A generalized fractal transform for measure-valued images

✍ Scribed by Davide La Torre; Edward R. Vrscay

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 349 KB
• Volume: 71
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2009.01.239

✦ Synopsis

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 Ł 2 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 , d Y ) of measure-valued images, µ : X → M(R g ), where X is the base or pixel space and M(R g ) is the set of probability measures supported on the greyscale range R g . A generalized fractal transform M is formulated over the metric space (Y , d Y ). Under suitable conditions, M : Y → Y is contractive, implying the existence of a unique fixed point measure-valued function μ = M μ.