In this dissertation, the problem of the construction of Fractal Interpolation Surfaces and their application in image compression is studied. We give exact conditions, so that this construction is valid and we introduce some free parameters that make our model as flexible as possible. In addition, we compute the box-counting dimension of a Fractal Interpolation Surface. Finally, we give a new ...

There has been growing interest in using the fractal dimension to study the hierarchical structures of soft materials after realising that fractality is an important property of natural and engineered materials. This work presents a method to quantify the internal architecture and the space-filling capacity of granular fractal aggregates by reconstructing the three-dimensional capacity dimensio...

We present a method to recover a fractal dimension of a multi-scale rough surface, the so-called correlation dimension, from the knowledge of the far-field scattered intensity. The results are validated by numerical experiments on Weierstrass-like surfaces.

The current prognostic parameters, including tumor volume, biochemistry, or immunohistochemistry, are not sufficient to reflect the properties of cancer cells that distinguish them from normal cells. Our focus is to evaluate the effects of a combination of microtubule-polymerizing Taxol and -depolymerizing colchicine on IAR20 PC1 liver cells by measuring the surface fractal dimension as a descr...

It has been shown that the fractal dimension has a strong correlation with human judgment of surface roughness. Besides the fractal dimension, which is the most important fractal feature, lacunarity describes the characteristics of fractals. This feature is used in some fields and has good performances. In the field of image processing and recognition, it is important to study the scale and rot...

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account the fact that partial contact may occur between the solids on all length scales. I present numerical results for the case where the substrate surface is self-affine fractal. When the fractal dimension is close to 2, complete contact typically occurs in the macroasper...

background & objectives: cancer is a serious problem for human being and is becoming a serious problem day-by-day .a prerequisite for any therapeutic modality is early diagnosis. automated cancer diagnosis by automatic image feature extraction procedures can be used as a feature extraction in the field of fractal dimension. the aim of this survey was to introduce a quantitative and objectiv...

This paper is concerned with the modeling of engineering images by the fractal properties of 6-point binary interpolating scheme. Association between the fractal behavior of the limit curve/surface and the parameter is obtained. The relationship between the subdivision parameter and the fractal dimension of the limit fractal curve of subdivision fractal is also presented. Numerical examples and...

Modern life style of women has made them more vulnerable to breast cancer and it is considered as the largest cause of mortality among women. This paper presents a novel method to classify mammograms into normal ones, with benign and malignant microcalcifications, and with malignant and benign tumors using fractal features derived from fractal dimension. Here, three fractal dimension estimation...

We report a numerical study of van der Waals adsorption and capillary condensation effects on self-similar fractal surfaces. An assembly of uncoupled spherical pores with a power-law distribution of radii is used to model fractal surfaces with adjustable dimensions. We find that the commonly used fractal Frankel-Halsey-Hill equation systematically fails to give the correct dimension due to cros...