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137
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 90 (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...
Query Processing in SpatialQuerybySketch
 Journal of Visual Languages and Computing
, 1997
"... SpatialQuerybySketch is the design of a query language for geographic information systems. It allows a user to formulate a spatial query by drawing the desired configuration with a pen on a touchsensitive computer screen and translates this sketch into a symbolic representation that can the proc ..."
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Cited by 77 (4 self)
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SpatialQuerybySketch is the design of a query language for geographic information systems. It allows a user to formulate a spatial query by drawing the desired configuration with a pen on a touchsensitive computer screen and translates this sketch into a symbolic representation that can the processed against a geographic database. Since the configurations queried usually do not match exactly the sketch, it is necessary to relax the spatial constraints drawn. This paper describes the representation of a sketch and outlines the design of the constraint relaxation methods used during query processing.
A Theory of Granular Partitions
, 2001
"... This paper presents an application of the theory of granular partitions proposed in (Smith and Brogaard, to appear), (Smith and Bittner 2001) to the phenomenon of vagueness. We understand vagueness as a semantic property of names and predicates. This is in contrast to those views which hold that the ..."
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Cited by 72 (34 self)
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This paper presents an application of the theory of granular partitions proposed in (Smith and Brogaard, to appear), (Smith and Bittner 2001) to the phenomenon of vagueness. We understand vagueness as a semantic property of names and predicates. This is in contrast to those views which hold that there are intrinsically vague objects or attributes in reality and thus conceive vagueness in a de re fashion. All entities are crisp, on de dicto view here defended, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We show that the theory of granular partitions provides a general framework within which we can understand the relation between terms and concepts on the one hand and their multiple referents or extensions on the other, and we show how it might be possible to formulate within this framework a solution to the Sorites paradox. 1.
Qualitative Representation of Spatial Knowledge in TwoDimensional Space
, 1994
"... Various relationbased systems, concerned with the qualitative representation and processing of spatial knowledge, have been developed in numerous application domains. In this article, we identify the common concepts underlying qualitative spatial knowledge representation, we compare the represen ..."
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Cited by 72 (22 self)
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Various relationbased systems, concerned with the qualitative representation and processing of spatial knowledge, have been developed in numerous application domains. In this article, we identify the common concepts underlying qualitative spatial knowledge representation, we compare the representational properties of the different systems, and we outline the computational tasks involved in relationbased spatial information processing. We also describe symbolic spatial indexes, relationbased structures that combine several ideas in spatial knowledge representation. A symbolic spatial index is an array that preserves only a set of spatial relations among distinct objects in an image, called the modeling space; the index array discards information, such as shape and size of objects, and irrelevant spatial relations. The construction of a symbolic spatial index from an input image can be thought of as a transformation that keeps only a set of representative points needed to define the relations of the modeling space. By keeping the relative arrangements of the representative points in symbolic spatial indexes and discarding all other points, we maintain enough information to answer queries regarding the spatial relations of the modeling space without the need to access the initial image or an object database. Symbolic spatial indexes can be used to solve problems involving route planning, composition of spatial relations, and update operations.
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 53 (6 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.
Spatial Relations, Minimum Bounding Rectangles, and Spatial Data Structures
 International Journal of Geographic Information Science
, 1997
"... Spatial relations are important in numerous domains, such as Spatial Query Languages, Image and Multimedia Databases, Reasoning and Geographic Applications. This paper is concerned with the retrieval of topological and direction relations using spatial data structures based on Minimum Bounding Re ..."
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Cited by 51 (13 self)
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Spatial relations are important in numerous domains, such as Spatial Query Languages, Image and Multimedia Databases, Reasoning and Geographic Applications. This paper is concerned with the retrieval of topological and direction relations using spatial data structures based on Minimum Bounding Rectangles. We describe topological and direction relations between region objects and we study the spatial information that Minimum Bounding Rectangles convey about the actual objects they enclose. Then we apply the results in Rtrees and their variations, R+trees and R* trees, in order to minimise the number of disk accesses for queries involving topological and direction relations. We also investigate queries that express complex spatial conditions in the form of disjunctions and conjunctions, and we discuss possible extensions.
Qualitative Spatial Reasoning Using Orientation, Distance, and Path Knowledge
 Applied Intelligence
, 1996
"... We give an overview of an approach to qualitative spatial reasoning based on directional orientation information as available through perception processes or natural language descriptions. Qualitative orientations in 2dimensional space are given by the relation between a point and a vector. The ..."
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Cited by 32 (0 self)
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We give an overview of an approach to qualitative spatial reasoning based on directional orientation information as available through perception processes or natural language descriptions. Qualitative orientations in 2dimensional space are given by the relation between a point and a vector. The paper presents our basic iconic notation for spatial orientation relations that exploits the spatial structure of the domain and explores a variety of ways in which these relations can be manipulated and combined for spatial reasoning. Using this notation, we explore a method for exploiting interactions between space and movement in this space for enhancing the inferential power. Finally, the orientationbased approach is augmented by distance information, which can be mapped into position constraints and vice versa.
Metric Details for NaturalLanguage Spatial Relations
 ACM Transactions on Information Systems
, 1998
"... Spatial relations often are desired answers that a geographic information system (GIS) should generate in response to a users query. Current GISs provide only rudimentary support for processing and interpreting naturallanguagelike spatial relations, because their models and representations are pri ..."
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Cited by 30 (2 self)
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Spatial relations often are desired answers that a geographic information system (GIS) should generate in response to a users query. Current GISs provide only rudimentary support for processing and interpreting naturallanguagelike spatial relations, because their models and representations are primarily quantitative, while naturallanguage spatial relations are usually dominated by qualitative properties. Studies of the use of spatial relations in natural language showed that topology accounts for a significant portion of the geometric properties. This paper develops a formal model that captures metricdetails for the description of naturallanguage spatial relations. The metric details are expressed as refinements of the categories identified by the 9intersection, a model for topological spatial relations, and provide a more precise measure than does topology alone as to whether a geometric configuration matches with a spatial term or not. Similarly, these measures help in identifying the spatial term that describes a particular configuration. Two groups of metric details are derived: splitting ratios as the normalized values of lengths and areas of intersections; and closeness measures as the normalized distances between disjoint object parts. The resulting model of topological and metric properties was calibrated for sixtyfour spatial terms in English, providing values for the best fit as well as value ranges for the significant parameters of each term. Three examples demonstrate how the framework and its calibrated values are used to determine the best spatial term for a relationship between two geometric objects.
Topological Relations between Regions in R² and Z²
, 1993
"... Users of geographic databases that integrate spatial data represented in vector and raster models, should not perceive the differences among the data models in which data are represented, nor should they be forced to apply different concepts depending on the model in which spatial data are repre ..."
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Cited by 28 (2 self)
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Users of geographic databases that integrate spatial data represented in vector and raster models, should not perceive the differences among the data models in which data are represented, nor should they be forced to apply different concepts depending on the model in which spatial data are represented. A crucial aspect of spatial query languages for such integrated systems is the need mechanisms to process queries about spatial relations in a consistent fashion. This paper compares topological relations between spatial objects represented in a continuous (vector) space of ## and a discrete (raster) space of ZZ . It applies the 9intersection, a frequently used formalism for topological spatial relations between objects represented in a vector data model, to describe topological relations for bounded objects represented in a raster data model. We found that the set of all possible topological relations between regions in ## is a subset of the topological relations that can be realized between two bounded, extended objects in ZZ . At a
Qualitative Spatial Reasoning about Line Segments
 ECAI 2000. Proceedings of the 14th European Conference on Artifical Intelligence
, 2000
"... . Representing and reasoning about orientation information is an important aspect of qualitative spatial reasoning. We present a novel approach for dealing with intrinsic orientation information by specifying qualitative relations between oriented line segments, the simplest possible spatial entitie ..."
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Cited by 28 (6 self)
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. Representing and reasoning about orientation information is an important aspect of qualitative spatial reasoning. We present a novel approach for dealing with intrinsic orientation information by specifying qualitative relations between oriented line segments, the simplest possible spatial entities being extended and having an intrinsic direction. We identify a set of 24 atomic relations which form a relation algebra and for which we compute relational compositions based on their algebraic semantics. Reasoning over the full algebra turns out to be NPhard. Potential applications of the calculus are motivated with a small example which shows the reasoning capabilities of the dipole calculus using constraintbased reasoning methods. 1 Introduction Qualitative representation of space abstracts from the physical world and enables computers to make predictions about spatial relations, even when precise quantitative information is not available [2]. Different aspects of space can be repr...