Markov Point Processes and Their Applications

Lieshout, M. N. M. van

doi:10.1142/p060

Cited by 197 publications

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“…It should be noted that this definition is different from the concept of a Markov point process considered in [9], where the conditional independence is assumed to hold given the process in some 'neighborhood' of A; see, e.g. [9, Theorem 2.1].…”

Section: Markovian Point Processesmentioning

confidence: 99%

“…At this point, it is worth noting that these processes should not be confused with the Markov point processes of [9], which are defined in a different way. More precisely, in [9] the process inside A is conditionally independent of the process outside A given the process on a set…”

Section: Introductionmentioning

confidence: 99%

“…More precisely, in [9] the process inside A is conditionally independent of the process outside A given the process on a set…”

Section: Introductionmentioning

confidence: 99%

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Conditionally Independent Increment Point Processes

Ibarrola

Prieto-Rumeau

2011

J. Appl. Probab.

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In this paper we introduce conditionally independent increment point processes, that is, processes that are conditionally independent inside and outside a bounded set A given N(A), the number of points in A. We show that these point processes can be characterized by means of the avoidance function of a multinomial 'support process', the solution of a suitably defined linear system of equations, and, finally, the infinitesimal matrix of a continuous-time Markov chain.

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Section: Markovian Point Processesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Conditionally Independent Increment Point Processes

Ibarrola

Prieto-Rumeau

2011

J. Appl. Probab.

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“…We model random configurations by a spatial point process, specifically, the Gibbs point process [23]. Let µ(·) be the distribution of a homogenous Poisson process of unit intensity, which is analogous to the Lebesgue measure on R d .…”

Section: Modelingmentioning

confidence: 99%

“…The first one is an avoidance strategy motivated by studies in social science showing that people keep a 'comfort zone' around themselves. We incorporate this dependency by a Strauss Model [23], which defines a pairwise potential interaction as…”

Section: Modelingmentioning

confidence: 99%

Crowd Detection with a Multiview Sampler

Collins

2010

Computer Vision – ECCV 2010

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Abstract. We present a Bayesian approach for simultaneously estimating the number of people in a crowd and their spatial locations by sampling from a posterior distribution over crowd configurations. Although this framework can be naturally extended from single to multiview detection, we show that the naive extension leads to an inefficient sampler that is easily trapped in local modes. We therefore develop a set of novel proposals that leverage multiview geometry to propose global moves that jump more efficiently between modes of the posterior distribution. We also develop a statistical model of crowd configurations that can handle dependencies among people and while not requiring discretization of their spatial locations. We quantitatively evaluate our algorithm on a publicly available benchmark dataset with different crowd densities and environmental conditions, and show that our approach outperforms other state-of-the-art methods for detecting and counting people in crowds.

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Point Processes, Spatial

Särkkä

2016

Wiley StatsRef: Statistics Reference Online

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The general theory of point processes has in the past been focused on temporal developments. In this article we will focus on spatial point processes, where points, or events, take place at spatial locations, and we identify each event with its location. We will mainly concentrate on planar stationary and isotropic (i.e., the distribution of the process is invariant under translations and rotations, respectively) processes, but will give some references to studies concerning inhomogeneous and anisotropic point pattern data.

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Markov Point Processes and Their Applications

Cited by 197 publications

References 0 publications

Conditionally Independent Increment Point Processes

Conditionally Independent Increment Point Processes

Crowd Detection with a Multiview Sampler

Point Processes, Spatial

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