Tomáš IČ, Jana FAIXOVÁ CHALACHANOVÁ

Extension of box counting method for calculating fractal dimension of digital raster surfaces

Ič, T., Faixová Chalachanová, J.: Extension of box counting method for calculating fractal dimension of digital raster surfaces. Kartografické listy, 2020, 28 (1).

Abstract: The roughness of the surface is one of the many attributes describing each surface. The roughness of surface can be described as a complex of positional and height variability of the surface. There are many methods for describing the roughness, but only a few of them are complex enough to exactly determine the degree of roughness surface. The main goal of this study is to point out the problem of the degree of surfaces roughness determining in order to bring a solution to this domain. From the number of methods and techniques for determination the degree of roughness the technique of fractal analysis called the box counting method was chosen in this work. This method is described in the first part of the paper. It forms the basis of the developed tool, which is used to calculate fractal, respectively box counting dimension. Its value can express the degree of roughness for any structure. For a possible future integration of this tool into the existing GIS software, the process of creation of the appropriate tool in the Python 3 programming language environment is described in the second part of this paper. The developed tool was tested on three real geosurfaces to verify its functionality and generation of the correct results.

Keywords: fractal geometry, box counting, degree of 2,5D surface roughness, GIS