A generalized fractal transform for measure-valued images

Davide La Torre and Edward R. Vrscay (ervrscay@uwaterloo.ca)

Departmental Working Papers from Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano

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.

Keywords: Measure-valued images; multifunctions; self-similarity; fractal (search for similar items in EconPapers)
Date: 2008-12-09
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://wp.demm.unimi.it/files/wp/2008/DEMM-2008_038wp.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 500 Can't connect to aaa.unimi.it:80 (nodename nor servname provided, or not known) (http://wp.demm.unimi.it/files/wp/2008/DEMM-2008_038wp.pdf [302 Found]--> http://aaa.unimi.it)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:mil:wpdepa:2008-38

Access Statistics for this paper

More papers in Departmental Working Papers from Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano Via Conservatorio 7, I-20122 Milan - Italy. Contact information at EDIRC.
Bibliographic data for series maintained by DEMM Working Papers (dipeco@unimi.it this e-mail address is bad, please contact repec@repec.org).