Basic properties of 2D-nonlinear scale-space representations of images are considered. First, local-energy filters are used to estimate the Hausdorff dimension, , of images. A new fractal dimension, , defined as a property of 2D-curvature representations on multiple scales, is introduced as a natural extension of traditional fractal dimensions, and it is shown that the two types of fractal dime...

In this paper, fractal monochrome image compression technique proposed by Jacquin is investigated for 24-bit true color image by encoding the RGB components' images independently. To exploit the spectral redundancy in RGB components, the root mean square error distortion measure in grayscale space is extended to 3-dimensional color space for fractal-based color image coding. Experimental result...

Using top-end high fidelity computer simulations we demonstrate the existence of a mechanism present in turbulent flows generated by multiscale or fractal objects and which has its origin in the multiscale or fractal space-scale structure of such turbulent flow generators. As a result of this space-scale unfolding mechanism, fractal grids can enhance scalar transfer and turbulent diffusion by o...

The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a class of deterministic fractal sets. The relationship between the basin and the fast basin of a point-fibred attractor is analyzed. To better understand the...

The applicability of fractal measurements to the ionospheric scattering function considered as a fractal object has already been demonstrated. Nevertheless in the high resolution method, the chaotic behavior of the object analyzed was deliberately restricted to the two dimensions of propagation delay and Doppler shift. Good results were obtained but we also realized that an important part of th...

We provide a solution to the problem of reconstructing a fractal interpolation function from its scale-space zeros. Every fractal interpolation function f has a graph that is the attractor of an iterated functions system deened by contractive maps w1; : : : ; wN. We construct approximations of these maps from ngerprints in scale-space.

The most popular \fractal-based" algorithms for both the representation as well as compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces, e.g. IFS with probabilities (IFSP), Iterated Fuzzy Set Systems (IFZS), Fractal Transforms (FT), the Bath Fractal Transform (BFT) and IFS with grey-level maps (IFSM). (FT and...

The fractal image compression technique models a natural image using a contractive mapping called fractal mapping in the image space. In this paper, we demonstrate that the fractal image coding algorithm is compatible with other image coding methods. In other words, we can encode only part of the image using fractal technique and model the remaining part using other algorithms. According to suc...

Fractals are measurable metric sets with non-integer Hausdorff dimensions. If electric and magnetic fields are defined on fractal and do not exist outside of fractal in Euclidean space, then we can use the fractional generalization of the integral Maxwell equations. The fractional integrals are considered as approximations of integrals on fractals. We prove that fractal can be described as a sp...