IDEAS home Printed from https://ideas.repec.org/p/mil/wpdepa/2008-38.html
   My bibliography  Save this paper

A generalized fractal transform for measure-valued images

Author

Listed:
  • Davide LA TORRE

    ()

  • Edward R. VRSCAY

    ()

Abstract

Fractal image coding generally seeks to express an image as a union of spatially contracted and greyscale modified copies of subsets of itself. Generally,images are represented as functions u(x) and the fractal coding method is conducted in the framework of L^2 or L^1. Here we formulate a method of fractal image coding on measure-valued images: At each point \mu(x) is a probability measure overthe range of allowed greyscale values. We construct a complete metric space (Y,d_Y )of measure-valued images, \mu : X -> M(Rg), where X is the base or pixel space and M(Rg) is the set of probability measures supported on the greyscale range Rg. A method of fractal transforms is formulated over the metric space (Y,d_Y ). Under suitable conditions, a transform M : Y -> Y is contractive, implying the existence of a unique fixed point measure-valued function \mu^*= M\mu^*. We also show that the pointwise moments of this measure satisfy a set of recursion relations that are generalizations of those satisfied by moments of invariant measures of Iterated Function Systems with Probabilities.

Suggested Citation

  • Davide LA TORRE & Edward R. VRSCAY, 2008. "A generalized fractal transform for measure-valued images," Departmental Working Papers 2008-38, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
  • Handle: RePEc:mil:wpdepa:2008-38
    as

    Download full text from publisher

    File URL: http://wp.demm.unimi.it/files/wp/2008/DEMM-2008_038wp.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2008. "From iterated function systems to iterated multifunction systems," Departmental Working Papers 2008-39, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    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. La Torre, Davide & Marsiglio, Simone & Privileggi, Fabio, 2011. "Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model," POLIS Working Papers 157, Institute of Public Policy and Public Choice - POLIS.
    2. Davide La Torre & Simone, Marsiglio & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-Similar Measures in Multi-Sector Endogenous Growth Models," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201509, University of Turin.

    More about this item

    Keywords

    Measure-valued images; multifunctions; self-similarity; fractal;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:mil:wpdepa:2008-38. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (DEMM Working Papers). General contact details of provider: http://edirc.repec.org/data/damilit.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.