Fractal analysis

About: Fractal analysis is a research topic. Over the lifetime, 6829 publications have been published within this topic receiving 141205 citations.

Surface defects detection based on anisotropy of local fractal dimensions

Abstract: In order to detect the defects in a random surface, the local fractal dimension(LFD) of the random surface image and its anisotropy are studied in this paper. An algorithm to estimate the anisotropy of local fractal dimensions based on moments of the increments is obtained, and the ratio of horizontal and vertical differential of LFD which can characterize the anisotropy of local fractal dimension is proposed. The parameter overcomes the local textual irregularities by representing the region stationary of a non-stationary rough surface. Images of variant random surfaces and defects are investigated. The results of experiments show that the method and parameter proposed are robust, which extract local morphologic features of roughness anisotropy in random surfaces distinctly. By measuring the rupture joint of the ratio, the defects in random surfaces can be detected and located sensitively.

Amplitude-phase type fractal screens and their application in phase-retrieval method

Abstract: In this paper the analysis and comparison of diffraction spectra of amplitude-phase type fractal screens are presented. Amplitude-phase type fractal screens based on well-known fractals, possess exact or statistical self-similarity, but have managed amplitude transmittance and phase shift. Modeling results show that diffraction spectrum of amplitude-phase type fractal screens possess prevailing power of high frequencies in comparison with spectra of fractal structures with binary transmittance and phase shift. Averaging scattering indicatrices for fractal screens with different parameters are presented. The problem of phase retrieval arises in various fields of science and engineering, including electron microscopy, biology, crystallography, astronomy, and optical imaging. At presence there is a great number of phase retrieval methods without reference wave based on iterative algorithms and additional intensity distribution registration. In this paper we propose the new phase retrieval method with using amplitude-phase type fractal screens.

Analysis of positron emission scans using descriptors based on fractal analysis

Abstract: The present disclosure is directed to systems and methods for the analysis of positron emission scans, or images to show or determine a level of complexity of a surface or structure within the scans to determine a clinical status of a subject, for example to identify, classify and/or grade a disease state or a disease progression of the subject. In an embodiment, the level of complexity can be determined using descriptors based on fractal analysis. In any one or more of the embodiments the disease state can be Alzheimer's disease, the disease progression can be mild cognitive impairment (MCI) progression to dementia or both.

CHAPTER 11 – Fractal Dimension and Analyte-Receptor Binding in Cells

Abstract: A fractal analysis of the binding of cellular analyte in solution to a (cellular) receptor immobilized on a biosensor surface provides a quantitative indication of the state of disorder (fractal dimension) and binding-rate coefficient on the surface. The fractal dimension value provides a quantitative measure of the degree of heterogeneity on the biosensor surface for the cellular analyte–receptor binding systems analyzed. Even though the cellular receptor is immobilized to a biosensor surface it does provide insights into the cellular analyte–receptor binding reaction. Both a single- and a dual-fractal analysis were utilized to provide an adequate fit. This was done by the regression analysis provided by Sigma plot. The dual-fractal analysis was utilized to provide an adequate fit in spite of not currently having a molecular basis for it. Quantitative expressions were developed for the binding-rate coefficient as a function of the fractal dimension. The fractal dimension is not a classical independent variable, as indicated earlier, such as analyte concentration. The binding-rate coefficient has been directly related to the fractal dimension for cellular analyte–receptor reactions occurring on biosensor surfaces. Even though the reaction is occurring on a biosensor surface, the analysis provides physical insights into cellular analyte–receptor reactions.