Skip to main content Accessibility help
×
Home

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

  • Rémi Blanc (a1), Pierre Baylou (a2), Christian Germain (a2) and Jean-Pierre Da Costa (a2)

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.

Copyright

Corresponding author

Corresponding author. E-mail: jean-pierre.dacosta@ims-bordeaux.fr

References

Hide All
Blanc, R. (2007). Apport des statistiques spatiales à l'élaboration de critères d'homogénéité et à l'inférence en analyse de textures; Application à la caractérisation de matériaux. Ph.D. thesis (in French), Bordeaux University.
Blanc, R., Da Costa, J.-P., Stitou, Y., Baylou, P. & Germain, C. (2008). Assessment of texture stationarity using the asymptotic behavior of the empirical mean and variance. IEEE Trans Image Processing 17(9), 14811490.
Blanc, R., Germain, C., Da Costa, J.-P., Baylou, P. & Cataldi, M. (2006). Fiber orientation measurements in composite materials. Composites Part A 37(2), 197206.
Cruz-Orive, L.M. & Myking, A.O. (1981). Stereological estimation of volume ratios by systematic sections. J Microsc 122(2), 143157.
Georget, D. & Peyroutou, C. (1990). Characterization of the γ′ phase in a superalloy by image analysis. In Proceedings of the High Temperature Materials for Power Engineering Conference, Liège, Belgium, pp. 13771386.
Germain, C., Blanc, R., Donias, M., Lavialle, O., Da Costa, J.-P. & Baylou, P. (2005). Estimating the section elevation angle of cubes on a cubic mesh. Application to nickel microstructure size estimation. Image Analysis and Stereology 24, 127134.
Lantuéjoul, C. (1991). Ergodicity and integral range. J Microsc 161(3), 387403.
Matheron, G. (1970). La théorie des variables régionalisées et ses applications. In Cahiers du centre de Morphologie Mathématique de Fontainebleau, Fasc. 5 (in French).Paris: Ecole Nationale Supérieure des Mines.
Matheron, G. (1989). Estimating and Choosing: An Essay on Probability in Practice. New York: Springer.
Ohser, J. & Mücklich, F. (2000). Statistical Analysis of Microstructures in Material Sciences. Chichester, U.K.: J. Wiley & Sons.
Politis, D. & Sherman, M. (2001). Moment estimation for statistics from marked point processes. J Royal Stat Soc B 63(2), 261275.
Russ, J.C. & Dehoff, R.T. (2000). Practical Stereology, 2nd Ed.New York: Plenum Press.
Serra, J. (1982). Image Analysis and Mathematical Morphology. London: Academic Press.
Sharifi-Salamatian, V., Pesquet-Popescu, B., Simony-Lafontaine, J. & Rigaut, J.-P. (2004). Index for spatial heterogeneity in breast cancer. J Microsc 216(2), 110122.
Sherman, M. (1996). Variance estimation for statistics computed from spatial lattice data. J Royal Stat Soc B 58(3), 509523.
Stoyan, D., Kendall, W.S. & Mecke, J. (1995). Stochastic Geometry and Its Applications, 2nd Ed.New York: J. Wiley & Sons.

Keywords

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

  • Rémi Blanc (a1), Pierre Baylou (a2), Christian Germain (a2) and Jean-Pierre Da Costa (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed