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Qualitative Representation of Positional Information
 ARTIFICIAL INTELLIGENCE
, 1997
"... A framework for the qualitative representation of positional information in a twodimensional space is presented. Qualitative representations use discrete quantity spaces, where a particular distinction is introduced only if it is relevant to the context being modeled. This allows us to build a flex ..."
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Cited by 108 (3 self)
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A framework for the qualitative representation of positional information in a twodimensional space is presented. Qualitative representations use discrete quantity spaces, where a particular distinction is introduced only if it is relevant to the context being modeled. This allows us to build a flexible framework that accommodates various levels of granularity and scales of reasoning. Knowledge about position in largescale space is commonly represented by a combination of orientation and distance relations, which we express in a particular frame of reference between a primary object and a reference object. While the representation of orientation comes out to be more straightforward, the model for distances requires that qualitative distance symbols be mapped to geometric intervals in order to be compared; this is done by defining structure relations that are able to handle, among others, order of magnitude relations; the frame of reference with its three components (distance system, s...
Similarity of Spatial Scenes
 7 th Symposium on Spatial Data Handling
, 1996
"... Similarity is the assessment of deviation from equivalence. Spatial similarity is complex due to the numerous constraining properties of geographic objects and their embedding in space. Among these properties, the spatial relations between geographic objectstopological, directional, and metrical ..."
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Cited by 61 (7 self)
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Similarity is the assessment of deviation from equivalence. Spatial similarity is complex due to the numerous constraining properties of geographic objects and their embedding in space. Among these properties, the spatial relations between geographic objectstopological, directional, and metricalare critical, because they capture the essence of a scene's structure. These relations can be categorized as a basis for similarity assessment. This paper describes a computational method to formally assess the similarity of spatial scenes based on the ordering of spatial relations. One scene is transformed into another through a sequence of gradual changes of spatial relations. The number of changes required yields a measure that is compared against others, or against a preexisting scale. Two scenes that require a large number of changes are less similar than scenes that require fewer changes.
Linguistic Description of Relative Positions in Images
 IEEE Trans. on Systems, Man and Cybernetics, part B
, 2000
"... Fuzzy set methods have been used to model and manage uncertainty in various aspects of image processing, pattern recognition and computer vision. Highlevel computer vision applications hold a great potential for fuzzy set theory because of its links to natural language. Linguistic scene description ..."
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Cited by 22 (9 self)
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Fuzzy set methods have been used to model and manage uncertainty in various aspects of image processing, pattern recognition and computer vision. Highlevel computer vision applications hold a great potential for fuzzy set theory because of its links to natural language. Linguistic scene description, a languagebased interpretation of regions and their relationships, is one such application that is starting to bear the fruits of fuzzy set theoretic involvement. In this paper, we are expanding on two earlier endeavors. We introduce new families of fuzzy directional relations that rely on the computation of histograms of forces. These families preserve important relative position properties. They provide inputs to a fuzzy rule base that produces logical linguistic descriptions along with assessments as to the validity of the descriptions. Each linguistic output uses hedges from a dictionary of about thirty adverbs and other terms that can be tailored to individual users. Excellent results from several synthetic and real image examples show the applicability of this approach. Keywords Relative Positions, Force Histograms, Spatial Relations, Linguistic Descriptions, Scene Understanding, Fuzzy Logic. 2 1.
Spatial Reasoning Rules in Multimedia Management Systems
 In Proc. International Conference on Multimedia Modeling
, 1996
"... this paper we consider various spatial relationships that are of general interest for retrieving data from multimedia databases. We present a unified representation of spatial objects for both topological and directional relations. Such a representation is based on Allen's temporal interval alg ..."
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Cited by 14 (5 self)
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this paper we consider various spatial relationships that are of general interest for retrieving data from multimedia databases. We present a unified representation of spatial objects for both topological and directional relations. Such a representation is based on Allen's temporal interval algebra. We also present a set of spatial inference rules, which allow us to make heterogeneous spatial relation deductions from existing directional and topological relations. For example, if we know A north of B, B overlap with C, and C north of D, then we derive A above D. Since all the rules are propositional Horn clauses, they can be easily integrated into any multimedia database by using either a simple inference engine or a lookup table. 1 Introduction
Fuzzy Spatial Relationships and Mobile Agent
"... This chapter discusses an integrated work in the definition and implementation of sets of fuzzy spatial relationships concerning topology and direction. We present our basic approach to defining these relationships as an extension to previous work in temporal relations. We also discuss several exten ..."
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Cited by 3 (0 self)
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This chapter discusses an integrated work in the definition and implementation of sets of fuzzy spatial relationships concerning topology and direction. We present our basic approach to defining these relationships as an extension to previous work in temporal relations. We also discuss several extensions to this approach that include refinements and alternate definitions. Two implementations are also described, one in a C++, Oracle database environment and another utilizing the expert system shell Fuzzy Clips. Finally we discuss the integration of this querying approach in an agentbased framework. Agent technology has become a leading implementation paradigm for distributed and complex systems, and has recently garnered much interest from researchers in the area of spatial databases. Agents offer many advantages with respect to intelligence abilities and mobility that can provide solutions for issues related to uncertainty in spatial data, such as those of spatial relationships.
FHistograms and Fuzzy Directional Spatial Relations
 Proceedings, LFA’99 (FrenchSpeaking Conference on Fuzzy Logic and Its Applications
, 1999
"... The quantitative (or fuzzy qualitative) assessment of directional spatial relationships (such as "to the right of", "above", "south of"...) between two areal objects often relies on the computation of a histogram of angles, which provides a representation of the relativ ..."
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Cited by 2 (2 self)
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The quantitative (or fuzzy qualitative) assessment of directional spatial relationships (such as "to the right of", "above", "south of"...) between two areal objects often relies on the computation of a histogram of angles, which provides a representation of the relative position of the objects. In a recent paper, the notion of the histogram of forces was introduced. Here, we show that this powerful tool of representation lends itself, with great flexibility, to the definition of directional spatial relations. Indeed, any family of directional relations that relied on the construction of angle histograms can be advantageously redefined using force histograms. Moreover, the notion of the histogram of forces enables radically new families to be conceived: definitions which correspond to a coherent and rational perception of the world, but nonrealizable by previous methods. Keywords Spatial relationships, parameter extraction, pattern recognition, scene analysis, fuzzy relations, fuzzy sets. 1.
Spatial Data Modeling: Issues and Implications on Geographic Information Systems
"... Even though the potential ability of Geographic Information System (GIS) as decision support for business activities has been widely recognized, the topic of Geographic Information Systems (GIS) has received little attention in the business literature. Spatial database systems provide the underlying ..."
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Cited by 1 (1 self)
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Even though the potential ability of Geographic Information System (GIS) as decision support for business activities has been widely recognized, the topic of Geographic Information Systems (GIS) has received little attention in the business literature. Spatial database systems provide the underlying database technology for Geographic Information Systems and other applications. Modeling spatial objects and their operations in spatial databases is a relatively new research area. Spatial data models should include constructs of highlevel abstractions, spatial entities, relationships, operators and a query language, which provides rich concepts to efficiently and effectively handle spatial data. We present a comprehensive survey of the current stateoftheart in spatial databases. This paper also examines issues related with modeling spatial complexity. We conclude the paper with directions for future research in spatial databases. Working Paper Even though the potential ability of Geographic Information System (GIS) as decision support for business activities has been widely recognized [Kelly 1996; Murphy 1996; Youtie and Brown 1996], the topic of Geographic Information Systems (GIS) has received little attention in business schools [Kuehn et al. 1994]. The applicability of
Composition for Cardinal Directions by Decomposing Horizontal and Vertical Constraints
 Proceedings of AAAI 2003 Spring Symposium, March 2426
, 2003
"... In this paper, we demonstrate how to group the nine cardinal directions into sets and use them to compute a composition table. Firstly, we define each cardinal direction in terms of a certain set of constraints. This is followed by decomposing the cardinal directions into sets corresponding to th ..."
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Cited by 1 (1 self)
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In this paper, we demonstrate how to group the nine cardinal directions into sets and use them to compute a composition table. Firstly, we define each cardinal direction in terms of a certain set of constraints. This is followed by decomposing the cardinal directions into sets corresponding to the horizontal and vertical constraints. We apply two different techniques to compute the composition of these sets. The first technique is an algebraic computation while the second is the typical technique of reasoning with diagrams. The rationale of applying the latter is for confirmation purposes. The use of typical composition tables for existential inference is rarely demonstrated. Here, we shall demonstrate how to use the composition table to answer queries requiring the common forward reasoning as well as existential inference.Also, we combine mereological and cardinal direction relations to create a hybrid model which is more expressive.
Design, Management
"... Representation of relative spatial relations between objects is required in many multimedia database applications. Quantitative representation of spatial relations taking into account shape, size, orientation and distance is often required. This cannot be accomplished by assimilating an object to el ..."
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Cited by 1 (0 self)
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Representation of relative spatial relations between objects is required in many multimedia database applications. Quantitative representation of spatial relations taking into account shape, size, orientation and distance is often required. This cannot be accomplished by assimilating an object to elementary entities such as the centroid or the minimum bounding rectangle. Thus many authors have proposed numerous representations based on the notion of histograms of angles. However, they can only represent directional relations, but not the topological spatial relations “inside” and “overlap. ” Moreover, distance information is not explicitly taken into account. To address these issues, we propose in this paper a new histogram representation called RHistogram that extends the histogram of angles by incorporating both angles and labeled distances. Dissimilarity between images is then defined by the distance between corresponding RHistograms. A prototype Query By Example (QBE) system using the RHistogram has been implemented. The effectiveness of our algorithm is demonstrated with experiments on two databases of 2000 synthetic images.
A Comparison of Inferences about Containers and Surfaces in SmallScale and LargeScale Spaces
, 2000
"... Inference mechanisms about spatial relations constitute an important aspect of spatial reasoning as they allow users to derive unknown spatial information from a set of known spatial relations. When formalized in the form of algebras, spatialrelation inferences represent a mathematically sound defi ..."
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Inference mechanisms about spatial relations constitute an important aspect of spatial reasoning as they allow users to derive unknown spatial information from a set of known spatial relations. When formalized in the form of algebras, spatialrelation inferences represent a mathematically sound definition of the behavior of spatial relations, which can be used to specify constraints in spatial query languages. Current spatial query languages utilize spatial concepts that are derived primarily from geometric principles, which do not necessarily match with the concepts people use when they reason and communicate about spatial relations. This paper presents an alternative approach to spatial reasoning by starting with a small set of spatial operators that are derived from concepts closely related to human cognition. This cognitive foundation comes from the behavior of image schemata, which are cognitive structures for organizing people's experiences and comprehension. From the operations and spatial relations of a smallscale space, a containersurface algebra is defined with nine basic spatial operatorsinside, outside, on, off, their respective converse relationscontains, excludes, supports, separated_from, and the identity relation equal. The containersurface algebra was applied to spaces with objects of different sizes and its inferences were assessed through humansubject experiments. Discrepancies between the containersurface algebra and the humansubject testing appear for combinations of spatial relations that result in more than one possible inference depending on the relative size of objects. For configurations with smallscale and largescale objects larger discrepancies were found because people use relations such as part of and at in lieu of in. Basic conc...