To the problem of automation of the process of determination of the fractal dimension

Abstract

In this paper, using various software products (Gwyddion, Mountains 9 DigitalSurf, Image Analysis P9) as well as our own program FractalSurface, we analyzed the possibilities of calculating the fractal dimension for various types of data using several numerical methods (cube counting method, triangulation method, variation method, as well as methods of the spectrum power, «scaling» analysis, morphological envelopes) and the possibilities for their working with the obtained values, such as: selecting a linear section of the graph for recalculating the final value of dimension, using matrix convolutional filters with different convolution kernels for image processing and of the batch analysis of the studied images. At the current time, there is no software product that would satisfy all the requirements for image analysis for the presence of self-affine structures, however, the availability of sufficient functionality mainly depends on the type of study. The comparative analysis of the obtained results allows us to evaluate the capabilities of the software product for further use as tools for automating the process of determining the fractal dimension and of the primary image processing.

Keywords

• fractal dimension
• cube counting method
• triangulation method
• variance method
• power spectrum method
• scaling analysis method
• morphological envelopes method
• image processing software