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Erschienen in:
2012 | OriginalPaper | Buchkapitel
On Fuzzy Fractal Transforms
verfasst von : R. Uthayakumar, M. Rajkumar
Erschienen in: Emerging Trends in Science, Engineering and Technology
Verlag: Springer India
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Abstract
Approximation of an image, a union of spatially—contracted and grayscale modified copies of subsets of itself is known as fractal image coding. Generally, images are considered as function u(x) in \( L^{2} \) or \( L^{\infty } , \) and fractal coding method is developed. In this article, a complete metric space \( ( \mathfrak{F},d_{\infty } ) \) of images on fuzzy fractal space \( \tilde{X} \) is constructed. A method of fractal image coding on fuzzy fractal space is introduced. A fuzzy fractal transform T is defined over the space \( (\mathfrak{F},d_{\infty } ) \), under suitable conditions, T: \( \mathfrak{F} \to \mathfrak{F} \) is contractive, implying the existence of a unique fixed point.