Having laid the general foundations in the previous chapters, we now study geometric processes in Rd and the random sets derived from them. By geometric processes we understand point processes of closed sets which are concentrated on geometrically distinguished subclasses of F′. In particular, we consider particle processes and flat processes. Particle processes are point processes in the subset C′ of nonempty compact sets. Special processes, in general more tractable, are obtained if only particles from the convex ring R or even the class K of convex bodies are admitted. A k-flat process is a point process in F′ whose intensity measure is concentrated on the space A(d, k) of k-dimensional flats (planes, affine subspaces) of Rd.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Geometric Models. In: Stochastic and Integral Geometry. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78859-1_4
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DOI: https://doi.org/10.1007/978-3-540-78859-1_4
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