Unbiased Stereological Estimation of d-Dimensional Volume in .n from an Isotropic Random Slice Through a Fixed Point

Unbiased stereological estimators of d-dimensional volume in .n are derived, based on information from an isotropic random r-slice through a specified point. The content of the slice can be subsampled by means of a spatial grid. The estimators depend only on spatial distances. As a fundamental lemma, an explicit formula for the probability that an isotropic random r-slice in .n through O hits a fixed point in .n is given.