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Setting out the principles of stereology from a statistical viewpoint, this book focuses on both
basic theory and practical implications. The authors discuss ways to effectively communicate …

This paper develops a significant extension of E. Lutwak's dual Brunn–Minkowski theory,
originally applicable only to star-shaped sets, to the class of bounded Borel sets. The focus …

The covariogram gK of a convex body K in Ed is the function which associates to each x∈
Ed the volume of the intersection of K with K+ x. In 1986 G. Matheron conjectured that for d …

The stereological estimation of second‐order descriptors of spatial architecture appears to
be inherently more time‐consuming and labour‐intensive than the estimation of first‐order …

Basic properties of finite subsets of the integer lattice ℤ n are investigated from the point of
view of geometric tomography. Results obtained concern the Minkowski addition of convex …

The covariogram gX of a measurable set X in ℝn is the function which associates to each
x∈ ℝ n the measure of the intersection of X with X+ x. We are interested in understanding …

The cross covariogram gK, L of two convex sets K, L⊂ Rn is the function which associates to
each x∈ Rn the volume of the intersection of K with L+ x. The problem of determining the …

Abstract According to Kendall (1989), in shape theory, The idea is to filter out effects
resulting from translations, changes of scale and rotations and to declare that shape is “what …

We propose strongly consistent algorithms for reconstructing the characteristic function $1
_K $ of an unknown convex body $ K $ in $\mathbb {R}^ n $ from possibly noisy …