scholarly journals Evaluation of fractal dimensions from bitmap image (Part: Algorithms)

2004 ◽  
Vol 52 (1) ◽  
pp. 175-182 ◽  
Author(s):  
Petr Koňas
Keyword(s):  
Mechanical Properties ◽  
Fractal Dimensions ◽  
Evaluation Process ◽  
Input Image ◽  
Richardson Method ◽  
Fractal Characteristics ◽  
Appropriate Scale ◽  
Image Part ◽  
Slit Island Method

The work assembled the complex application for evaluation of main fractal characteristics from input image. New simple modifications of evaluation of positive cells according to appropriate scale were implemented. Detail description of theory for each method and description of evaluation process was included. Filtration modification (which is able to estimate the structure which belongs only to specified scale) was introduced together with volumetric modification that allows selecting of optional ratio for determination of positive cells. Also, Richardson method and Slit-Island method were converted to algorithm form. Program was compiled for processing of the following projects about influence between fractal dimensions and mechanical properties of tested materials.

Determination of the Box-Counting Fractal Dimension of Pore Distribution in Eggshell Based on Scanning Electron Microscopy Image Analysis

2011 ◽  
Vol 341-342 ◽  
pp. 776-779 ◽  
Author(s):  
Kai Zhang ◽  
Shu Cai Wang
Keyword(s):  
Fractal Dimensions ◽  
Negative Slope ◽  
Box Counting ◽  
Microscopy Image ◽  
Fractal Characteristics ◽  
Object Of Study ◽  
The Relationship ◽  
Microscopy Image Analysis ◽  
Electronic Microscope

The fractal characteristics of pore structures were investigated using duck eggshells as an object of study. The images of the sharp end, the equator and the blunt end of the eggshells were acquired by using scanning electronic microscope. The image processing operations were conducted for the preprocessing and the image converted into binary image. Then we developed programs based on the principle of changing megascopic degree and applied them to plot thelgN(δ)~lg(δ).The relationship betweenlgN(δ)andlg(δ)maintained linearity over a range [2,64] pixels. Therefore, the fractal dimensions of pore distributions were obtained from the negative slope by regression analysis. The experimental results showed that the fractal feature of the pore in eggshells was remarkable. The analysis confirmed that the blunt end of the eggshell in the pore distributions was more obvious than the sharp end and the equator.

Basic set of experiments for determination of mechanical properties of sand

2014 ◽  
Vol 62 (1) ◽  
pp. 129-137
Author(s):  
A. Sawicki ◽  
J. Mierczyński
Keyword(s):  
Mechanical Properties ◽  
Soil Mechanics ◽  
Physical And Mechanical Properties ◽  
Local Strain ◽  
Initial State ◽  
Laboratory Equipment ◽  
Additional Information ◽  
Basic Set ◽  
Initial Anisotropy

Abstract A basic set of experiments for the determination of mechanical properties of sands is described. This includes the determination of basic physical and mechanical properties, as conventionally applied in soil mechanics, as well as some additional experiments, which provide further information on mechanical properties of granular soils. These additional experiments allow for determination of steady state and instability lines, stress-strain relations for isotropic loading and pure shearing, and simple cyclic shearing tests. Unconventional oedometric experiments are also presented. Necessary laboratory equipment is described, which includes a triaxial apparatus equipped with local strain gauges, an oedometer capable of measuring lateral stresses and a simple cyclic shearing apparatus. The above experiments provide additional information on soil’s properties, which is useful in studying the following phenomena: pre-failure deformations of sand including cyclic loading compaction, pore-pressure generation and liquefaction, both static and caused by cyclic loadings, the effect of sand initial anisotropy and various instabilities. An important feature of the experiments described is that they make it possible to determine the initial state of sand, defined as either contractive or dilative. Experimental results for the “Gdynia” model sand are shown.

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