Skip to main content
SpringerLink
Log in

Fractal Dimension of GrayScale Images

  • Conference paper
  • First Online:
Progress in Computing, Analytics and Networking

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 710))

Abstract

Fractal dimension (FD) is a necessary aspect for characterizing the surface roughness and self-similarity of complex objects. However, fractal dimension gradually established its importance in the area of image processing. A number of algorithms for estimating fractal dimension of digital images have been reported in many literatures. However, different techniques lead to different results. Among them, the differential box-counting (DBC) was most popular and well-liked technique in digital domain. In this paper, we have presented an efficient differential box-counting mechanism for accurate estimation of FD with less fitting error as compared to existing methods like original DBC, relative DBC (RDBC), and improved box-counting (IBC) and improved DBC (IDBC). The experimental work is carried out by one set of fourteen Brodatz images. From this experimental result, we found that the proposed method performs best among the existing methods in terms of less fitting error.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight 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

References

  1. Chen, W.S., Yuan, S.Y., Hsieh, C.M.,: Two algorithms to estimate fractal dimension of gray-level images. Optical Engineering. 42 (2003) 2452–2464

    Google Scholar 

  2. Asvestas, P., Matsopoulos, G.K., Nikita, K.S.,: A power differentiation method of fractal dimension estimation for 2-D signals. Journal of Visual Communication and Image Representation 9 (1998) 392–400

    Google Scholar 

  3. Mandelbrot, B.B.,: Fractal Geometry of Nature. San Francisco: Freeman (1982)

    Google Scholar 

  4. Lopes, R., Betrouni, N.,: Fractal and multifractal analysis: A review, Medical Image Analysis. 13 (2009) 634–649

    Google Scholar 

  5. Balghonaim, A.S., Keller, J.M.,: A maximum likelihood estimate for two-variable fractal surface. IEEE Transactions on Image Processing. 7 (1998) 1746–1753.

    Google Scholar 

  6. Peitgen, H.O., Jurgens, H., Saupe, D.,: Chaos and Fractals: New Frontiers of Science, first ed, Springer, Berlin (1992)

    Google Scholar 

  7. Gangepain, J.J, Carmes, C.R.,: Fractal approach to two dimensional and three dimensional surface roughness. Wear 109 (1986) 119–126

    Google Scholar 

  8. Sarker, N., Chaudhuri, B.B.,: An efficient differential box-counting approach to compute fractal dimension of image. IEEE Transactions on Systems Man and Cybernetics 24 (1994) 115–120

    Google Scholar 

  9. Buczkowski, S., Kyriacos, S., Nekka, F., Cartilier, L.,: The modified box-counting method: analysis of some characteristics parameters. Pattern Recognition. 3 (1998) 411–418

    Google Scholar 

  10. Jin, X.C., Ong, S.H., Jayasooriah, A practical method for estimating fractal dimension. Pattern Recognition Letter. 16 (1995) 457–464

    Google Scholar 

  11. Li, J., Du, Q., Sun, C.,: An improved box-counting method for image fractal dimension estimation. Pattern Recognition 42(2009) 2460–2469

    Google Scholar 

  12. Liu, Y., Chen, L., Wang, H., Jiang, L., Zhang, Yi., Zhao, J., Wang, D., Zhao, Y., Song, Y.,: An improved differential box-counting method to estimate fractal dimensions of gray-level images. Journal of visual communication and Image Representation 25 (2014) 1102–1111

    Google Scholar 

  13. Wenlu, X., Weixin, X.,: Fractal-based analysis of time series data and features extraction. Chinese Signal Processing Journal 13 (1997) 98–104

    Google Scholar 

  14. Yu, L., Zhang, D., Wang, K., Yang, W.,: Coarse iris classification using box-counting to estimate fractal dimensions. Pattern Recognition 38 (2005) 1791–1798

    Google Scholar 

  15. Nayak, S.R., Ranganath, A., Mishra. J.: Analysing fractal dimension of color Images. Computational Intelligence and Networks (CINE), International Conference on. IEEE. (2015) 156–159.

    Google Scholar 

  16. Nayak, S.R., Mishra, J.,: An improved method to estimate the fractal dimension of colour images. Perspectives in Science. 8 (2016) 412–416

    Google Scholar 

  17. Nayak, S.R., Mishra, J.,: An improved algorithm to estimate the fractal dimension of gray scale images. SCOPES2016. 3 (2016) 1109–1114

    Google Scholar 

  18. Biswas, M.K., Ghose, T., Guha, S., Biswas, P.K.,: Fractal dimension estimation for texture images: a parallel approach. Pattern Recognition Letters. 19 (1998) 309–313

    Google Scholar 

  19. Brodatz, P.,: Texture: A Photographic Album for Artists and Designers, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology, College of Engineering and Technology, Bhubaneswar, India

    Soumya Ranjan Nayak

  2. Department of Computer Science and Application, College of Engineering and Technology, Bhubaneswar, India

    Jibitesh Mishra

  3. Department of Computer Science and Engineering, College of Engineering and Technology, Bhubaneswar, India

    Pyari Mohan Jena

Authors
  1. Soumya Ranjan Nayak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jibitesh Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pyari Mohan Jena
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Soumya Ranjan Nayak .

Editor information

Editors and Affiliations

  1. School of Computer Engineering, KIIT University, Bhubaneswar, Odisha, India

    Prasant Kumar Pattnaik

  2. School of Computer Engineering, KIIT University, Bhubaneswar, Odisha, India

    Siddharth Swarup Rautaray

  3. School of Computer Engineering, KIIT University, Bhubaneswar, Odisha, India

    Himansu Das

  4. Department of Computer Science and Engineering, Sri Sivani College of Engineering, Srikakulam, Andhra Pradesh, India

    Janmenjoy Nayak

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Nayak, S.R., Mishra, J., Jena, P.M. (2018). Fractal Dimension of GrayScale Images. In: Pattnaik, P., Rautaray, S., Das, H., Nayak, J. (eds) Progress in Computing, Analytics and Networking. Advances in Intelligent Systems and Computing, vol 710. Springer, Singapore. https://doi.org/10.1007/978-981-10-7871-2_22

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-7871-2_22

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-7870-5

  • Online ISBN: 978-981-10-7871-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation