An effective method to compute the box-counting dimension based on the mathematical definition and intervals

Wu, Jiaxin; Jin, Xin; Mi, Shuo; Tang, Jinbo

doi:10.1016/j.rineng.2020.100106

Cited by 62 publications

(26 citation statements)

References 7 publications

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“…Fractal analysis was performed based on Hausdorff-Besicovitch dimension by the box-counting method, 22,37 which involved partitioning the FRF segmented binary image of the ICC networks into several grid of boxes of equal size e 9 e. The procedure was performed for different values of e ranging from 2 to 512 (image size) in increments of powers of 2. Boxes containing at least one ICC pixel were considered positive, and those without any ICC pixels were considered negative.…”

Section: Icc Network Analysismentioning

confidence: 99%

Analysis of Regional Variations of the Interstitial Cells of Cajal in the Murine Distal Stomach Informed by Confocal Imaging and Machine Learning Methods

Mah

Avci

et al. 2022

Cel. Mol. Bioeng.

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Introduction-The network of Interstitial Cells of Cajal (ICC) plays a plethora of key roles in maintaining, coordinating, and regulating the contractions of the gastrointestinal (GI) smooth muscles. Several GI functional motility disorders have been associated with ICC degradation. This study extended a previously reported 2D morphological analysis and applied it to 3D spatial quantification of three different types of ICC networks in the distal stomach guided by confocal imaging and machine learning methods. The characterization of the complex changes in spatial structure of the ICC network architecture contributes to our understanding of the roles that different types of ICC may play in postprandial physiology, pathogenesis, and/or amelioration of GI dsymotility-bridging structure and function. Methods-A validated classification method using Trainable Weka Segmentation was applied to segment the ICC from a confocal dataset of the gastric antrum of a transgenic mouse, followed by structural analysis of the segmented images. Results-The machine learning model performance was compared to manually segmented subfields, achieving an area under the receiver-operating characteristic (AUROC) of 0.973 and 0.995 for myenteric ICC (ICC-MP; n = 6) and intramuscular ICC (ICC-IM; n = 17). The myenteric layer in the distal antrum increased in thickness (from 14.5 to 34 lm) towards the lesser curvature, whereas the thickness decreased towards the lesser curvature in the proximal antrum (17.7 to 9 lm). There was an increase in ICC-MP volume from proximal to distal antrum (406,960 ± 140,040 vs. 559,990 ± 281,000 lm 3 ; p = 0.000145). The % of ICC volume was similar for ICC-LM and for ICC-CM between proximal (3.6 ± 2.3% vs. 3.1 ± 1.2%; p = 0.185) and distal antrum (3.2 ± 3.9% vs. 2.5 ± 2.8%; p = 0.309). The aver-age % volume of ICC-MP was significantly higher than ICC-IM at all points throughout sample (p < 0.0001). Conclusions-The segmentation and analysis methods provide a high-throughput framework of investigating the structural changes in extended ICC networks and their associated physiological functions in animal models.

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Section: Icc Network Analysismentioning

confidence: 99%

Analysis of Regional Variations of the Interstitial Cells of Cajal in the Murine Distal Stomach Informed by Confocal Imaging and Machine Learning Methods

Mah

Avci

et al. 2022

Cel. Mol. Bioeng.

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“…Calculations with various sizes of this box, of course, require a long calculation time. However, even so, the box-counting method has the advantage that it can be implemented for complex or simple fractals on natural and artificial fractals [22].…”

Section: Box-counting Methodsmentioning

confidence: 99%

Combination of Coarse-Grained Procedure and Fractal Dimension for Epileptic EEG Classification

Rahmawati

Rizal

Silalahi

2021

Indonesian J. Comput. Cybern. Syst.

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Epilepsy, cured by some offered treatments such as medication, surgery, and dietary plan, is a neurological brain disorder due to disturbed nerve cell activity characterized by repeated seizures. Electroencephalographic (EEG) signal processing detects and classifies these seizures as one of the abnormality types in the brain within temporal and spectral content. The proposed method in this paper employed a combination of two feature extractions, namely coarse-grained and fractal dimension, a challenge to obtain a highly accurate procedure to evaluate and predict the epileptic EEG signal of normal, interictal, and seizure classes. The result of classification accuracy using variance fractal dimension (VFD) and quadratic support machine vector (SVM) with a number scale of 10 is 99% as the highest one, excellent performance of the predictive model in terms of the error rate. In addition, a higher scale number does not determine a higher accuracy in this study.

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“…The proposed fractal dimension D is the box-counting (Minkowski) dimension

applied in space according to the formula

where

denotes edge length of the sliding cube,

is the 3D data set of image voxels. The dimension is estimated by least squares method through a linear equation:

where

and

[ 51 ]. To obtain the dimension D , a gliding box of size

is used.…”

Section: Methodsmentioning

confidence: 99%

Changes in Fabric Surface Pilling under Laser Ablation

Korzeniewska

Gocławski

Sekulska‐Nalewajko

et al. 2020

Sensors

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Textiles require finishing to improve their usability and functionality but in the first place, to reduce of pilling tendency, which affects all kinds of synthetic and natural fabrics. Several laser ablation tests have been applied to the selected fabrics with different chemical composition to reveal the impact of this process on the pilling behavior. To reflect the pilling changes, two textural descriptors have been proposed to textile images obtained with optical coherence tomography (OCT). They showed the trend to reduce values with increasing laser power applied to the tested fabrics. It has been demonstrated, that in the case of textiles based on polyester threads, laser modification of the product surface led to a significant reduction in their tendency for pilling.

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An effective method to compute the box-counting dimension based on the mathematical definition and intervals

Cited by 62 publications

References 7 publications

Analysis of Regional Variations of the Interstitial Cells of Cajal in the Murine Distal Stomach Informed by Confocal Imaging and Machine Learning Methods

Analysis of Regional Variations of the Interstitial Cells of Cajal in the Murine Distal Stomach Informed by Confocal Imaging and Machine Learning Methods

Combination of Coarse-Grained Procedure and Fractal Dimension for Epileptic EEG Classification

Changes in Fabric Surface Pilling under Laser Ablation

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