IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v43y2010i1p57-67.html
   My bibliography  Save this article

Multifractal analysis of three-dimensional histogram from color images

Author

Listed:
  • Chauveau, Julien
  • Rousseau, David
  • Richard, Paul
  • Chapeau-Blondeau, François

Abstract

Natural images, especially color or multicomponent images, are complex information-carrying signals. To contribute to the characterization of this complexity, we investigate the possibility of multiscale organization in the colorimetric structure of natural images. This is realized by means of a multifractal analysis applied to the three-dimensional histogram from natural color images. The observed behaviors are confronted to those of reference models with known multifractal properties. We use for this purpose synthetic random images with trivial monofractal behavior, and multidimensional multiplicative cascades known for their actual multifractal behavior. The behaviors observed on natural images exhibit similarities with those of the multifractal multiplicative cascades and display the signature of elaborate multiscale organizations stemming from the histograms of natural color images. This type of characterization of colorimetric properties can be helpful to various tasks of digital image processing, as for instance modeling, classification, indexing.

Suggested Citation

  • Chauveau, Julien & Rousseau, David & Richard, Paul & Chapeau-Blondeau, François, 2010. "Multifractal analysis of three-dimensional histogram from color images," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 57-67.
    • Handle: RePEc:eee:chsofr:v:43:y:2010:i:1:p:57-67
    DOI: 10.1016/j.chaos.2010.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077910000093
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2010.08.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wu, Ming-Sheng & Teng, Wei-Chih & Jeng, Jyh-Horng & Hsieh, Jer-Guang, 2006. "Spatial correlation genetic algorithm for fractal image compression," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 497-510.
    2. Stanley, H.E. & Amaral, L.A.N. & Goldberger, A.L. & Havlin, S. & Ivanov, P.Ch. & Peng, C.-K., 1999. "Statistical physics and physiology: Monofractal and multifractal approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 309-324.
    3. Su, Zhi-Yuan & Wu, Tzuyin & Wang, Shu-Yin, 2009. "Local scaling and multifractal spectrum analyses of DNA sequences – GenBank data analysis," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1750-1765.
    4. Chapeau-Blondeau, François & Chauveau, Julien & Rousseau, David & Richard, Paul, 2009. "Fractal structure in the color distribution of natural images," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 472-482.
    5. Plamen Ch. Ivanov & Luís A. Nunes Amaral & Ary L. Goldberger & Shlomo Havlin & Michael G. Rosenblum & Zbigniew R. Struzik & H. Eugene Stanley, 1999. "Multifractality in human heartbeat dynamics," Nature, Nature, vol. 399(6735), pages 461-465, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lahmiri, Salim, 2016. "Image characterization by fractal descriptors in variational mode decomposition domain: Application to brain magnetic resonance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 235-243.
    2. Chéné, Yann & Belin, Étienne & Rousseau, David & Chapeau-Blondeau, François, 2013. "Multiscale analysis of depth images from natural scenes: Scaling in the depth of the woods," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 135-149.
    3. Martsepp, Merike & Laas, Tõnu & Laas, Katrin & Priimets, Jaanis & Tõkke, Siim & Mikli, Valdek, 2022. "Dependence of multifractal analysis parameters on the darkness of a processed image," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 182-198.
    2. Mukli, Peter & Nagy, Zoltan & Eke, Andras, 2015. "Multifractal formalism by enforcing the universal behavior of scaling functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 150-167.
    3. França, Lucas Gabriel Souza & Montoya, Pedro & Miranda, José Garcia Vivas, 2019. "On multifractals: A non-linear study of actigraphy data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 612-619.
    4. Pyko, Nikita S. & Pyko, Svetlana A. & Markelov, Oleg A. & Karimov, Artur I. & Butusov, Denis N. & Zolotukhin, Yaroslav V. & Uljanitski, Yuri D. & Bogachev, Mikhail I., 2018. "Assessment of cooperativity in complex systems with non-periodical dynamics: Comparison of five mutual information metrics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1054-1072.
    5. Loiseau, Patrick & Médigue, Claire & Gonçalves, Paulo & Attia, Najmeddine & Seuret, Stéphane & Cottin, François & Chemla, Denis & Sorine, Michel & Barral, Julien, 2012. "Large deviations estimates for the multiscale analysis of heart rate variability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5658-5671.
    6. Pawe{l} O'swik{e}cimka & Stanis{l}aw Dro.zd.z & Mattia Frasca & Robert Gk{e}barowski & Natsue Yoshimura & Luciano Zunino & Ludovico Minati, 2020. "Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses," Papers 2004.03319, arXiv.org.
    7. Yang, Xiaodong & Du, Sidan & Ning, Xinbao & Bian, Chunhua, 2008. "Mass exponent spectrum analysis of human ECG signals and its application to complexity detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3546-3554.
    8. Billat, Véronique L. & Mille-Hamard, Laurence & Meyer, Yves & Wesfreid, Eva, 2009. "Detection of changes in the fractal scaling of heart rate and speed in a marathon race," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(18), pages 3798-3808.
    9. Yang, Xiaodong & Ning, Xinbao & Wang, Jun, 2007. "Multifractal analysis of human synchronous 12-lead ECG signals using multiple scale factors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 413-422.
    10. Chen, Yanguang, 2014. "Multifractals of central place systems: Models, dimension spectrums, and empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 266-282.
    11. Vitanov, Nikolay K. & Sakai, Kenshi & Dimitrova, Zlatinka I., 2008. "SSA, PCA, TDPSC, ACFA: Useful combination of methods for analysis of short and nonstationary time series," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 187-202.
    12. Zhang, Yin & Li, Jin & Wang, Jun, 2017. "Exploring stability of entropy analysis for signal with different trends," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 60-67.
    13. Yao, Wenpo & Yao, Wenli & Wang, Jun, 2021. "A novel parameter for nonequilibrium analysis in reconstructed state spaces," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    14. Wu, Yue & Shang, Pengjian & Chen, Shijian, 2019. "Modified multifractal large deviation spectrum based on CID for financial market system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1331-1342.
    15. Currenti, Gilda & Negro, Ciro Del & Lapenna, Vincenzo & Telesca, Luciano, 2005. "Fluctuation analysis of the hourly time variability of volcano-magnetic signals recorded at Mt. Etna Volcano, Sicily (Italy)," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1921-1929.
    16. Jovanovic, Tijana & Mejía, Alfonso & Gall, Heather & Gironás, Jorge, 2016. "Effect of urbanization on the long-term persistence of streamflow records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 208-221.
    17. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of periodic and quasi-periodic trends in detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 777-784.
    18. Rodriguez, Eduardo & Echeverria, Juan C. & Alvarez-Ramirez, Jose, 2009. "Fractality in electrocardiographic waveforms for healthy subjects and patients with ventricular fibrillation," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1046-1054.
    19. Stosic, Tatijana & Telesca, Luciano & Stosic, Borko, 2021. "Multiparametric statistical and dynamical analysis of angular high-frequency wind speed time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    20. Guan, Sihai & Wan, Dongyu & Yang, Yanmiao & Biswal, Bharat, 2022. "Sources of multifractality of the brain rs-fMRI signal," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:43:y:2010:i:1:p:57-67. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.