Clasificación Automática de Sujetos con Deterioro Cognitivo Leve mediante la Caracterización Fractal 3D en Imágenes Cerebrales de Resonancia Magnética

2021 ◽  
Author(s):  
◽  
J. Solis-Poot
Keyword(s):  
Fractal Dimension ◽  
Magnetic Resonance Images ◽  
Brain Volumes ◽  
Box Counting ◽  
Fractal Index ◽  
Discrete Compactness ◽  
Healthy Control ◽  
Morphological Indices ◽  
Two Populations

Sixty brain volumes were analyzed from separate magnetic resonance images in two populations: healthy control subjects and subjects with mild cognitive impairment. For each element, the Box Counting algorithm was applied to obtain the characterization of the 3D Fractal Dimension that it presented. In addition, other morphological indices of volume, discrete compactness and surrounding area were added. Finally, a classification strategy is implemented using the Gaussian Process with a radial-based Kernel to compare the correct discrimination in the populations studied. The classifier model after the validation process gave a 60% success rate for the fractal dimension and for the morphological indices. The highest hit rate was when both metrics were combined with 80%. With these results, it is believed that the fractal index could become a biomarker for the prediagnosis of Alzheimer's disease, although for this, more studies are needed in the future.

scholarly journals Fractal Characterization of Earthquake occurrences in Nigeria

2019 ◽  
Vol 1 ◽  
pp. 281-287
Author(s):  
N N Abdulsalam ◽  
O Ologe
Keyword(s):  
Fractal Dimension ◽  
Active Zone ◽  
Hazard Analysis ◽  
B Value ◽  
Google Earth ◽  
Counting Method ◽  
Microsoft Word ◽  
Box Counting ◽  
Box Counting Method

Fractal characterization of Earthquake occurrences in Nigeria was carried out in order to know the b-value of tremor occurrences in the country. This will help in hazard analysis and research in the geological and geophysical structures of Nigeria. The method used in determining the b-value is the box counting method, but for simplicity, we used circle. The areas that are tremor prone were posted on a digitized Nigeria map using Google earth and Surfer 7.0 software. The computation with the box counting method was performed with picked radius of the circle from 50km - 350km and the average number of points that falls within each circle were recorded. The graph of log r (the logarithms of radius of circle or scale) against log <N> (logarithms of average number of points) was plotted using grapher and excels Microsoft word and the slope of the graph was determined. The determined slope gave the fractal dimension and the b-value was thus calculated. In this work, a b-value of 0.6 was obtained indicating that Nigeria falls within seismically less active zone.

scholarly journals Fractal dimension of external linear contour of human cerebellum (magnetic resonance imaging study)

2021 ◽  
Vol 27 (2) ◽  
pp. 16-22
Author(s):  
N.I. Maryenko ◽  
O.Y. Stepanenko
Keyword(s):  
Fractal Dimension ◽  
Magnetic Resonance ◽  
Fractal Analysis ◽  
Spatial Configuration ◽  
Magnetic Resonance Images ◽  
Counting Method ◽  
Average Value ◽  
Box Counting ◽  
Human Cerebellum ◽  
Box Counting Method

Fractal analysis is a method of mathematical analysis, which provides quantitative assessment of the spatial configuration complexity of the anatomical structures and may be used as a morphometric method. The purpose of the study was to determine the values of the fractal dimension of the outer linear contour of human cerebellum by studying the magnetic resonance images of the brain using the authors’ modification of the caliper method and compare to the values determined using the box counting method. Brain magnetic resonance images of 30 relatively healthy persons aged 18-30 years (15 men and 15 women) were used in the study. T2-weighted digital magnetic resonance images were studied. The midsagittal MR sections of the cerebellar vermis were investigated. The caliper method in the author’s modification was used for fractal analysis. The average value of the fractal dimension of the linear contour of the cerebellum, determined using the caliper method, was 1.513±0.008 (1.432÷1.600). The average value of the fractal dimension of the linear contour of the cerebellum, determined using the box counting method, was 1.530±0.010 (1.427÷1.647). The average value of the fractal dimension of the cerebellar tissue as a whole, determined using the box counting method, was 1.760±0.006 (1.674÷1.837). The values of the fractal dimension of the outer linear contour of the cerebellum, determined using the caliper method and the box counting method were not statistically significantly different. Therefore, both methods can be used for fractal analysis of the linear contour of the cerebellum. Fractal analysis of the outer linear contour of the cerebellum allows to quantify the complexity of the spatial configuration of the outer surface of the cerebellum, which is difficult to estimate using traditional morphometric methods. The data obtained from this study and the methodology of the caliper method of fractal analysis in the author’s modification can be used for morphometric investigations of the human cerebellum in morphological studies, as well as in assessment of cerebellar MR images for diagnostic purposes.

FRACTAL CHARACTERIZATION OF ULTRASONIC SIGNALS FROM POLYCRYSTALLINE MATERIALS

Fractals ◽  
1995 ◽  
Vol 03 (01) ◽  
pp. 1-8
Author(s):  
DEBASHREE DUTTA ◽  
S.N. GANGULY ◽  
P. BARAT ◽  
P. MUKHERJEE ◽  
S.K. BANDYOPADHYAY ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Sampling Rate ◽  
Polycrystalline Materials ◽  
Ultrasonic Signals ◽  
Box Counting ◽  
Power Spectral ◽  
Box Counting Method ◽  
Pulse Echo ◽  
First Time

For the first time the concept of fractal geometry is introduced to characterize discrete time domain ultrasonic signals scattered from polycrystalline materials aluminium and brass using the pulse echo method. The fractal dimension of these scattered signals was evaluated using the box counting method and power spectral method. These signals possess unique fractal dimension which remains invariant with the change in sampling rate of signal capturing. The fractal dimension evaluated by the above two methods remains constant in case of aluminium but gives remarkably different values for brass. This observation is interpreted on the basis of the variation of scattering mechanism in these two materials.

3D box-counting algorithm for calculating fractal dimension of cities

2010 ◽  
Vol 30 (8) ◽  
pp. 2070-2072
Author(s):  
Le-shan ZHANG ◽  
Ge CHEN ◽  
Yong HAN ◽  
Tao ZHANG
Keyword(s):  
Fractal Dimension ◽  
Box Counting ◽  
Counting Algorithm

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

CT Image Analysis on the Meso-Damage of Construction Waste Recycled Brick

2012 ◽  
Vol 588-589 ◽  
pp. 1930-1933
Author(s):  
Guo Song Han ◽  
Hai Yan Yang ◽  
Xin Pei Jiang
Keyword(s):  
Fractal Dimension ◽  
Strain Curve ◽  
Ct Image ◽  
Stress Strain Curve ◽  
Crack Evolution ◽  
Construction Waste ◽  
Box Counting ◽  
Industrial Ct ◽  
Ct Image Analysis ◽  
Box Counting Method

Based on industrial CT technique, Meso-mechanical experiment was conducted on construction waste recycled brick to get the real-time CT image and stress-strain curve of brick during the loading process. Box counting method was used to calculate the fractal dimension of the inner pore transfixion and crack evolution. The results showed that lots of pore in the interfacial transition zone mainly resulted in the damage of the brick. With the increase of stress, the opening through-pore appeared and crack expanded, and the fractal dimension increased.

Differences in and correlations between cognitive abilities and brain volumes in healthy control, mild cognitive impairment, and Alzheimer disease groups

2016 ◽  
Vol 29 (4) ◽  
pp. 473-480 ◽  
Author(s):  
Soon-Cheol Chung ◽  
Mi-Hyun Choi ◽  
Hyung-Sik Kim ◽  
Jung-Chul Lee ◽  
Sung-Jun Park ◽  
...  
Keyword(s):  
Cognitive Impairment ◽  
Mild Cognitive Impairment ◽  
Alzheimer Disease ◽  
Cognitive Abilities ◽  
Brain Volumes ◽  
Healthy Control

Outer Cutoff Value for the Box-Counting Method for Fractal Analysis of the Nucleus Using Kirsch Edge Detection

2020 ◽  
pp. 1-8
Author(s):  
Haruhiko Yoshioka ◽  
Kouki Minami ◽  
Hirokazu Odashima ◽  
Keita Miyakawa ◽  
Kayo Horie ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Edge Detection ◽  
Fractal Analysis ◽  
Nuclear Size ◽  
Original Position ◽  
Cytological Diagnosis ◽  
Cutoff Value ◽  
Position Bias ◽  
Box Counting ◽  
Nuclear Rotation

<b><i>Objective:</i></b> The complexity of chromatin (i.e., irregular geometry and distribution) is one of the important factors considered in the cytological diagnosis of cancer. Fractal analysis with Kirsch edge detection is a known technique to detect irregular geometry and distribution in an image. We examined the outer cutoff value for the box-counting (BC) method for fractal analysis of the complexity of chromatin using Kirsch edge detection. <b><i>Materials:</i></b> The following images were used for the analysis: (1) image of the nucleus for Kirsch edge detection measuring 97 × 122 pix (10.7 × 13.4 μm) with a Feret diameter of chromatin mesh (<i>n</i> = 50) measuring 17.3 ± 1.8 pix (1.9 ± 0.5 μm) and chromatin network distance (<i>n</i> = 50) measuring 4.4 ± 1.6 pix (0.49 ± 0.18 μm), and (2) sample images for Kirsch edge detection with varying diameters (10.4, 15.9, and 18.1 μm) and network width of 0.4 μm. <b><i>Methods:</i></b> Three types of bias that can affect the outcomes of fractal analysis in cytological diagnosis were defined. (1) Nuclear position bias: images of 9 different positions generated by shifting the original position of the nucleus in the middle of a 256 × 256 pix (28.1 μm) square frame in 8 compass directions. (2) Nuclear rotation bias: images of 8 different rotations obtained by rotating the original position of the nucleus in 45° increments (0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°). (3) Nuclear size bias: images of varying size (diameter: 190 pix [10.4 μm], 290 pix [15.9 μm], and 330 pix [18.1 μm]) with the same mesh pattern (network width: 8 pix [0.4 μm]) within a 512 × 512 pix square. Different outer cutoff values for the BC method (256, 128, 64, 32, 16, and 8 pix) were applied for each bias to assess the fractal dimension and to compare the coefficient of variation (CV). <b><i>Results:</i></b> The BC method with the outer cutoff value of 32 pix resulted in the least variation of fractal dimension. Specifically, with the cutoff value of 32 pix, the CV of nuclear position bias, nuclear rotation bias, and nuclear size bias were &#x3c;1% (0.1, 0.4, and 0.3%, respectively), with no significant difference between the position and rotation bias (<i>p</i> = 0.19). Our study suggests that the BC method with the outer cutoff value of 32 pix is suitable for the analysis of the complexity of chromatin with chromatin mesh.

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