New method for estimating fractal dimension in 3D space and its application to complex surfaces

Babič, Matej (author), Miliaresis, George (author), Sodnik, Jošt (author), Mikoš, Matjaž (author), Ambu, Rita (author), Calì, Michele (author)

The concept of "surface modeling" generally describes the process of representing a physical or artificial surface by a geometric model, namely a mathematical expression. Among the existing techniques applied for the characterization of a surface, terrain modeling relates to the representation of the natural surface of the Earth. Cartographic terrain or relief models as three-dimensional representations of a part of the Earth's surface convey an immediate and direct impression of a landscape and are much easier to understand than two-dimensional models. This paper addresses a major problem in complex surface modeling and evaluation consisting in the characterization of their topography and comparison among different textures, which can be relevant in different areas of research. A new algorithm is presented that allows calculating the fractal dimension of images of complex surfaces. The method is used to characterize different surfaces and compare their characteristics. The proposed new mathematical method computes the fractal dimension of the 3D space with the average space component of Hurst exponent H, while the estimated fractal dimension is used to evaluate, compare and characterize complex surfaces that are relevant in different areas of research. Various surfaces with both methods were analyzed and the results were compared. The study confirms that with known coordinates of a surface, it is possible to describe its complex structure. The estimated fractal dimension is proved to be an ideal tool for measuring the complexity of the various surfaces considered.

• Language: English
• Keywords: image analysis, fractal dimension, surface, space component, hurst exponent H.
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2019
• Number of pages: Str. 2154-2159
• Numbering: Letn. 9, št. 6
• PID: 20.500.12556/RUL-114836
• UDC: 55
• ISSN on article: 2088-5334
• DOI: 10.18517/ijaseit.9.6.9480
• COBISS.SI-ID: 9010785
• Publication date in RUL: 18.03.2020

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
• Licensing start date: 18.03.2020

Secondary language

• Language: Slovenian
• Keywords: analiza slik, fraktali, površine, prostorske komponente, Hurstov eksponent H