Iconic indexing by 2-D strings
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the representation and estimation of spatial uncertainly
International Journal of Robotics Research
Robust regression and outlier detection
Robust regression and outlier detection
On the description of the relative position of fuzzy patterns
Pattern Recognition Letters
Estimating uncertain spatial relationships in robotics
Autonomous robot vehicles
Approximate spatial reasoning: integrating qualitative and quantitative constraints
International Journal of Approximate Reasoning
Fuzzy Sets and Systems - Special issue on fuzzy methods for computer vision and pattern recognition
A New Way to Represent the Relative Position between Areal Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fuzzy Relative Position Between Objects in Image Processing: A Morphological Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Maintaining knowledge about temporal intervals
Communications of the ACM
Fuzzy Logic Techniques for Autonomous Vehicle Navigation
Fuzzy Logic Techniques for Autonomous Vehicle Navigation
Comparison of spatial relation definitions in computer vision
ISUMA '95 Proceedings of the 3rd International Symposium on Uncertainty Modelling and Analysis
Probabilistic robot navigation in partially observable environments
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Estimating the absolute position of a mobile robot using position probability grids
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
GNet: A generalized network model and its applications in qualitative spatial reasoning
Information Sciences: an International Journal
International Journal of Geographical Information Science - Digital Gazetteer Research
Qualitative Spatial Representation and Reasoning for Data Integration of Ocean Observational Systems
APWeb/WAIM '09 Proceedings of the Joint International Conferences on Advances in Data and Web Management
$\mathcal{I}$-SQE: A Query Engine for Answering Range Queries over Incomplete Spatial Databases
KES '09 Proceedings of the 13th International Conference on Knowledge-Based and Intelligent Information and Engineering Systems: Part II
FQAS '09 Proceedings of the 8th International Conference on Flexible Query Answering Systems
International Journal of Approximate Reasoning
Probability issues in locality descriptions based on Voronoi neighbor relationship
Journal of Visual Languages and Computing
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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.