Modern light-, laser- and electron microscopes, as well as scanners yield almost exclusively digital pixel (2D) or voxel (3D) images, for which classical stereological methods are inapt. This project addresses the intriguing mathematical and statistical questions arising when studying the interplay between objects in the real world and their digital representations.

With the exception of volume and surface area very little is known about the quality of existing estimators for additive geometric characteristics, like the Euler characteristic, integrated mean curvature or general intrinsic volumes. The recently achieved results for estimators of surface area and their asymptotic worst case error are based on a theoretical breakthrough in digital stereology obtained by members of the project group and Jan Rataj, Prague. We aim at establishing a novel set of digital estimators for intrinsic volumes and their variances, using a very general Steiner type formula for arbitrary closed sets.