Most natural surfaces and surfaces of engineering interest, e.g., polished or sandblasted surfaces, are self-affine fractal over a wide range of length scales, with the fractal dimension Df 1⁄4 2:15 0:15. We give several examples illustrating this and a simple argument, based on surface fragility, for why the fractal dimension usually is \2.3. A kinetic model of sandblasting is presented, which...

This paper investigates the use of fractal metrics for discrimination of copper surface textures. Measurements of copper surfaces, using contacting profilometry, provided the raw data for the fractal analysis. The samples tested included copper foil samples and a copper lead frame, typical of those in use in plastic electronic packages. The fractal Hausdorf dimension and upper/lower ranges of f...

Based on the standard fractal transformation in the spatial domain, simple relations may be found relating coefficients in detail(high-pass) subbands in the wavelet domain. In this paper, we devise a hybrid image compression using fractal-wavelet prediction where the causal similarity among blocks of different subbands in a wavelet decomposition of the image is exploited. The proposed coding sc...

The soft fault diagnosis of nonlinear analog circuits is an important guarantee of the stable and reliable operation of electronic products. In view of the low accuracy and heavy computation load of current soft fault diagnosis methods for nonlinear analog circuits, this paper presents a soft fault diagnosis method for nonlinear analog circuits based on fractal theory. Analyzing the single-frac...

Why does fractal image compression work? What is the implicit image model underlying fractal block coding? How can we characterize the types of images for which fractal block coders will work well? These are the central issues we address. We introduce a new wavelet-based framework for analyzing block-based fractal compression schemes. Within this framework we are able to draw upon insights from...

Fractal Image compression uses different fractals is lossy compression technique. Textures and natural images are compressed & decompressed using fractal image compression. As there is repeation in the other parts of the same image. In proposed methodology, complete image is converted into mathematical equations. These equations are used to convert images into fractal codes. After reception the...

In this study, we propose a wavelet based speech data interpolation technique using the fractal characteristics of the speech. The aim of the method is to double the sampling rate, providing higher resolution while preserving the fractal characteristics of the speech signal. The method is applied to synthetic fractal signals and the results are compared with the linearly interpolated ones. Voic...

This paper proposes an improved version for the JSEG color image segmentation algorithm, combining the classical JSEG algorithm with a local fractal operator that measures the fractal dimension of each pixel, thus improving the boundary detection. Furthermore, the sensitivity of color variation is enhanced when working with the original color value, instead of quantized color information. Exper...

54 Generally, a fractal most often referred to as “a rough shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole.” The father of fractal geometry Benoît Mandelbrot formulated this term in 1975. A fractal has a complicated shape. Certain features characterize a graphical representation of the fractal by mathematical equation: it is self...

Paddy is one of major crops grown in China. Fractal dimension is an important parameter used to describe geometrical characteristics of many natural objects. The objective of this study is to investigate mathematical relationships between the fractal dimension and the yield of the paddy spike based on the fractal theory and the image processing technologies. The color images of paddy spikes wer...