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- Simone Klenk, Volker Schmidt, Evgueni Spodarev
- Comput. Geom.
- 2006

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)

- Ralph Guderlei, Simone Klenk, Johannes Mayer, Volker Schmidt, Evgueni Spodarev
- Image Vision Comput.
- 2007

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)

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)

- Evgueni Spodarev, Volker Schmidt
- ISMM
- 2005

Random closed sets (RACS) in the d–dimensional Euclidean space are considered , whose realizations belong to the extended convex ring. A family of non-parametric estimators is investigated for the simultaneous estimation of the vector of all specific Minkowski functionals (or, equivalently, the specific intrinsic volumes) of stationary RACS. The… (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)

A new fast algorithm is proposed for simultaneous computation of all Minkowski functionals (or, equivalently, intrinsic volumes) of sets from the convex ring in R d discretized with respect to a given rectangular lattice. For this purpose, a certain kind of polyhedral approximation is used to reconstruct their boundary structure. Furthermore, two efficient… (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)

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