Probes, populations, samples, measurements and relations in stereology

Abstract

This summary paper provides an overview of the content of stereology. The typical problem at hand centers around some three dimensional object that has an internal structure that determines its function, performance, or response. To understand and quantify the geometry of that structure it is necessary to probe it with geometric entities: points, lines, planes volumes, etc. Meaningful results are obtained only if the set of probes chosen for use in the assessment is drawn uniformly from the population of such probes for the structure as a whole. This requires an understanding of the population of each kind of probe. Interaction of the probes with the structure produce geometric events which are the focus of stereological measurements. In almost all applications the measurement that is made is a simple count of the number of these events. Rigorous application of these requirements for sample design produce unbiased estimates of geometric properties of features in the structure no matter how complex are the features or what their arrangement in space. It is this assumption-free characteristic of the methodology that makes it a powerful tool for characterizing the internal structure of three dimensional objects.