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GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION

Year 2022, Volume: 10 Issue: 1, 1 - 10, 25.02.2022

Derya Çelik Ali Deniz Yunus Özdemir

https://doi.org/10.20290/estubtdb.988203

Abstract

Fractal image compression is a method to compress images which significantly reduces the storage to keep data of the images, using partial iterated function systems. In this work we generalize classical fractal image compression method to the graph-directed case.

Keywords

image compression fractals graph-directed fractals

Project Number

19ADP045

References

  • [1] Barnsley M. Fractals Everywhere, Academic Press, San Diego, 1988.
  • [2] Barnsley M. Fractal modelling of real world images, in: The Science of Fractal Images, H.-O. Peitgen and D. Saupe (eds.), Springer-Verlag, New York, 1988.
  • [3] Barnsley M, Sloan AD. A better way to compress images, Byte Magazine, 1988.
  • [4] Demir B, Deniz A, Koçak Ş, Ureyen AE. Tube formulas for graph-directed fractals. Fractals 2010; 18: 349–361.
  • [5] Edgar G. Measure, Topology and Fractal Geometry, Springer, New York, 2008.
  • [6] Fischer Y. Fractal Image Compression-Theory and Application, Springer, New York, 1994.
  • [7] Hutchinson JE. Fractals and self similarity. Indiana Univ. Math. J. 1981; 30: 713–747.
  • [8] Jacquin AE. Image coding based on a fractal theory of iterated contractive image transformations. IEEE Trans. Image Processing 1992; 1:18-30.
  • [9] Lu G. Fractal image compression. Signal Processing: Image Communication1993; 5: 327–343.
  • [10] Mauldin RD, Williams SC. Hausdorff dimension in graph directed constructions. Trans. Amer. Math. Soc. 1988; 309: 811–829.

GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION

Year 2022, Volume: 10 Issue: 1, 1 - 10, 25.02.2022

Derya Çelik Ali Deniz Yunus Özdemir

https://doi.org/10.20290/estubtdb.988203

Abstract

Fractal image compression is a method to compress images, which significantly reduces the storage to keep data of the images, using partial iterated function systems. In this work, we generalize the classical fractal image compression method to the graph-directed case.

Fractal image compression is a method to compress images, which significantly reduces the storage to keep data of the images, using partial iterated function systems. In this work, we generalize the classical fractal image compression method to the graph-directed case.

Keywords

Image compression Fractals Graph-directed fractals

Supporting Institution

Eskişehr Technical University

Project Number

19ADP045

Thanks

This work is supported by the Eskişehir Technical University Research Fund Under Contract 19ADP045.

References

  • [1] Barnsley M. Fractals Everywhere, Academic Press, San Diego, 1988.
  • [2] Barnsley M. Fractal modelling of real world images, in: The Science of Fractal Images, H.-O. Peitgen and D. Saupe (eds.), Springer-Verlag, New York, 1988.
  • [3] Barnsley M, Sloan AD. A better way to compress images, Byte Magazine, 1988.
  • [4] Demir B, Deniz A, Koçak Ş, Ureyen AE. Tube formulas for graph-directed fractals. Fractals 2010; 18: 349–361.
  • [5] Edgar G. Measure, Topology and Fractal Geometry, Springer, New York, 2008.
  • [6] Fischer Y. Fractal Image Compression-Theory and Application, Springer, New York, 1994.
  • [7] Hutchinson JE. Fractals and self similarity. Indiana Univ. Math. J. 1981; 30: 713–747.
  • [8] Jacquin AE. Image coding based on a fractal theory of iterated contractive image transformations. IEEE Trans. Image Processing 1992; 1:18-30.
  • [9] Lu G. Fractal image compression. Signal Processing: Image Communication1993; 5: 327–343.
  • [10] Mauldin RD, Williams SC. Hausdorff dimension in graph directed constructions. Trans. Amer. Math. Soc. 1988; 309: 811–829.
There are 10 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Derya Çelik This is me 0000-0003-2499-791X

Ali Deniz This is me 0000-0003-3833-6397

Yunus Özdemir 0000-0002-6890-2997

Project Number 19ADP045
Publication Date February 25, 2022
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

APA Çelik, D., Deniz, A., & Özdemir, Y. (2022). GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 10(1), 1-10. https://doi.org/10.20290/estubtdb.988203
AMA Çelik D, Deniz A, Özdemir Y. GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. February 2022;10(1):1-10. doi:10.20290/estubtdb.988203
Chicago Çelik, Derya, Ali Deniz, and Yunus Özdemir. “GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 10, no. 1 (February 2022): 1-10. https://doi.org/10.20290/estubtdb.988203.
EndNote Çelik D, Deniz A, Özdemir Y (February 1, 2022) GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 10 1 1–10.
IEEE D. Çelik, A. Deniz, and Y. Özdemir, “GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION”, Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, vol. 10, no. 1, pp. 1–10, 2022, doi: 10.20290/estubtdb.988203.
ISNAD Çelik, Derya et al. “GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 10/1 (February 2022), 1-10. https://doi.org/10.20290/estubtdb.988203.
JAMA Çelik D, Deniz A, Özdemir Y. GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2022;10:1–10.
MLA Çelik, Derya et al. “GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, vol. 10, no. 1, 2022, pp. 1-10, doi:10.20290/estubtdb.988203.
Vancouver Çelik D, Deniz A, Özdemir Y. GRAPH-DIRECTED FRACTAL IMAGE COMPRESSION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2022;10(1):1-10.