Principles of an image-based algorithm for the quantification of dependencies between particle selections in sampling studies - Synopsis

A generalization of Gy?s model for the fundamental sampling error introduced the new ?parameter for the dependent selection of particles?, denoted as Cij. This allows for modeling deviations from the ideal situation where the selection of a pair of particles is composed of two independent selections. The generalized model potentially leads to more accurate variance estimates in the case of clustering of particles, differences in densities or sizes of the particles or repulsive inter-particle forces. A straightforward and practically applicable method is needed for the determination of this parameter for miscellaneous mixtures in industrial settings. In this contribution, the feasibility of using digital image analysis to determine this parameter Cij, will be demonstrated. Line transect sampling of a digital image was used to construct a transition probability matrix. A new algorithm to derive quantitative estimates for Cij will be presented and discussed. The applicability was verified by a photograph of zirconium silicate particles of sizes typical for industries dealing with pharmaceutical, food/feed, and environmental applications. Conditions affecting the practical applicability are identified and potential pitfalls will be discussed, including e.g. how a potential unrepresentative surface can affect the quality of the estimate of Cij.