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

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 ◽

10.1239/aap/1035227989 ◽

1998 ◽

Vol 30 (1) ◽

pp. 1-35 ◽

Cited By ~ 14

Author(s):

Jesper Møller ◽

Rasmus Plenge Waagepetersen

Keyword(s):

Random Fields ◽

Markov Random Fields ◽

Point Processes ◽

Marked Point ◽

Marked Point Processes ◽

Connected Components ◽

Spatial Continuity ◽

New Class ◽

Inference Problems ◽

Markov Random

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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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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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.

Download Full-text