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 Ł2 or Ł∞. In this paper we formulate a method of fractal image coding on measure-valued images: At each point x, μ (x) is a probability measure over the range of allowed greyscale values. We construct a complete metric space (Y, dY) of measure-valued images, μ : 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 generalized fractal transform M is formulated over the metric space (Y, dY). Under suitable conditions, M : Y → Y is contractive, implying the existence of a unique fixed point measure-valued function over(μ, ̄) = M over(μ, ̄).

A generalized fractal transform for measure-valued images / D. La Torre, E.R. Vrscay. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 71:12(2009 Dec 15), pp. e1598-e1607. [10.1016/j.na.2009.01.239]

A generalized fractal transform for measure-valued images

D. La Torre
Primo
;
2009

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 Ł2 or Ł∞. In this paper we formulate a method of fractal image coding on measure-valued images: At each point x, μ (x) is a probability measure over the range of allowed greyscale values. We construct a complete metric space (Y, dY) of measure-valued images, μ : 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 generalized fractal transform M is formulated over the metric space (Y, dY). Under suitable conditions, M : Y → Y is contractive, implying the existence of a unique fixed point measure-valued function over(μ, ̄) = M over(μ, ̄).
Fractal transforms; Iterated function systems; Measure-valued images; Multifunctions; Self-similarity
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/05 - Analisi Matematica
15-dic-2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/146361
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