An extensive update to a classic text Stochastic geometry and spatial statistics play a
fundamental role in many modern branches of physics, materials sciences, engineering …

Taking and analyzing images of materials' microstructures is essential for quality control,
choice and design of all kind of products. Today, the standard method still is to analyze 2D …

We find conditions ensuring the existence of the outer Minkowski content for d-dimensional
closed sets in R^ d, in connection with regularity properties of their boundaries. Moreover …

The densities of the intrinsic volumes–in 3D the volume density, surface density, the density
of the integral of the mean curvature and the density of the Euler number–are a very useful …

Let $\alpha\in (1, 2] $ and $ X $ be an $\mathbb R^ d $-valued symmetric $\alpha $-stable
Lévy process starting at $0 $. We consider the closure $ S_t $ of the path described by $ X …

The K-hull of a compact set A⊆ R d, where K⊆ R d is a fixed compact convex body, is the
intersection of all translates of K that contain A. A set is called K-strongly convex if it …

Abstract Let Ξ n={ξ 1,⋯, ξ n} be a sample of n independent points distributed in a regular
closed element K of the extended convex ring in R d according to a probability measure μ on …

This paper establishes expectation and variance asymptotics for statistics of the Poisson–
Voronoi approximation of general sets, as the underlying intensity of the Poisson point …

A local method for estimating surface area and surface area measure of three-dimensional
objects from discrete binary images is presented. A weight is assigned to each 2× 2× 2 …

The standard convex closed hull of a set is defined as the intersection of all images, under
the action of a group of rigid motions, of a half-space containing the given set. In this paper …