Higuchi Dimension of Digital Images

There exist several methods for calculating the fractal dimension of objects represented as 2D digital images. For example, Box counting, Minkowski dilation or Fourier analysis can be employed. However, there appear to be some limitations. It is not possible to calculate only the fractal dimension of an irregular region of interest in an image or to perform the calculations in a particular direction along a line on an arbitrary angle through the image. The calculations must be made for the whole image. In this paper, a new method to overcome these limitations is proposed. 2D images are appropriately prepared in order to apply 1D signal analyses, originally developed to investigate nonlinear time series. The Higuchi dimension of these 1D signals is calculated using Higuchi's algorithm, and it is shown that both regions of interests and directional dependencies can be evaluated independently of the whole picture. A thorough validation of the proposed technique and a comparison of the new method to the Fourier dimension, a common two dimensional method for digital images, are given. The main result is that Higuchi's algorithm allows a direction dependent as well as direction independent analysis. Actual values for the fractal dimensions are reliable and an effective treatment of regions of interests is possible. Moreover, the proposed method is not restricted to Higuchi's algorithm, as any 1D method of analysis, can be applied

FACILE SYNTHESIS OF MnO/CARBON/CARBON NANOTUBE NANOHYBRIDS USING DENTAL RESINS AS SOLVENT AND CARBON SOURCE

Manganese (II) Oxide (MnO) and its composites with carbon have attracted wide attention as high performance lithium-ion battery anode. An in situ, facile method for preparing MnO/carbon/carbon nanotubes nanohybrids has been developed using dental difunctional methacrylate monomers as solvent and carbon source. With this method, the solvent disposal process is totally circumvented. The MnO nanoparticles are homogeneously incorporated into the carbon matrix, within which the CNTs are homogeneously dispersed. Systematic characterization on the crystallographic phase and morphology of MnO, content and nature of carbon matrix, and electrochemical performance of the MnO/C/CNTs has been performed. A significant improvement of rate performance with the incorporation of CNTs has been observed compared to the bare MnO/C nanohybrids. It is confirmed by the significant reduction of the charge transfer impedance measured by electrochemical impedance spectroscopy