Skip to main content
SpringerLink
Log in

Fuzzy Relation Equations for Compression/Decompression Processes of Colour Images in the RGB and YUV Colour Spaces

  • Published:
Fuzzy Optimization and Decision Making Aims and scope Submit manuscript

Abstract

We use particular fuzzy relation equations for compression/decompression of colour images in the RGB and YUV spaces, by comparing the results of the reconstructed images obtained in both cases. Our tests are made over well known images of 256×256 pixels (8 bits per pixel in each band) extracted from Corel Gallery. After the decomposition of each image in the three bands of the RGB and YUV colour spaces, the compression is performed using fuzzy relation equations of “min - → t ” type, where “t” is the Lukasiewicz t-norm and “→ t ” is its residuum. Any image is subdivided in blocks and each block is compressed by optimizing a parameter inserted in the Gaussian membership functions of the fuzzy sets, used as coders in the fuzzy equations. The decompression process is realized via a fuzzy relation equation of max-t type. In both RGB and YUV spaces we evaluate and compare the root means square error (RMSE) and the consequentpeak signal to noise ratio (PSNR) on the decompressed images with respect to the original image under several compression rates.

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

Similar content being viewed by others

References

  • Di Martino F., Loia V., Sessa S. (2003a). “A Method in the Compression/Decompression of Images by Using Fuzzy Equations and Fuzzy Similarities”. Proceedings of Conference IFSA 2003 (Istanbul, Turkey, 29/6-2/7/2003), pp. 524–527.

  • Di Martino F., Loia V., Sessa S. (2003b). “A Method for Coding/Decoding Images by Using Fuzzy Relation Equations,” Proceedings of Conference IFSA 2003 (Istanbul, Turkey, 29/6–2/7/2003), Lecture Notes in Artificial Intelligence, Vol. 2715, Berlin: Springer, pp. 436–441.

  • A. Di Nola et al. (1989) Fuzzy Relations Equations and Its Applications to Knowledge Engineering Kluwer Academic Publications Dordrecht

    Google Scholar 

  • E.P. Klement R. Mesiar E. Pap (2000) Triangular Norms Kluwer Academic Publications Dordrecht

    Google Scholar 

  • V. Loia W. Pedrycz S. Sessa (2002) ArticleTitle“Fuzzy Relation Calculus in the Compression and Decompression of Fuzzy Relations” International Journal of Image and Graphics. 2 IssueID4 617–631 Occurrence Handle10.1142/S0219467802000871

    Article  Google Scholar 

  • H. Nobuhara K. Hirota W. Pedrycz (2000) ArticleTitle“Fast Solving Method of Fuzzy Relational Equations and Its Application to Lossy Image Compression” IEEE Transactions of Fuzzy Systems. 8 IssueID3 325–334 Occurrence Handle10.1109/91.855920

    Article  Google Scholar 

  • H. Nobuhara K. Hirota W. Pedrycz (2005) ArticleTitle“Relational Image Compression: Optimizations through the Design of Fuzzy Coders and YUV Colour Space” Soft Computing. 9 471–479 Occurrence Handle10.1007/s00500-004-0366-7

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computational Intelligence and System Science, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, 226–8502, Japan

    H. Nobuhara & K. Hirota

  2. Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università degli Studi di Napoli “Federico II”, Via Monteoliveto 3, 80134, Napoli, Italy

    F. Di. Martino & S. Sessa

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, T6R 2G7, Canada

    W. Pedrycz

Authors
  1. H. Nobuhara
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Hirota
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Di. Martino
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. W. Pedrycz
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. S. Sessa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Nobuhara.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nobuhara, H., Hirota, K., Martino, F.D. et al. Fuzzy Relation Equations for Compression/Decompression Processes of Colour Images in the RGB and YUV Colour Spaces. Fuzzy Optim Decis Making 4, 235–246 (2005). https://doi.org/10.1007/s10700-005-1892-1

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10700-005-1892-1

Keywords

Search

Navigation