A program for fractal and multifractal analysis of two-dimensional binary images: Computer algorithms versus mathematical theory

Perrier, Edith; Tarquis, Ana M.; Dathe, Annette

doi:10.1016/j.geoderma.2006.03.023

Cited by 51 publications

(32 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…41 The fractal analyses depend on the fractal analysis methods, including the algorithm and specific calculation used. 22,27,31,36,39,40 In our study, the most appropriate method of fractal analysis for the analyzed surfaces is morphological envelopes. 23 In this method 26 the upper and lower envelopes are calculated by morphological opening and closing using a structuring element which is a horizontal line segment of length e. The graph of the calculated volume for surfaces (Ve) is drawn as a function of the scale (size of the structuring elements): ln(Ve)/ln(e).…”

Section: Fractal Analysis Of the Texturementioning

confidence: 82%

“…22 It also determines how the fractal differs from Euclidean objects. 36,37,39 There are many computational approaches for estimating the fractal dimension, 22,27,31,36,40 including box-counting, mass--radius, and density-density correlation function method. In ophthalmology, fractal and multifractal analyses have been applied for the quantitative description of irregular surface microstructures.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractal Analysis of AFM Images of the Surface of Bowman’s Membrane of the Human Cornea

et al. 2014

View full text Add to dashboard Cite

The objective of this study is to further investigate the ultrastructural details of the surface of Bowman's membrane of the human cornea, using atomic force microscopy (AFM) images. One representative image acquired of Bowman's membrane of a human cornea was investigated. The three-dimensional (3-D) surface of the sample was imaged using AFM in contact mode, while the sample was completely submerged in optisol solution. Height and deflection images were acquired at multiple scan lengths using the MFP-3D AFM system software (Asylum Research, Santa Barbara, CA), based in IGOR Pro (WaveMetrics, Lake Oswego, OR). A novel approach, based on computational algorithms for fractal analysis of surfaces applied for AFM data, was utilized to analyze the surface structure. The surfaces revealed a fractal structure at the nanometer scale. The fractal dimension, D, provided quantitative values that characterize the scale properties of surface geometry. Detailed characterization of the surface topography was obtained using statistical parameters, in accordance with ISO 25178-2: 2012. Results obtained by fractal analysis confirm the relationship between the value of the fractal dimension and the statistical surface roughness parameters. The surface structure of Bowman's membrane of the human cornea is complex. The analyzed AFM images confirm a fractal nature of the surface, which is not taken into account by classical surface statistical parameters. Surface fractal dimension could be useful in ophthalmology to quantify corneal architectural changes associated with different disease states to further our understanding of disease evolution.

show abstract

Section: Fractal Analysis Of the Texturementioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Fractal Analysis of AFM Images of the Surface of Bowman’s Membrane of the Human Cornea

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Information on the pore size distribution is easily available from image analysis (2-D representative soil sections are enough) see Bartoli et al (1999) for how to measure the pore distribution and also Perrier et al (2006) for how to compute the mass fractal dimension for an 2-D image of the pore-solid interface. Information on the connectivity of the pore network is more difficult to obtain in a direct way.…”

Section: Discussionmentioning

confidence: 99%

Percolation properties of 3-D multiscale pore networks: how connectivity controls soil filtration processes

2010

View full text Add to dashboard Cite

Abstract. Quantifying the connectivity of pore networks is a key issue not only for modelling fluid flow and solute transport in porous media but also for assessing the ability of soil ecosystems to filter bacteria, viruses and any type of living microorganisms as well inert particles which pose a contamination risk. Straining is the main mechanical component of filtration processes: it is due to size effects, when a given soil retains a conveyed entity larger than the pores through which it is attempting to pass. We postulate that the range of sizes of entities which can be trapped inside soils has to be associated with the large range of scales involved in natural soil structures and that information on the pore size distribution has to be complemented by information on a critical filtration size (CFS) delimiting the transition between percolating and non percolating regimes in multiscale pore networks. We show that the mass fractal dimensions which are classically used in soil science to quantify scaling laws in observed pore size distributions can also be used to build 3-D multiscale models of pore networks exhibiting such a critical transition. We extend to the 3-D case a new theoretical approach recently developed to address the connectivity of 2-D fractal networks (Bird and Perrier, 2009). Theoretical arguments based on renormalisation functions provide insight into multi-scale connectivity and a first estimation of CFS. Numerical experiments on 3-D prefractal media confirm the qualitative theory. These results open the way towards a new methodology to estimate soil filtration efficiency from the construction of soil structural models to be calibrated on available multiscale data.

show abstract

“…Several authors maintain that the exact value of the mass fractal dimension cannot be readily calculated Bird et al, 2006;Perrier et al, 2006). Tel and Vicsek (1987), for instance, proposed practical methods to compute it, indicating that the standard methods for determining fractal dimensions must be applied with some caution.…”

Section: Introductionmentioning

confidence: 99%

Influence of thresholding in mass and entropy dimension of 3-D soil images

Tarquis

Heck

Grau³

et al. 2008

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

Abstract. With the advent of modern non-destructive tomography techniques, there have been many attempts to analyze 3-D pore space features mainly concentrating on soil structure. This analysis opens a challenging opportunity to develop techniques for quantifying and describe pore space properties, one of them being fractal analysis.Undisturbed soil samples were collected from four horizons of Brazilian soil and 3-D images at 45 µm resolution. Four different threshold criteria were used to transform computed tomography (CT) grey-scale imagery into binary imagery (pore/solid) to estimate their mass fractal dimension (D m ) and entropy dimension (D 1 ). Each threshold criteria had a direct influence on the porosity obtained, varying from 8 to 24% in one of the samples, and on the fractal dimensions. Linear scaling was observed over all the cube sizes, however depending on the range of cube sizes used in the analysis, D m could vary from 3.00 to 2.20, realizing that the threshold influenced mainly the scaling in the smallest cubes (length of size from 1 to 16 voxels).D m and D 1 showed a logarithmic relation with the apparent porosity in the image, however, the increase of both values respect to porosity defined a characteristic feature for each horizon that can be related to soil texture and depth.

show abstract

A program for fractal and multifractal analysis of two-dimensional binary images: Computer algorithms versus mathematical theory

Cited by 51 publications

References 5 publications

Fractal Analysis of AFM Images of the Surface of Bowman’s Membrane of the Human Cornea

Fractal Analysis of AFM Images of the Surface of Bowman’s Membrane of the Human Cornea

Percolation properties of 3-D multiscale pore networks: how connectivity controls soil filtration processes

Influence of thresholding in mass and entropy dimension of 3-D soil images

Contact Info

Product

Resources

About