Markov connected component fields

A new class of Gibbsian models with potentials associated with the connected components or homogeneous parts of images is introduced. For these models the neighbourhood of a pixel is not fixed as for Markov random fields, but is given by the components which are adjacent to the pixel. The relationship to Markov random fields and marked point processes is explored and spatial Markov properties are established. Extensions to infinite lattices are also studied, and statistical inference problems including geostatistical applications and statistical image analysis are discussed. Finally, simulation studies are presented which show that the models may be appropriate for a variety of interesting patterns, including images exhibiting intermediate degrees of spatial continuity and images of objects against background.

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Markov connected component fields

Advances in Applied Probability ◽

10.1017/s0001867800048400 ◽

1996 ◽

Vol 28 (2) ◽

pp. 340-340

Author(s):

Jesper M⊘ller ◽

Rasmus Waagepetersen

Keyword(s):

Markov Random Fields ◽

Point Processes ◽

Marked Point ◽

Marked Point Processes ◽

Connected Components ◽

New Class ◽

Inference Problems ◽

Infinite Lattices ◽

The Relationship ◽

Markov Properties

A new class of Gibbsian models with potentials associated with the connected components or homogeneous parts of images is introduced. The relationship with Markov random fields and marked point processes is explored and spatial Markov properties are established. Further, extensions to infinite lattices are studied. Statistical inference problems including geostatistical applications and statistical image analysis are also discussed. Finally, simulation studies are presented which show that the models may be appropriate for a variety of interesting patterns.

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COMBINE MARKOV RANDOM FIELDS AND MARKED POINT PROCESSES TO EXTRACT BUILDING FROM REMOTELY SENSED IMAGES

ISPRS Annals of Photogrammetry Remote Sensing and Spatial Information Sciences ◽

10.5194/isprsannals-i-3-365-2012 ◽

2012 ◽

Vol I-3 ◽

pp. 365-370 ◽

Cited By ~ 8

Author(s):

D. Chai ◽

W. Förstner ◽

M. Ying Yang

Keyword(s):

Random Fields ◽

Markov Random Fields ◽

Point Processes ◽

Marked Point ◽

Remotely Sensed ◽

Marked Point Processes ◽

Markov Random ◽

Remotely Sensed Images

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Random Marked Sets

Advances in Applied Probability ◽

10.1239/aap/1346955256 ◽

2012 ◽

Vol 44 (3) ◽

pp. 603-616 ◽

Cited By ~ 10

Author(s):

F. Ballani ◽

Z. Kabluchko ◽

M. Schlather

Keyword(s):

Random Fields ◽

Covariance Function ◽

Point Processes ◽

Marked Point ◽

Positive Definiteness ◽

Gaussian Random Fields ◽

Marked Point Processes ◽

Random Set ◽

Geostatistical Methods ◽

New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

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Random Marked Sets

Advances in Applied Probability ◽

10.1017/s0001867800005796 ◽

2012 ◽

Vol 44 (03) ◽

pp. 603-616 ◽

Cited By ~ 8

Author(s):

F. Ballani ◽

Z. Kabluchko ◽

M. Schlather

Keyword(s):

Random Fields ◽

Covariance Function ◽

Point Processes ◽

Marked Point ◽

Positive Definiteness ◽

Gaussian Random Fields ◽

Marked Point Processes ◽

Random Set ◽

Geostatistical Methods ◽

New Class

We aim to link random fields and marked point processes, and, therefore, introduce a new class of stochastic processes which are defined on a random set in . Unlike for random fields, the mark covariance function of a random marked set is in general not positive definite. This implies that in many situations the use of simple geostatistical methods appears to be questionable. Surprisingly, for a special class of processes based on Gaussian random fields, we do have positive definiteness for the corresponding mark covariance function and mark correlation function.

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An Introduction to Spatial Point Processes and Markov Random Fields

International Statistical Review ◽

10.2307/1403035 ◽

1981 ◽

Vol 49 (1) ◽

pp. 21 ◽

Cited By ~ 44

Author(s):

Valerie Isham

Keyword(s):

Random Fields ◽

Markov Random Fields ◽

Point Processes ◽

Spatial Point Processes ◽

Spatial Point ◽

Markov Random

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A GRAPH BASED MODEL FOR THE DETECTION OF TIDAL CHANNELS USING MARKED POINT PROCESSES

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprsarchives-xl-3-w3-115-2015 ◽

2015 ◽

Vol XL-3/W3 ◽

pp. 115-121 ◽

Cited By ~ 1

Author(s):

A. Schmidt ◽

F. Rottensteiner ◽

U. Soergel ◽

C. Heipke

Keyword(s):

Point Processes ◽

Marked Point ◽

Marked Point Processes ◽

Current Status ◽

Connected Components ◽

Tidal Channels ◽

Sampling Step ◽

Channel System ◽

Current Configuration ◽

Graph Based Model

In this paper we propose a new method for the automatic extraction of tidal channels in digital terrain models (DTM) using a sampling approach based on marked point processes. In our model, the tidal channel system is represented by an undirected, acyclic graph. The graph is iteratively generated and fitted to the data using stochastic optimization based on a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler and simulated annealing. The nodes of the graph represent junction points of the channel system and the edges straight line segments with a certain width in between. In each sampling step, the current configuration of nodes and edges is modified. The changes are accepted or rejected depending on the probability density function for the configuration which evaluates the conformity of the current status with a pre-defined model for tidal channels. In this model we favour high DTM gradient magnitudes at the edge borders and penalize a graph configuration consisting of non-connected components, overlapping segments and edges with atypical intersection angles. We present the method of our graph based model and show results for lidar data, which serve of a proof of concept of our approach.

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