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New Method for Estimating Fractal Dimension in 3D Space and Its Application to Complex Surfaces

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@article{IJASEIT9480,
   author = {Matej Babič and George Ch. Miliaresis and Matjaž Mikoš and Rita Ambu and Michele Calì},
   title = {New Method for Estimating Fractal Dimension in 3D Space and Its Application to Complex Surfaces},
   journal = {International Journal on Advanced Science, Engineering and Information Technology},
   volume = {9},
   number = {6},
   year = {2019},
   pages = {2154--2159},
   keywords = {image analysis; fractal dimension; surface; space component; hurst exponent H.},
   abstract = {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.},
   issn = {2088-5334},
   publisher = {INSIGHT - Indonesian Society for Knowledge and Human Development},
   url = {http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=9480},
   doi = {10.18517/ijaseit.9.6.9480}
}

EndNote

%A Babič, Matej
%A Miliaresis, George Ch.
%A Mikoš, Matjaž
%A Ambu, Rita
%A Calì, Michele
%D 2019
%T New Method for Estimating Fractal Dimension in 3D Space and Its Application to Complex Surfaces
%B 2019
%9 image analysis; fractal dimension; surface; space component; hurst exponent H.
%! New Method for Estimating Fractal Dimension in 3D Space and Its Application to Complex Surfaces
%K image analysis; fractal dimension; surface; space component; hurst exponent H.
%X 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.
%U http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=9480
%R doi:10.18517/ijaseit.9.6.9480
%J International Journal on Advanced Science, Engineering and Information Technology
%V 9
%N 6
%@ 2088-5334

IEEE

Matej Babič,George Ch. Miliaresis,Matjaž Mikoš,Rita Ambu and Michele Calì,"New Method for Estimating Fractal Dimension in 3D Space and Its Application to Complex Surfaces," International Journal on Advanced Science, Engineering and Information Technology, vol. 9, no. 6, pp. 2154-2159, 2019. [Online]. Available: http://dx.doi.org/10.18517/ijaseit.9.6.9480.

RefMan/ProCite (RIS)

TY  - JOUR
AU  - Babič, Matej
AU  - Miliaresis, George Ch.
AU  - Mikoš, Matjaž
AU  - Ambu, Rita
AU  - Calì, Michele
PY  - 2019
TI  - New Method for Estimating Fractal Dimension in 3D Space and Its Application to Complex Surfaces
JF  - International Journal on Advanced Science, Engineering and Information Technology; Vol. 9 (2019) No. 6
Y2  - 2019
SP  - 2154
EP  - 2159
SN  - 2088-5334
PB  - INSIGHT - Indonesian Society for Knowledge and Human Development
KW  - image analysis; fractal dimension; surface; space component; hurst exponent H.
N2  - 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.
UR  - http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=9480
DO  - 10.18517/ijaseit.9.6.9480

RefWorks

RT Journal Article
ID 9480
A1 Babič, Matej
A1 Miliaresis, George Ch.
A1 Mikoš, Matjaž
A1 Ambu, Rita
A1 Calì, Michele
T1 New Method for Estimating Fractal Dimension in 3D Space and Its Application to Complex Surfaces
JF International Journal on Advanced Science, Engineering and Information Technology
VO 9
IS 6
YR 2019
SP 2154
OP 2159
SN 2088-5334
PB INSIGHT - Indonesian Society for Knowledge and Human Development
K1 image analysis; fractal dimension; surface; space component; hurst exponent H.
AB 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.
LK http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=9480
DO  - 10.18517/ijaseit.9.6.9480