Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T20:52:40.069Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  30 March 2010

Rémi Blanc ,
Pierre Baylou ,
Christian Germain  and
Jean-Pierre Da Costa
Rémi Blanc
Affiliation:
Rémi Blanc, Computer Vision Laboratory, ETHZ, Sternwartstrasse 7, ETH-Zentrum, CH-8092 Zürich, Switzerland
Pierre Baylou
Affiliation:
IMS, LAPS Department, CNRS UMR 5218, University of Bordeaux, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence, France
Christian Germain
Affiliation:
IMS, LAPS Department, CNRS UMR 5218, University of Bordeaux, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence, France
Jean-Pierre Da Costa*
Affiliation:
IMS, LAPS Department, CNRS UMR 5218, University of Bordeaux, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence, France
*
Corresponding author. E-mail: jean-pierre.dacosta@ims-bordeaux.fr
Get access

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.

Keywords

measurement uncertaintyphase fractionsingle section stereologyspatial statisticsnickel base superalloyscanning electron microscopy
Type
Instrumentation and Software: Development and Applications
Information
Microscopy and Microanalysis , Volume 16 , Issue 3 , June 2010 , pp. 273 - 281
Copyright
Copyright © Microscopy Society of America 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

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.Google Scholar
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), 1481–1490.CrossRefGoogle ScholarPubMed
Blanc, R., Germain, C., Da Costa, J.-P., Baylou, P. & Cataldi, M. (2006). Fiber orientation measurements in composite materials. Composites Part A 37(2), 197–206.CrossRefGoogle Scholar
Cruz-Orive, L.M. & Myking, A.O. (1981). Stereological estimation of volume ratios by systematic sections. J Microsc 122(2), 143–157.CrossRefGoogle ScholarPubMed
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. 1377–1386.Google Scholar
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, 127–134.CrossRefGoogle Scholar
Lantuéjoul, C. (1991). Ergodicity and integral range. J Microsc 161(3), 387–403.CrossRefGoogle Scholar
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.Google Scholar
Matheron, G. (1989). Estimating and Choosing: An Essay on Probability in Practice. New York: Springer.CrossRefGoogle Scholar
Ohser, J. & Mücklich, F. (2000). Statistical Analysis of Microstructures in Material Sciences. Chichester, U.K.: J. Wiley & Sons.Google Scholar
Politis, D. & Sherman, M. (2001). Moment estimation for statistics from marked point processes. J Royal Stat Soc B 63(2), 261–275.CrossRefGoogle Scholar
Russ, J.C. & Dehoff, R.T. (2000). Practical Stereology, 2nd Ed.New York: Plenum Press.CrossRefGoogle Scholar
Serra, J. (1982). Image Analysis and Mathematical Morphology. London: Academic Press.Google Scholar
Sharifi-Salamatian, V., Pesquet-Popescu, B., Simony-Lafontaine, J. & Rigaut, J.-P. (2004). Index for spatial heterogeneity in breast cancer. J Microsc 216(2), 110–122.CrossRefGoogle ScholarPubMed
Sherman, M. (1996). Variance estimation for statistics computed from spatial lattice data. J Royal Stat Soc B 58(3), 509–523.Google Scholar
Stoyan, D., Kendall, W.S. & Mecke, J. (1995). Stochastic Geometry and Its Applications, 2nd Ed.New York: J. Wiley & Sons.Google Scholar