An Approximated Box Height for Differential-Box-Counting Method to Estimate Fractal Dimensions of Gray-Scale Images

Panigrahy, Chinmaya; García‐Pedrero, Ángel; Seal, Ayan; Rodríguez-Esparragón, Dionisio; Mahato, Nihar Kumar; Gonzalo-Martín, Consuelo

doi:10.3390/e19100534

Cited by 32 publications

(11 citation statements)

References 20 publications

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“…The FD assessing of a document is a promising method as it is a fast one and can be cost effective and easily to implemented. In this respect, further studies have to be carried out to implement the box method using the J-image freeware for assessing the FD of the documents [30,31]…”

Section: Discussionmentioning

confidence: 99%

Studies Concerning the Usage of the Intrinsic Morphological and Chemical Features of Some Common and Document Paper Types as Security Items

Pencea¹,

Turcu²,

Miculescu³

et al. 2018

Rev. Chim.

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The paper addresses the usage of the intrinsic security features which is a challenge for lowering the document protection costs. Three types of papers were investigated using ESEM-EDS and ED(P)-XRFS in order to identify and characterize overt and covert intrinsic items. The paper shows that some of the intrinsic morphological features of document paper can be successfully used as taggants. The chemical compositions can be used as internal marks for forensic authentication of the ballpoint pen imprints. Two new ways are proposed for enhancing the document safety protection: the usage of the fractal dimension of the paper pattern and the intentional admixture into paper mass of cheaper substances as taggants in conjunction with SEM and XRF techniques.

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Section: Discussionmentioning

confidence: 99%

Studies Concerning the Usage of the Intrinsic Morphological and Chemical Features of Some Common and Document Paper Types as Security Items

Pencea¹,

Turcu²,

Miculescu³

et al. 2018

Rev. Chim.

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“…First the whole image is considered, then with each iteration the box size is decreased by a factor of two and thus plotting all the values for each iteration the slope of the common line by this points is considered as the fractal dimension [24]. There is a disadvantage of this method which we faced during our calculations, that this method is simple for 2-D body but when 3-D is considered the number of box count increases at a very high rate which requires more memory to store box counts and thus the calculation cost increases rapidly [25]. Most of the time the program crashes before achieving the accurate result (although it depends on the capacity of the computer).…”

Section: Box Counting Methodsmentioning

confidence: 99%

Fatigue crack analysis of ferrite material by acoustic emission technique

Khan¹,

Rashid²,

Hidaka³

et al. 2019

JMES

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Recently in various fields, numerous researches are going on for the assessment of material damage on the basis of crack initiation and propagation. Various methods are available in NDT for this purpose, among which analysis using released acoustic emission (AE) waves due to crack propagation is very effective due to its dynamic monitoring features. Various approaches are proposed for long time to make it an ideal method for accurate monitoring of crack behaviors in materials. In fragmentation theory there are some proportionality among the relations of AE event, AE energy, area and volume of cracks etc., which are calculated from the released AE waves from any dynamic crack. It has been found that the necessity of calculating the fractal dimension is important in verifying these relationships. This parameter is emphasized for determining the geometry of the irregularity in crack surface and crack volume. In this paper a novel approach based on image processing is proposed to find out the fractal dimension for analyzing the crack propagation characteristics. Finally, the proportionality relationships of AE parameters with crack propagation behavior in ferrite cast iron under fatigue loading are demonstrated experimentally.

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“…It gives fractal dimension through counting the number of boxes the image covers. This method can be used on the twodimensional images of approximate fractal structures (Mandelbrot, 1982, Panigrahy et al, 2017. However, this method's success depends on the resolution of the images.…”

Section: Dimension Calculations Of Approximate and Statistical Fractalsmentioning

confidence: 99%

“…Some other fractals, called statistical fractals, have numerical measures. Dimensions of quasi or statistical fractals can be estimated approximately (Panigrahy et al, 2017). Examples of exact, approximate and statistical fractals are presented in Fig.…”

Section: Introductionmentioning

confidence: 99%

Fractal Dimension as a Diagnostic Tool for Cardiac Diseases

Öztürk¹

2019

IJCET

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The discovery of fractal geometry has been one of the major developments in mathematics. Fractals, defined as selfsimilar structures, provide a new approach to the understanding of irregular structures. The dimensions of complete fractals can be easily calculated as real numbers with the fractal geometry approach. However, most of the structures in nature do not demonstrate self-similarity fully, and different approaches are needed for dimension calculations. These structures with semi-fractal properties are known as quasi fractals. Fractals derived from time series are called statistical fractals and they are an example for quasi fractals. Various methods have been developed to estimate the dimensions of statistical fractals. In this study, the methods which predict dimension in statistical fractals were investigated and the most suitable method for time series was identified. Fractal dimensions were calculated by using ECGs of 236 individuals, and the data set was divided into four disease groups and a control group of healthy individuals. Various statistical analyses were performed using the fractal dimensions of the graphs computed with MATLAB. Statistical hypothesis tests showed that the differences between the group mean of fractal dimensions are significant. Fractal dimensions of ECGs have the potential to be used as a diagnostic tool in the diagnosis of heart diseases.

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An Approximated Box Height for Differential-Box-Counting Method to Estimate Fractal Dimensions of Gray-Scale Images

Cited by 32 publications

References 20 publications

Studies Concerning the Usage of the Intrinsic Morphological and Chemical Features of Some Common and Document Paper Types as Security Items

Studies Concerning the Usage of the Intrinsic Morphological and Chemical Features of Some Common and Document Paper Types as Security Items

Fatigue crack analysis of ferrite material by acoustic emission technique

Fractal Dimension as a Diagnostic Tool for Cardiac Diseases

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