Microprobe images of solidification studies are well known to be subject to a Poisson noise. That is, the radiation count at a pixel x for a certain element may be considered to be an observation of a Poisson random variable whose parameter is equal to the true chemical concentration of the element at x. By modeling the image as a random function, we are able to use geostatistical techniques to perform various filtering operations. This filtering of the image itself may be done using linear kriging. For explicitely nonlinear problems such as the estimation of the underlying histogram of the noisy image, or the estimation of the probability that locally the concentration passes a certain value (this probability is needed for segregation studies), it is usually not possible to use linear techniques as they give biased results. For this reason, we applied the nonlinear technique of Disjunctive Kriging to these nonlinear problems. Linear kriging needs only second order statistical models ( covariance functions or variograms) while disjunctive kriging needs bivariate distribution models. This approach 1s illustrated by examples of filtering of various X-ray mappings in steel samples.
Daly, C.; Jeulin, D.; and Benoît, D.
"Nonlinear Statistical Filtering and Applications to Segregation in Steels from Microprobe Images,"
Scanning Microscopy: Vol. 1992
, Article 13.
Available at: https://digitalcommons.usu.edu/microscopy/vol1992/iss6/13