This study presents a new method based on the combination of cryptography and information hiding methods. Firstly, the image is encoded by the Double Random Phase Encoding (DRPE) technique. The real and imaginary parts of the encoded image are subsequently embedded into an enlarged normalized host image. DRPE demands two random phase mask keys to decode the decrypted image at the destination. T...

Fractal compression schemes do not t into the standard transform coder paradigm and have proven diicult to analyze. The theory of iterated function systems motivates a broad class of fractal schemes but does not give much guidance for their implementation. We introduce a wavelet-based framework for analyzing fractal block coders which simpliies these schemes considerably. We show that fractal b...

Microscopic structures of porous media are mainly reconstructed using physical experimental methods and numerical reconstruction methods. However, their accuracy is closely related to the resolution of real rock core images and polishing techniques of core chips amongst others, which significantly limit the development of micro-network flow simulation. In this paper, we proposed a new method fo...

In this paper, a series of studies to reinforced concrete cracks have been done by image graying, calibrating, image denoising, image enhancement and image segmentation, and the binary image of cracks is finally obtained. Using the Box Method, the fractal dimension of cracks is determined. The relationships between the fractal dimension of surface cracks in the cracking beam under three-point l...

This dissertation examines the theory and applications of fractal interpolation. Its main contribution is the parameter identification, algorithmic construction and applications of fractal interpolation. We focus on the self-affine and piecewise self-affine fractal interpolation functions that are based on the theory of iterated function systems. Specifically, we present two novel methods for p...

A method to determine the time to fracture taking into account the physical mechanisms of rnicrocracks and crack formation is developed on the basis of the fractal model of fracture. The fractal dimension of a crack at different stages of its growth is determined theoretically. The damage evolution law which allows for the kinetic and microstructural properties of a material is obtained on the ...

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...

Nature has inspired many scientists and engineers to solve problems through observation and mimicry. One such example is heat transfer enhancement. The enormous natural heat and mass transfer phenomena have led engineers to seek solutions to heat transfer enhancement problems from nature. Fractal geometries are found in respiratory and vascular systems of plants and animals, such as blood vesse...

The stress-strain relationship of frozen soil is important to indicate the strength of frozen soils in use. According to traditional mechanics, the stress-strain relationship in geomaterials is a smooth curve. However, some studies have shown that the real stress-strain curves of geomaterials, such as concrete, rock and frozen soil, are step-like and that they have fractal characteristics. Ther...

Curvature measures are an important tool in geometric measure theory and other fields of mathematics for describing the geometry of sets in Euclidean space. But the ‘classical’ concepts of curvature are not directly applicable to fractal sets. We try to bridge this gap between geometric measure theory and fractal geometry by introducing a notion of curvature for fractals. For compact sets F ⊆ R...