Fractals are popular because of their ability to create complex images using only several simple codes. This is possible by capturing image redundancy and presenting the image in compressed form using the self similarity feature. For many years fractals were used for image compression. In the last few years they have also been used for face recognition. In this research we present new fractal m...

Most fractal image coding methods rely upon collage coding , that is, nding a fractal transform operator Tc that sends a target image u as close as possible to itself. The xed point attractor uc of Tc is generally a good approximation to u. However, it is well known that collage coding does not necessarily yield an optimal attractor, i.e., one for which the approximation error jju ? ucjj is min...

Region-based functionality offered by the MPEG-4 video compression standard is also appealing for still images, for example to permit object-based queries of a still-image database. A popular method for still-image compression is fractal coding. However, traditional fractal image coding uses rectangular range and domain blocks. Although new schemes have been proposed that merge small blocks int...

In this paper, the transformation function used in fractal image compression is chosen in such a way that its unique fix point is a close approximation of the input image. Compression occurs because storing the details of the image transform also known as encoding takes up much less space than the original image. Decompression or decoding involves applying the transform repeatedly to an arbitra...

Fractals are a promising framework for several applications other than image coding and trasmission, such as database indexing, texture mapping and pattern recognition problems such as writer authentication. However, fractal based algorithms are strongly asymmetric because, in spite of the linearity of the decoding phase, the coding process is very time consuming. Many different solutions have ...

This paper reports on investigations concerning the performance of fractal transforms. Emerging from the structural constraints of fractal coding schemes, lower bounds for the reconstruction error are given without regarding quantization noise. This implies finding an at least locally optimal transformation matrix. A full search approach is by definition optimal but also intractable for practic...

Fractal techniques applied in the area of signal coding suffer from the lack of an analytical description, especially if the question of convergence at the decoder is addressed. For this purpose an expensive eigenvalue calculation of the transformation matrix during the encoding process is necessary which is in general computational infeasible. In this paper the conditional equation for the eig...

Why does fractal image compression work? What properties must an image have for fractal block coders to work well? What is the implicit image model underlying fractal image compression? The behavior of fractal block coders is clear for deterministically self-similar structures. In this paper we examine the behavior of these coders on statistically self-similar structures. Speci cally, we examin...

There is a considerable amount of literature about image denoising using wavelet-based methods. Some new ideas where also reported using fractal methods. In this paper we propose a hybrid wavelet-fractal denoising method. Using a non-subsampled overcomplete wavelet transform we present the image as a collection of translation invariant copies in different frequency subbands. Within this multipl...

Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying...