## Spatial Relations, Minimum Bounding Rectangles, and Spatial Data Structures (1997)

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Venue: | International Journal of Geographic Information Science |

Citations: | 51 - 13 self |

### BibTeX

@ARTICLE{Papadias97spatialrelations,,

author = {Dimitris Papadias and Yannis Theodoridis},

title = {Spatial Relations, Minimum Bounding Rectangles, and Spatial Data Structures},

journal = {International Journal of Geographic Information Science},

year = {1997},

volume = {11},

pages = {111--138}

}

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### Abstract

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 R-trees 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.

### Citations

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(Show Context)
Citation Context ... be used for query optimisation techniques in MBR-based data structures. 4. 2 Spatial Data Structures based on MBRs The most promising group of spatial data structures based on MBRs includes R-trees (=-=Guttman, 1984-=-) and their variations. The R-tree data structure is a height-balanced tree, which consists of intermediate and leaf nodes (R-trees are direct extensions of B-trees in k-dimensions). The MBRs of the a... |

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564 | A Spatial Logic Based on Regions and Connection
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(Show Context)
Citation Context ...hat can be defined using the previous conjunctions only the following eight illustrated in Table 1 are valid. These relations are proved to be pairwise disjoint, and they provide a complete coverage (=-=Randell et al., 1992-=-). For each of the primitive relations Table 1 includes some intersection points. The term primary object denotes the object to be located and the term reference object denotes the object in relation ... |

502 |
Semontics and Cognition
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(Show Context)
Citation Context ...nted out by several researchers in areas including Geographic and Multimedia Databases (Papadias et at., 1994a, Sistta et at. 1994), Spatial Reasoning (Glasgow and Papadias, 1992), Cognitive Science (=-=Jackendoff, 1983-=-) and Linguistics (Herskovits, 1986). This paper shows how direction and topological relations between region objects can be processed in Spatial Databases. Conventional Database Management Systems ar... |

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213 |
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(Show Context)
Citation Context ...s then uniquely determined by the four intersections between their boundaries and interiors. Tests with human subjects have shown evidence that this model, and its extension the 9-intersection model (=-=Egenhofer, 1991-=-) have potential for defining cognitivety meaningful spatial predicates (Mark and Egenhofer, 1994). As a result there have been implementations in commercial systems (e.g., MGE, 1993; Keighan, 1993). ... |

163 | Using orientation information for qualitative spatial reasoning. Theories and Methods of Spatio-Temporal Reasoning in Geographic Space
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Citation Context ...ueries depending on the application needs. Figure 1 goes here Fig. 1 A geographic example involving direction relations Most of previous work on direction relations has concentrated on point objects (=-=Freksa, 1992-=-; Frank, 1992) where objects are abstracted as single points (e.g., center of mass, center of symmetry etc.). Our work extends previous approaches by dealing with extended objects instead of points. P... |

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Citation Context ...ant for numerous practical applications that involve queries of the form "find all land parcels adjacent to the main park". Our approach on topological relations is based on the 4-intersecti=-=on model (Egenhofer and Franzosa, 1991-=-). According to the 4-intersection model, each object is represented as a point set which has an interior and a boundary; the topological relation between two objects is then uniquely determined by th... |

104 |
Qualitative spatial reasoning about distances and directions in geographical space
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(Show Context)
Citation Context ...ng on the application needs. Figure 1 goes here Fig. 1 A geographic example involving direction relations Most of previous work on direction relations has concentrated on point objects (Freksa, 1992; =-=Frank, 1992-=-) where objects are abstracted as single points (e.g., center of mass, center of symmetry etc.). Our work extends previous approaches by dealing with extended objects instead of points. Peuquet and Ci... |

99 | Topological relations in the world of minimum bounding rectangles: a study with R-trees. Sigmod record
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(Show Context)
Citation Context ...ns could enclose objects that satisfy the query relation). The table refers to contiguous or non-contiguous region objects. If we assume contiguity we can restrict the output MBRs for some relations (=-=Papadias et al., 1995-=-). Table 3 goes here Table 3 MBRs to be retrieved for topological relations The above mapping from topological relations between actual objects to relations between MBRs refers to leaf nodes. In order... |

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(Show Context)
Citation Context ...(p denotes the primary object), qj be a point of object q (q denotes the reference object), and X and Y be functions that return the x and y coordinate of a point. According to our projection method (=-=Papadias and Sellis, 1994-=-), there are nine possible ways to put a primary point with respect to a reference point in the plane and therefore nine pairwise disjoint relations that provide a complete coverage. These relations a... |

63 |
An implementation and performance analysis of spatial data access methods
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(Show Context)
Citation Context ...t expensive ones. Furthermore, when the data density becomes high it is possible that all of the entries in a full node coincide on the same point of the plane. In 14 such cases R+-trees do not work (=-=Greene, 1989-=-). This happened for some data sets involving large MBRs during our tests. The irregular behaviour of R+-trees is due to the lack of overlap between nodes, which results to the quick exclusion of the ... |

58 | Comparison of Approximations of Complex Objects Used for Approximation-Based Query - Brinkhoff, Kriegel, et al. - 1993 |

55 |
Language and Spatial Cognition
- Herskovits
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(Show Context)
Citation Context ...areas including Geographic and Multimedia Databases (Papadias et at., 1994a, Sistta et at. 1994), Spatial Reasoning (Glasgow and Papadias, 1992), Cognitive Science (Jackendoff, 1983) and Linguistics (=-=Herskovits, 1986-=-). This paper shows how direction and topological relations between region objects can be processed in Spatial Databases. Conventional Database Management Systems are designed to store one-dimensional... |

48 | Modeling topological spatial relations: Strategies for query processing - Clementini, Sharma, et al. - 1994 |

43 | Assessing the Consistency of Complete and Incomplete Topological Information. Geographic Systems 1 - Egenhofer, Sharma - 1993 |

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27 | T.K.Sellis.``A pictorial query-by-example language
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(Show Context)
Citation Context ...in Geographical Databases (Grigni et at., 1995), ordinal relations to describe aggregation hierarchies (Kainz et at., 1993), and direction relations have been incorporated in Spatial Query Languages (=-=Papadias and Sellis, 1995-=-). Topological relations describe concepts of neighbourhood, incidence and overlap and stay invariant under transformations such as scaling and rotation. They are important for numerous practical appl... |

27 | A model for expressing topological integrity constraints in geographic databases - HADZILACOS, TRYFONA - 1992 |

26 | Modeling Spatial Relations and Operations with Partially Ordered Sets
- Kainz, Egenhofer, et al.
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(Show Context)
Citation Context ... v overlap v covered by v inside v equal v covers v contains. The subset of topological relations that deal with the concepts of inclusion and containment have been called ordinal or order relations (=-=Kainz et al. 1993-=-). Based on the above definitions we can define the following ordinal relations: - in(p,q) --- inside(p,q)v covered by(p,q) - consists of(p,q) --- contains(p,q)v covers(p,q). Topological (and ordinal)... |

24 | Range Queries Involving Spatial Relations: A Performance Analysis - Theodoridis, Papadias - 1995 |

18 | Calibrating the meanings of spatial predicates from natural language: Line-region relations
- Mark, Egenhofer
- 1994
(Show Context)
Citation Context ...ors. Tests with human subjects have shown evidence that this model, and its extension the 9-intersection model (Egenhofer, 1991) have potential for defining cognitivety meaningful spatial predicates (=-=Mark and Egenhofer, 1994-=-). As a result there have been implementations in commercial systems (e.g., MGE, 1993; Keighan, 1993). Direction relations (north, north east) deal with order in space. Unlike topological relations, t... |

18 | The semantics of relations in 2-D space using representative points: Spatial indexes - Papadias, Sellis - 1993 |

14 | The retrieval of direction relations using r-trees - Papadias, Theodoridis, et al. - 1994 |

13 | Definitions of Line-Line Relations for Geographic Databases - Egenhofer - 1994 |

12 | Constraint-Based Reasoning in Geographic Databases: The Case of Symbolic Arrays - Papadias, Frank, et al. - 1994 |

9 | A Pictorial Language for the Retrieval of Spatial Relations from Image Databases - Papadias, Sellis - 1994 |

9 | The use of spatial relationships to aid spatial database retrieval - Peuquet - 1986 |

9 | A Qualitative Spatial Reasoner - Sharma, Flewelling, et al. - 1994 |

7 | The Retrieval of Direction Relations Using R trees - Papadias, Theodoridis, et al. - 1994 |

5 | Counter-Intuitive Geographic "Facts": Clues for Spatial Reasoning at Geographic Scales - Mark - 1992 |

4 | Determining Spatial Relations between Lines and Regions in Arc/Info using the 9Intersection Model - Mark, Xia - 1994 |

3 |
Managing Spatial Data within the Framework of the Relational Model
- Keighan
- 1993
(Show Context)
Citation Context ...(Egenhofer, 1991) have potential for defining cognitivety meaningful spatial predicates (Mark and Egenhofer, 1994). As a result there have been implementations in commercial systems (e.g., MGE, 1993; =-=Keighan, 1993-=-). Direction relations (north, north east) deal with order in space. Unlike topological relations, there are not widely accepted definitions of direction relations; a number of different definitions, ... |