Advanced Search
MyIDEAS: Login to save this paper or follow this series

A generalized fractal transform for measure-valued images


Author Info

  • Davide LA TORRE


  • Edward R. VRSCAY



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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL:
Download Restriction: no

Bibliographic Info

Paper provided by Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano in its series Departmental Working Papers with number 2008-38.

as in new window
Date of creation: 09 Dec 2008
Date of revision:
Handle: RePEc:mil:wpdepa:2008-38

Contact details of provider:
Postal: Via Conservatorio 7, I-20122 Milan - Italy
Phone: +39 02 50321522
Fax: +39 02 50321505
Web page:
More information through EDIRC

Related research

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

This paper has been announced in the following NEP Reports:


No references listed on IDEAS
You can help add them by filling out this form.


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

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.


This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


Access and download statistics


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) The email address of this maintainer does not seem to be valid anymore. Please ask DEMM Working Papers to update the entry or send us the correct address.

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.