSciNet  Google Scholar 

  25. Lukac, R.: Adaptive Color Image Filtering Based on Center Weighted Vector Directional Filters. Multidimensional Systems and Signal Processing 15, 169–196 (2004)

    Article  MATH  Google Scholar 

  26. MacAdam, D.L.: Visual sensitivities to color differences in daylight. J. Opt. Soc. Am. 33, 247–274 (1942)

    Article  Google Scholar 

  27. Pitas, I.: Digital image processing algorithms and applications. John Wiley & Sons, Chichester (2000)

    Google Scholar 

  28. Plataniotis, K.N., Venetsanopoulos, A.N.: Color Image processing and applications. Springer, Berlin (2000)

    Google Scholar 

  29. Santini, S., Jain, R.: Similarity Measures. IEEE Transactions on pattern recognition and machine intelligence 21(9), 871–883 (1999)

    Article  Google Scholar 

  30. Sapena, A.: A contribution to the study of fuzzy metric spaces. Appl. Gen. Topology 2(1), 63–76 (2001)

    MATH  MathSciNet  Google Scholar 

  31. Smolka, B., Lukac, R., Chydzinski, A., Plataniotis, K.N., Wojciechowski, W.: Fast adaptive similarity based impulsive noise reduction filter. Real-Time Imaging 9(4), 261–276 (2003)

    Article  Google Scholar 

  32. Szczepanski, M., Smolka, B., Plataniotis, K.N., Venetsanopoulos, A.N.: On the distance function approach to color image enhancement. Discrete Applied Mathematics 139, 283–305 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  33. Trahanias, P.E., Karakos, D., Venetsanopoulos, A.N.: Vector Directional Filters: a new class of multichannel image processing filters. IEEE Trans. Image Process. 2(4), 528–534 (1993)

    Article  Google Scholar 

  34. Van der Weken, D., Nachtegael, M., Kerre, E.E.: Using similarity measures and homogeneity for the comparison of images. Image and Vision Computing 22(9), 695–702 (2004)

    Article  Google Scholar 

  35. Wang, W.J.: New similarity measures on fuzzy sets and on elements. Fuzzy sets and systems 85(3), 305–309 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  36. Yong, D., Wenkang, S., Feng, D., Qi, L.: A new similarity measure of generalized fuzzy numbers and its application to pattern recognition. Pattern Recognition Letters 25(8), 875–883 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Expresión Gráfica en, la Ingeniería, Universidad Politécnica de Valencia, E.P.S. de Gandia, Carretera Nazaret-Oliva s/n, 46730, Grao de Gandia (Valencia), Spain

    Samuel Morillas, Guillermo Peris-Fajarnés & Pedro Latorre

  2. Departamento Matemática Aplicada, Universidad Politécnica de Valencia, E.P.S. Gandia, Carretera Nazaret-Oliva s/n, 46730, Grao de Gandia (Valencia), Spain

    Valentín Gregori

Authors
  1. Samuel Morillas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Valentín Gregori
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guillermo Peris-Fajarnés
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pedro Latorre
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering Department, University of Waterloo,  

    Mohamed Kamel

  2. FEUP - Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, P.O. Box, 4200-465, Porto, Portugal

    Aurélio Campilho

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Morillas, S., Gregori, V., Peris-Fajarnés, G., Latorre, P. (2005). A New Vector Median Filter Based on Fuzzy Metrics. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2005. Lecture Notes in Computer Science, vol 3656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11559573_11

Download citation

  • DOI: https://doi.org/10.1007/11559573_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29069-8

  • Online ISBN: 978-3-540-31938-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation