According to the value of fractal dimension, the basic elements of material microstructures can be divided into two classes: regular objects (whose fractal dimensions are integer) and irregular objects (whose fractal dimensions are fractional). Accordingly, the system of quantitative analysis for material microstructures is also categorized into regular- and irregularobject-measurements. Statistics has been used to describe the features of the basic elements, which is the fundamental of parameter estimation in objectmeasurement. The establishment of fractal geometry has provided the basic theory for the quantitative description of irregular objects, while the combination of fractal geometry and statistics is a powerful tool for the quantitative description of material microstructures.
KeywordsFractal Dimension Probability Density Function Standard Normal Distribution Quantitative Description Fractal Geometry
Unable to display preview. Download preview PDF.