Fractal dimension based on Minkowski‐Bouligand method using exponential dilations

Luppe, Maximiliam

doi:10.1049/el.2015.0156

Cited by 7 publications

(3 citation statements)

References 5 publications

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“…The fractal dimension measures the ability of a self-similar structure to fill the three-dimensional space it occupies. The fractal dimension of the capillary network was calculated on the skeletonized image using the Minkowski–Bouligan method [ 17 ], also called Box Counting method, with BoneJ plugin.…”

Section: Methodsmentioning

confidence: 99%

3D Imaging and Quantitative Characterization of Mouse Capillary Coronary Network Architecture

Nicolas

Roux

2021

Biology

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Characterization of the cardiac capillary network structure is of critical importance to understand the normal coronary functional properties and coronary microvascular diseases. The aim of our study was to establish an accessible methodology for 3D imaging and 3D processing to quantitatively characterize the capillary coronary network architecture in mice. Experiments were done on C57BL/6J mice. 3D imaging was performed by light sheet microscopy and confocal microscopy on iDISCO+ optical cleared hearts after labelling of the capillary endothelium by lectin injection. 3D images were processed with the open source software ImageJ. Non-visual image segmentation was based of the frequency distribution of the voxel greyscale values, followed by skeletonization and distance mapping. Capillary networks in left and right ventricles and septum were characterized by the volume network density, the fractal dimension, the number of segments and nodes and their ratio, the total network length, and the average length, diameter, and tortuosity of the segments. Scale-dependent parameter values can be impacted by the resolution limit of the 3D imaging technique. The proposed standardized methodology for 3D image processing is easily accessible for a biologist in terms of investment and difficulty level, and allows the quantification of the 3D capillary architecture and its statistical comparison in different conditions.

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Section: Methodsmentioning

confidence: 99%

3D Imaging and Quantitative Characterization of Mouse Capillary Coronary Network Architecture

Nicolas

Roux

2021

Biology

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“… 38 The calculation of the fractal dimension from the vascular skeleton can be done automatically with ImageJ “BoneJ” plugin 39 that uses the Minkowski-Bouligand “box counting” method. 40 …”

Section: Morphometric Descriptorsmentioning

confidence: 99%

3D imaging and morphometric descriptors of vascular networks on optically cleared organs

Nicolas,

Dinet,

Roux

2023

iScience

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“…Minkowski-Bouligand dimension (MBD) [30], is a way of estimating the fractal dimension, by imaging the pattern lying over an equally-spaced grid and counting how many boxes are required to cover [31]. The box counting method can get the curve of required boxes with the grid scale [32].…”

Section: Minkowski-bouligand Dimensionmentioning

confidence: 99%

Fractal Dimension Estimation for Developing Pathological Brain Detection System Based on Minkowski-Bouligand Method

et al. 2016

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It is of enormous significance to detect abnormal brains automatically. This paper develops an efficient pathological brain detection system based on the artificial intelligence method. We first extract brain edges by a Canny edge detector. Next, we estimated the fractal dimension using box counting method with grid sizes of 1, 2, 4, 8, and 16, respectively. Afterward, we employed the single-hidden layer feedforward neural network. Finally, we proposed an improved particle swarm optimization based on three-segment particle representation, time-varying acceleration coefficient, and chaos theory. This three-segment particle representation encodes the weights, biases, and number of hidden neuron. The statistical analysis showed the proposed method achieves the detection accuracies of 100%, 98.19%, and 98.08% over three benchmark data sets. Our method costs merely 0.1984 s to predict one image. Our performance is superior to the 11 state-of-the-art approaches.INDEX TERMS Minkowski Bouligand dimension, genetic algorithm, artificial bee colony, logistic map, number of hidden neuron, K-fold cross validation.

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Fractal dimension based on Minkowski‐Bouligand method using exponential dilations

Cited by 7 publications

References 5 publications

3D Imaging and Quantitative Characterization of Mouse Capillary Coronary Network Architecture

3D Imaging and Quantitative Characterization of Mouse Capillary Coronary Network Architecture

3D imaging and morphometric descriptors of vascular networks on optically cleared organs

Fractal Dimension Estimation for Developing Pathological Brain Detection System Based on Minkowski-Bouligand Method

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