Fractal compression

Abstract: The author proposes an independent and novel approach to image coding, based on a fractal theory of iterated transformations. The main characteristics of this approach are that (i) it relies on the assumption that image redundancy can be efficiently exploited through self-transformability on a block-wise basis, and (ii) it approximates an original image by a fractal image. The author refers to the approach as fractal block coding. The coding-decoding system is based on the construction, for an original image to encode, of a specific image transformation-a fractal code-which, when iterated on any initial image, produces a sequence of images that converges to a fractal approximation of the original. It is shown how to design such a system for the coding of monochrome digital images at rates in the range of 0.5-1.0 b/pixel. The fractal block coder has performance comparable to state-of-the-art vector quantizers. >

Abstract: From the contents: Recent theoretical results on fast encoding and decoding methods, various schemes for encoding images using fractal methods, and theoretical models for the encoding/decoding process.- Working C code for a fractal encoding/decoding scheme capable of encoding images in a few seconds, decoding at arbitrary resolution, and achieving high compression rations.- Experimental results from various schemes showing their capability and forming the basis for a sophisticated implementation.- A list of previously unresearched projects containing both new ideas and inhancements to the schemes discussed in the book.- A comparison of the fractal schemes in the book with JPEG, commercial fractal software, and wavelet methods.

Abstract: Fractals are geometric or data structures which do not simplify under magnification. Fractal Image Compression is a technique which associates a fractal to an image. On the one hand, the fractal can be described in terms of a few succinct rules, while on the other, the fractal contains much or all of the image information. Since the rules are described with less bits of data than the image, compression results. Data compression with fractals is an approach to reach high compression ratios for large data streams related to images. The high compression ratios are attained at a cost of large amounts of computation. Both lossless and lossy modes are supported by the technique. The technique is stable in that small errors in codes lead to small errors in image data. Applications to the NASA mission are discussed.

Abstract: Fractal geometry is receiving increased attention as a model for natural phenomena In this paper we first present a new method for estimating the fractal dimension from image surfaces and show that it performs better at describing and segmenting generated fractal sets Since the fractal dimension alone is not sufficient to characterize natural textures, we define a new class of texture measures based on the concept of lacunarity and use them, together with the fractal dimension, to describe and segment natural texture images