Evgueni Spodarev

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We give algorithms for the simultaneous computation of the area, boundary length and connectivity (the so–called Minkowski functionals) of binary images. It is assumed that a binary image is a discretization of a two–dimensional polyconvex set which is a union of convex components. Edge–corrected versions of these algorithms are used for the estimation of(More)
An algorithm is proposed for the simultaneous computation of all Minkowski functionals (except for the volume) of sets from the convex ring in R d discretized with respect to a given regular lattice. For this purpose, a polyhedral approximation is used to reconstruct their boundary structure. In the planar case d = 2, the performance and precision of the(More)
Stationary random closed sets Ξ in R d are considered whose realizations belong to the extended convex ring. A new approach is proposed to joint estimation of the specific intrinsic volumes V 0 (Ξ),. .. , V d (Ξ) of Ξ, including the specific Euler–Poincaré characteristic V 0 (Ξ), the specific surface area 2V d−1 (Ξ), and the volume fraction V d (Ξ) of Ξ.(More)
A kriging based on residuals is employed for spatial extrapolation of anisotropic directional road–traffic data. The set of data considered in the present paper includes, among others, the actual geographic positions and velocities of approximately 300 test vehicles in downtown Berlin. They are transmitted to a central station within regular time intervals.(More)
A method of spatial extrapolation of traffic data is proposed. The traffic data is given by GPS signals over downtown Berlin sent by approximately 300 taxis. To reconstruct the traffic situation at a given time spatially, i.e. in the form of traffic maps, kriging with moving neighborhood based on residuals is used. Due to significant anisotropy in directed(More)
The Boolean model of Wiener sausages is a random closed set that can be thought of as a random collection of parallel neighborhoods of independent Wiener paths in space. It describes e.g. the target detection area of a network of sensors moving according to the Brownian dynamics whose initial locations are chosen in the medium at random. In the paper, the(More)
Es sei Φ d k ein stationärer Prozess von k–Ebenen in R d , also eine zufälli-ge höchstens abzählbare Ansammlung von k–dimensionalen Ebenen in R d. Ferner wird die Stationarität von Φ d k vorausgesetzt, also die Invarianz des Verteilungsgesetzes des Prozesses gegenüber Verschiebungen in R d. Die wich-tigsten Charakteristiken von Φ d k sind seine Intensität(More)