SUMMARYWe survey the use of Markov models from stochastic geometry as priors in 'high-level' computer vision, in

We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the n-point correlation functions and reduce to cross J -and D-functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions. We derive ratio-unbiased minus sampling estimators for our statistics and illustrate their use on a data set of wildfires.

ABSTRACT. We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationarity spatio-temporal point processes. The statistic is defined in terms of the n-point correlation functions of the point process, and it generalizes the J -function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to the spatio-temporal K-function. We further discuss its explicit form under some specific model assumptions and derive ratio-unbiased estimators. We finally illustrate the use of our statistic in practice.

a b s t r a c tThe goal of this paper is to give an overview of random tessellation models. We discuss the classic isotropic Poisson line tessellation in some detail and then move on to more complicated models, including Arak-Clifford-Surgailis polygonal Markov fields and their Gibbs field counterparts, crystal growth models such as the Poisson-Voronoi, Johnson-Mehl and Laguerre random tessellations, and the STIT nesting scheme. An extensive list of references is included as a guide to the literature.