Convergence of numerical box-counting and correlation integral multifractal analysis techniques

1997 ◽  
Vol 30 (9) ◽  
pp. 1565-1570 ◽  
Author(s):  
L.V. Meisel ◽  
M.A. Johnson
Keyword(s):  
Multifractal Analysis ◽  
Correlation Integral ◽  
Analysis Techniques ◽  
Box Counting

scholarly journals Multifractal analysis of oceanic chlorophyll maps remotely sensed from space

Ocean Science ◽  
2011 ◽  
Vol 7 (2) ◽  
pp. 219-229 ◽  
Author(s):  
L. de Montera ◽  
M. Jouini ◽  
S. Verrier ◽  
S. Thiria ◽  
M. Crepon
Keyword(s):  
Turbulent Mixing ◽  
Multifractal Analysis ◽  
Numerical Models ◽  
Specific Region ◽  
Dominant Effect ◽  
Passive Scalars ◽  
Analysis Techniques ◽  
Low Cloud ◽  
Scale Range ◽  
Low Cloud Cover

Abstract. Phytoplankton patchiness has been investigated with multifractal analysis techniques. We analyzed oceanic chlorophyll maps, measured by the SeaWiFS orbiting sensor, which are considered to be good proxies for phytoplankton. The study area is the Senegalo-Mauritanian upwelling region, because it has a low cloud cover and high chlorophyll concentrations. Multifractal properties are observed, from the sub-mesoscale up to the mesoscale, and are found to be consistent with the Corssin-Obukhov scale law of passive scalars. This result indicates that, in this specific region and within this scale range, turbulent mixing would be the dominant effect leading to the observed variability of phytoplankton fields. Finally, it is shown that multifractal patchiness can be responsible for significant biases in the nonlinear source and sink terms involved in biogeochemical numerical models.

scholarly journals Multifractal analysis of oceanic chlorophyll maps remotely sensed from space

2011 ◽  
Vol 8 (1) ◽  
pp. 55-84
Author(s):  
L. de Montera ◽  
M. Jouini ◽  
S. Verrier ◽  
S. Thiria ◽  
M. Crepon
Keyword(s):  
Turbulent Mixing ◽  
Multifractal Analysis ◽  
Numerical Models ◽  
Remotely Sensed ◽  
Dominant Effect ◽  
Passive Scalars ◽  
Nonlinear Source ◽  
Analysis Techniques ◽  
Scale Range ◽  
Source And Sink

Abstract. Phytoplankton patchiness has been investigated with multifractal analysis techniques. We analyzed oceanic chlorophyll maps, measured by the SeaWiFS orbiting sensor, which are considered to be good proxies for phytoplankton. Multifractal properties are observed, from the sub-mesoscale up to the mesoscale, and are found to be consistent with the Corssin-Obukhov scale law of passive scalars. This result indicates that, within this scale range, turbulent mixing would be the dominant effect leading to the observed variability of phytoplankton fields. Finally, it is shown that multifractal patchiness can be responsible for significant biases in the nonlinear source and sink terms involved in biogeochemical numerical models.

scholarly journals Classification of texture using random box counting and binarization methods

2021 ◽  
Vol 10 (1) ◽  
pp. 533-540
Author(s):  
Wijdan Jaber AL-kubaisy ◽  
Maha Mahmood
Keyword(s):  
Image Processing ◽  
Fractal Dimension ◽  
Blood Cells ◽  
Multifractal Analysis ◽  
Vision System ◽  
White Blood Cells ◽  
Real Life ◽  
Self Similarity ◽  
Box Counting

The heterogeneous texture classifications with the complexity of structures provide variety of possibilities in image processing, as an example of the multifractal analysis features. The task of texture analysis is a highly significant field of study in the field of machine vision. Most of the real-life surfaces exhibit textures and an efficiently modelled vision system must have the ability to deal with this variety of surfaces. A considerable number of surfaces maintain a self-similarity quality as well as statistical roughness at different scales. Fractals could provide a great deal of advantages; also, they are popular in the process of modelling these properties in the tasks related to the field of image processing. With two distinct methods, this paper presents classification of texture using random box counting and binarization methods calculate the estimation measures of the fractal dimension BCM. There methods are the banalization and random selecting boxes. The classification of the white blood cells is presented in this paper based on the texture if it is normal or abnormal with the use of a number of various methods.

scholarly journals Correlation between the fractal of aftershock spatial distribution and active fault on Sumatra

2019 ◽  
Author(s):  
Bahary Setyawan ◽  
Benyamin Sapiie
Keyword(s):  
Spatial Distribution ◽  
Fractal Dimension ◽  
Active Fault ◽  
Fault System ◽  
Counting Method ◽  
Correlation Integral ◽  
Box Counting ◽  
Point Correlation ◽  
Box Counting Method ◽  
Earthquake Doublet

Abstract. This study discusses the correlation between the fractal of spatial epicentre distribution of aftershock (D2) and active fault (D0) in the Sumatra region. We identified 15 earthquakes in this region that were followed by aftershock cluster and related to the Sumatra Fault Zone or Southern Andaman West Fault. The spatial epicentre distribution of the aftershock was estimated by using two-point correlation integral and the D2 values found were varying from 1.03 ± 0.03 to 1.68 ± 0.08. We estimated the fractal dimension of the active fault by using Box–Counting Method and found that the variation of D0 values in the range of 0.95 ± 0.03 to 1.16 ± 0.01. Positive correlation was found in this study and two patterns were identified that had similar slope with different intercept. However, there was also a correlation that had steeper slope. The steeper slope was related to earthquake doublet mechanism that could generate more random spatial distribution of the aftershock in the fault system.

Tsunamis and rapid coastal remodeling: Linking energy and fractal dimension

2019 ◽  
Vol 44 (4) ◽  
pp. 550-571 ◽  
Author(s):  
Carlo Donadio ◽  
Guido Paliaga ◽  
John D Radke
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Empirical Expression ◽  
Correlation Integral ◽  
Integral Methods ◽  
Box Counting ◽  
Before And After ◽  
Geomorphic Features ◽  
Geometry Analysis ◽  
Tsunami Energy

Tsunamis are one of several processes that contribute to coastal remodeling. This research interpreted geomorphic features over time to better understand if a relationship exists between the flash remodeling of coasts, expressed by bidimensional-fractal dimensions, and known tsunami energy. Fractal geometry analysis, through the box-counting and correlation integral methods, was applied to the physiography of four oceanic coastlands: three in Sumatra, Indonesia, and one in Japan, hit by tsunamis in the last 14 years. Their shoreline fractal dimensions before and after the events and the present-day ones were calculated and compared. Results highlighted any difference or convergence of calculated fractal dimensions. Significant numerical variations of fractal dimensions of the shores before and after each tsunami were registered, and those values gradually decreased post-tsunami. These shorelines, considered stable before tsunamis, increased in physiographic irregularity up to 5–11% immediately after the phenomena; this slowly diminished to 2–5% about 8 to 15 years later; and finally to 3–6% present-day, compared to the pre-event shorelines. Considering these changes of the fractal dimension and the hydrodynamic energy of the tsunami, responsible for the abrupt coastal remodeling, a simple empirical expression and evaluation of the residual resilience is proposed. As a first step, a real physical meaning, in terms of energy, is attributed to the (dimensionless) fractal dimension.

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