Modelling and analysis of 3‐D arrangements of particles by point processes with examples of application to biological data obtained by confocal scanning light microscopy

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Abstract
Within the concept of point processes, a review is presented of quantities which can be used in studies of three-dimensional (3-D) aggregates of particles. Suitable characteristics and estimators are given for both unmarked and marked point processes. To demonstrate the feasibility of such quantitative approaches, an application in histology, dealing with 3-D arrangements of cell nuclei in rat liver, is described. Using a confocal scanning light microscope, 3-D images are recorded and image analysis used to obtain the coordinates of the centroid, together with the volume and DNA content, of each cell nucleus. Examples of results are given, using both unmarked and marked point processes. In the latter case, cell type, nuclear volume and ploidy group are suitable marks.