On connected component Markov point processes

@article{Chin1999OnCC,
  title={On connected component Markov point processes},
  author={Y. C. Chin and Adrian J. Baddeley},
  journal={Advances in Applied Probability},
  year={1999},
  volume={31},
  pages={279 - 282}
}
We note some interesting properties of the class of point processes which are Markov with respect to the ‘connected component’ relation. Results in the literature imply that this class is closed under random translation and independent cluster generation with almost surely non-empty clusters. We further prove that it is closed under superposition. A wide range of examples is also given. 
Markov interacting component processes
A generalization of Markov point processes is introduced in which interactions occur between connected components of the point pattern. A version of the Hammersley-Clifford characterization theorem
A note on the superposition of Markov point processes
We show that independent superposition of Markov point processes with respect to the same neighbourhood relation preserves the Hammersley--Clifford factorisation up to second order. If the processes
Propagation of Spatial Interaction under Superposition
We show that the superposition of two independent Markov point processes with respect t-O the same neighbourhood relation exhibits no second order interactions. and no third order ones if the point
REMARK ON THE PALM INTENSITY OF NEYMAN-SCOTT CLUSTER POINT PROCESSES
The present paper is concerned with notes on the Palm intensity of Neyman-Scott cluster point processes. The Palm intensity is known as the most important and informative second-order characteristic
Applications of stochastic geometry in image analysis
A discussion is given of various stochastic geometry models (random fields, sequential object processes, polygonal field models) which can be used in intermediate and high-level image analysis. Two
Fast Simulation of Markov Cluster
Spatial point processes have been used by scientists in various disciplines such as astronomy, ecology, geology and urban planning. Cluster processes are a special case where the point patterns to be
Is-ClusterMPP: clustering algorithm through point processes and influence space towards high-dimensional data
TLDR
Is-ClusterMPP is a new unsupervised clustering algorithm through adaptive MCMC sampling of a marked point processes of interacting balls that solves the problem of local heterogeneity in densities and prevents the impact of the global density in the detection of unbalanced classes.
A note on pooling of labels in random fields
This paper studies the effect on the interaction structure arising from merging labels in certain classes of random field models.
Classification non Supervisée de Données Multidimensionnelles par les Processus Ponctuels Marqués
TLDR
Un nouvel algorithme non supervise de classification des donnees multidimensionnelles consiste a detecter les prototypes des classes presentes dans un echantillon and a appliquer l’algorithme KNN pour the classification of toutes les observations.
...
1
2
...

References

SHOWING 1-10 OF 11 REFERENCES
Markov properties of cluster processes
TLDR
It is shown that a Poisson cluster point process is a nearest-neighbour Markov point process if the clusters have uniformly bounded diameter, and when the parent Poisson process is replaced by a Markov or nearest-NEighbourMarkovpoint process, the resulting cluster process is also nearest-Neighbourmarkov, provided all clusters are non-empty.
Nearest-Neighbour Markov Point Processes and Random Sets
Summary The Markov point processes introduced by Ripley & Kelly are generalised by replacing fixed-range spatial interactions by interactions between neighbouring particles, where the neighbourhood
Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes
The area-interaction process and the continuum random-cluster model are characterized in terms of certain functional forms of their respective conditional intensities. In certain cases, these two
Simulation Procedures and Likelihood Inference for Spatial Point Processes
An alternative algorithm to the usual birth-and-death procedure for simulating spatial point processes is introduced. The algorithm is used in a discussion of unconditional versus conditional
Characterisation results and Markov chain Monte Carlo algorithms including exact simulation for some
A terminal box for a lifting magnet has a bottom mounting surface to be secured to the casing of the lifting magnet over a pair of apertures in the casing through which the coil conductor leads pass.
Markov chain Monte Carlo and spatial point processes In Stochastic Geometry: likelihood and computation
  • Markov chain Monte Carlo and spatial point processes In Stochastic Geometry: likelihood and computation
  • 1998
Markov properties of clusterprocesses
  • Adv in Appl . Probab .
  • 1996
Markovproperties of cluster processes
  • Adv in Appl . Probab .
  • 1996
Simulation and likelihood inference for spatial point processes
  • Scandinavian Journal of Statistics
  • 1994
Simulation and likelihood inference forspatial point processes
  • Scandinavian Journal of Statistics
  • 1994
...
1
2
...