# 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.

## 11 Citations

Markov interacting component processes

- MathematicsAdvances in Applied Probability
- 2000

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

- Mathematics
- 1999

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

- 2005

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

- Mathematics
- 2013

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

- Computer Science
- 2009

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

- 2007

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

- Computer ScienceAdv. Data Anal. Classif.
- 2020

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

- Computer Science, Mathematics
- 2009

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

- Computer Science, PhilosophyARIMA J.
- 2015

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.

ClusterMPP: An unsupervised density-based clustering algorithm via Marked Point Process

- Computer ScienceIntell. Data Anal.
- 2017

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