Difference between revisions of "Publications/dehak.05.pami"

From LRDE

 
Line 5: Line 5:
 
| title = Spatial reasoning with relative incomplete information on relative positioning
 
| title = Spatial reasoning with relative incomplete information on relative positioning
 
| journal = IEEE Transactions on Pattern Analysis and Machine Intelligence
 
| journal = IEEE Transactions on Pattern Analysis and Machine Intelligence
| pages = 1473–1484
+
| pages = 1473 to 1484
 
| volume = 27
 
| volume = 27
 
| number = 9
 
| number = 9

Latest revision as of 17:56, 4 January 2018

Abstract

This paper describes a probabilistic method of inferring the position of a point with respect to a reference point knowing their relative spatial position to a third point. We address this problem in the case of incomplete information where only the angular spatial relationships are known. The use of probabilistic representations allows us to model prior knowledge. We derive exact formulae expressing the conditional probability of the position given the two known angles, in typical cases: uniform or Gaussian random prior distributions within rectangular or circular regions. This result is illustrated with respect to two different simulations: The first is devoted to the localization of a mobile phone using only angular relationships, the second, to geopositioning within a city. This last example uses angular relationships and some additional knowledge about the position.


Bibtex (lrde.bib)

@Article{	  dehak.05.pami,
  author	= {R\'eda Dehak and Isabelle Bloch and Henri Ma{\^\i}tre},
  title		= {Spatial reasoning with relative incomplete information on
		  relative positioning},
  journal	= {IEEE Transactions on Pattern Analysis and Machine
		  Intelligence},
  year		= 2005,
  pages		= {1473--1484},
  volume	= 27,
  month		= sep,
  number	= 9,
  abstract	= {This paper describes a probabilistic method of inferring
		  the position of a point with respect to a reference point
		  knowing their relative spatial position to a third point.
		  We address this problem in the case of incomplete
		  information where only the angular spatial relationships
		  are known. The use of probabilistic representations allows
		  us to model prior knowledge. We derive exact formulae
		  expressing the conditional probability of the position
		  given the two known angles, in typical cases: uniform or
		  Gaussian random prior distributions within rectangular or
		  circular regions. This result is illustrated with respect
		  to two different simulations: The first is devoted to the
		  localization of a mobile phone using only angular
		  relationships, the second, to geopositioning within a city.
		  This last example uses angular relationships and some
		  additional knowledge about the position.}
}