Assessment of Texture Stationarity Using the Asymptotic Behavior of the Empirical Mean and Variance

Blanc, Rémy; Costa, Jean-Pierre da; Stitou, Y.; Baylou, Pierre; Germain, Christian

doi:10.1109/tip.2008.2001403

Cited by 6 publications

(6 citation statements)

References 25 publications

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“…The fluctuations of the dispersion variance seen on Figure 8c,d are typical of strongly periodic structures (Blanc et al, 2008) corresponding to the regular disposition of the γ′ particles and γ channels. These fluctuations admit an upper envelope that can be extrapolated to get the estimate σ̃ 2D 2 of the variance σ 2D 2 of τ̃ 2D .…”

Section: Resultsmentioning

confidence: 66%

“…Specifically, an image is said to be homogeneous for the mean if the dispersion variance decreases asymptotically as fast as or faster than the inverse of the image size (Lantuéjoul, 1991; Blanc et al, 2008). In this case, the image can be considered as representative of its generating stochastic process, and the corresponding estimator is consistent, i.e., with a variance vanishing when the image size grows to infinity.…”

Section: Methodsmentioning

confidence: 99%

“…If the image homogeneity is confirmed, i.e., if the asymptotic decrease appears to be as fast as s −1 or faster, the variance of the mean estimator is estimated by extrapolating the dispersion variance curve up to window size S . The detailed demonstration is out of the scope of this article, and we direct the interested reader to Blanc et al (2008) and references therein for more details.…”

Section: Methodsmentioning

confidence: 99%

“…Second, the statistical aspects related to the representativeness of the available image sample must be tackled. This involves the analysis of the spatial distribution of the phase of interest and the evaluation of the statistical properties of the phase fraction estimator (Lantuéjoul, 1991; Blanc et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

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Confidence Bounds for the Estimation of the Volume Phase Fraction from a Single Image in a Nickel Base Superalloy

et al. 2010

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Abstract:We propose an image-based framework to evaluate the uncertainty in the estimation of the volume fraction of specific microstructures based on the observation of a single section. These microstructures consist of cubes organized on a cubic mesh, such as monocrystalline nickel base superalloys. The framework is twofold: a model-based stereological analysis allows relating two-dimensional image observations to three-dimensional microstructure features, and a spatial statistical analysis allows computing approximate confidence bounds while assessing the representativeness of the image. The reliability of the method is assessed on synthetic models. Volume fraction estimation variances and approximate confidence intervals are computed on real superalloy images in the context of material characterization.

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Section: Resultsmentioning

confidence: 66%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Confidence Bounds for the Estimation of the Volume Phase Fraction from a Single Image in a Nickel Base Superalloy

et al. 2010

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“…Uncertainties for , , , and 50 follow from the standard errors of the moments ( [39]; Benedict and Gould, 1996; [40]) based on the standard deviations of the observed distributions. The uncertainty calculation for the information content follows Shannon [29].…”

Section: Resultsmentioning

confidence: 99%

Large-Scale Analysis of Relationships between Mineral Dust, Ice Cloud Properties, and Precipitation from Satellite Observations Using a Bayesian Approach: Theoretical Basis and First Results for the Tropical Atlantic Ocean

Klüser

Popp

2017

Advances in Meteorology

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Mineral dust and ice cloud observations from the Infrared Atmospheric Sounding Interferometer (IASI) are used to assess the relationships between desert dust aerosols and ice clouds over the tropical Atlantic Ocean during the hurricane season 2008. Cloud property histograms are first adjusted for varying cloud top temperature or ice water path distributions with a Bayesian approach to account for meteorological constraints on the cloud variables. Then, histogram differences between dust load classes are used to describe the impact of dust load on cloud property statistics. The analysis of the histogram differences shows that ice crystal sizes are reduced with increasing aerosol load and ice cloud optical depth and ice water path are increased. The distributions of all three variables broaden and get less skewed in dusty environments. For ice crystal size the significant bimodality is reduced and the order of peaks is reversed. Moreover, it is shown that not only are distributions of ice cloud variables simply shifted linearly but also variance, skewness, and complexity of the cloud variable distributions are significantly affected. This implies that the whole cloud variable distributions have to be considered for indirect aerosol effects in any application for climate modelling.

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Full 3D investigation and characterisation of capillary collapse of a loose unsaturated sand using X-ray CT

et al. 2013

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International audienceThe aim of this paper is to characterise in 3D the capillary collapse phenomenon using X-ray Computed Tomography (X-ray CT) during water infiltration into a partially saturated soil. To understand the mechanisms leading to capillary collapse, we progressivelly saturated a specimen of sand by controlling the water pressure using the negative water column technique. During this imbibition process, we followed the granular structure using X-ray CT. The microstructure was analysed to assess the volume of water filling the pores and deformation of the granular skeleton using Volumetric Digital Image Correlation tools. Matheron's granulometry was used in parallel to characterize the initial microstructure and its evolution during the imbibition. We show that the collapse phenomenon can occur in a clean sand and can be controlled continuously with the negative water column technique. The volume change of the specimen at local scale started at a particular water content which coincided with the coalescence of capillary bridges between grain clusters. Gravity effects leading to a non-negligible gradient of the hydrostatic pressure along the specimen's height were observed and induced a vertical gradient of strain. Localisation of the vertical strain on conical surfaces and of the volumetric strain and water content at the bottom corner of the specimen appeared during the imbibition process. These localisations are thought to be due to an inhomogeneity of the initial density or/and an effect of cell walls facilitating the sliding of grains and the provision of water along preferential paths. However, in spite of those localisations, macroscopic measurements at the scale of the sample were representative of the local behaviour of the unsaturated sand. © 2013 Springer-Verlag Berlin Heidelberg

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Assessment of Texture Stationarity Using the Asymptotic Behavior of the Empirical Mean and Variance

Cited by 6 publications

References 25 publications

Confidence Bounds for the Estimation of the Volume Phase Fraction from a Single Image in a Nickel Base Superalloy

Confidence Bounds for the Estimation of the Volume Phase Fraction from a Single Image in a Nickel Base Superalloy

Large-Scale Analysis of Relationships between Mineral Dust, Ice Cloud Properties, and Precipitation from Satellite Observations Using a Bayesian Approach: Theoretical Basis and First Results for the Tropical Atlantic Ocean

Full 3D investigation and characterisation of capillary collapse of a loose unsaturated sand using X-ray CT

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