We consider selected geometric properties of 2D or 3D sets, given in form of binary digital pictures, and discuss their estimation. The properties examined are perimeter and area in 2D, and surface area and volume in 3D. We evaluate common estimators in stereology and digital geometry according to their multiprobe or multigrid convergence properties, and precision and efficiency of estimations....

Stereology is the part of imaging science in which the three-dimensional structure of a body is determined from two-dimensional views. Although it is relatively easy to determine volume information from 2-D slices, it is nontrivial in general to determine other physical properties such as internal surface areas unless the medium is known to have some simple symmetry such as isotropy. For this r...

Stereological studies are more and more frequent in literature, particularly in the development/evolution, pathology, and neurosciences areas. The stereology challenge is to understand the structural inner three-dimensional arrangement based on the analysis of the structure slices only showing two-dimensional information. Cavalieri and Scherle's methods to estimate volume, and Buffon's needle p...

Design-based stereology is the gold standard of morphometry in lung research. Here, we analyze the current use of morphometric and stereological methods in lung research and provide an overview on recent methodological developments and biological observations made by the use of stereology. Based on this analysis we hope to provide useful recommendations for a good stereological practice to furt...