Egenhofer, M. (1994). Deriving the composition of binary topological relations. Journal of Visual Languages and Computing, 5:133--149.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and C. If the set of complete and sound 2 spatial relations between A and B and between B and C are considered, then the full set of compositions of relations can be represented in a composition table. Much research work have recently been devoted to the study of the computation of such tables [Ege94, RCC92] However, composition tables have been derived only for a few specific shapes and types of spatial objects. In general, limitations of the different methods for spatial reasoning are as follows. ffl Spatial reasoning is studied only between objects of similar types, e.g. between two ....

.... such as before, after and ( for example, a b b c a c) and to the subset relations such as contain and inside (for example, inside(A; B) inside(B; C) inside(A; C) east(A;B) east(B; C) east(A; C) Transitive property of the subset relations was employed by Egenhofer [Ege94] for reasoning over topological relationships between simple regions. Transitive property of the order relations has been utilized by Mukerjee Joe [MJ90] Guesgen [Gue89] ffl Theorem proving (elimination) If the domain studied does not contain relations which possess the transitivity ....

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M.J. Egenhofer. Deriving the composition of Binary Topological Relations. Journal of Visual Languages and Computing, 5:133--149, 1994.

....and consider only the relational part. Since the calculus handles relations, no knowledge about the concrete geometrical objects is necessary. Relation algebras were introduced into spatial reasoning by Egenhofer Sharma (1992) with additional results published in Egenhofer Sharma (1993) Egenhofer (1994). Many well known spatial relations can be expressed by the relation operators and constants, #, and the single relation C,for example, P # ##C# #C#; part of (1.7) PP # P ##I: proper part of (1.8) O # P## P overlap (1.9) PO# O ###P # P## partially overlap (1.10) EC # C ##O external contact ....

Egenhofer, M. (1994). Deriving the composition of binary topological relations. Journal of Visual Languages and Computing, 5, 133--149.

.... (Lakoff and Johnson 1980, Johnson 1987) The formalization of spatial relations has, therefore, been an active area of research at least since 1989 (Mark et al. 1995) Topological relations between simply connected regions were treated in (Egenhofer 1989) and extensive work has followed from this (Egenhofer 1994). Metric relations between point like objects, especially cardinal directions (Frank 1991b, Frank 1991a, Freksa 1991, Hernndez 1991) and approximate distances (Frank 1992, Hernndez et al. 1995, Frank 1996b) were discussed. Other efforts dealt with orderings among configurations of points ....

....problem, which makes succinct definition for changes impossible (Hayes 1977, McCarthy 1985) McCarthy (1980, 1986) proposed situation calculus with circumscription as an extension of the logical theory to overcome this limitation. 4. 2 Relations Calculus The behavior of topological relations (Egenhofer 1994, Papadias and Sellis 1994) but also cardinal directions and approximate distances (Hernndez et al. 1995, Freksa 1991, Frank 1992, Frank 1996b) can be analyzed using the relations calculus (Schroeder 1895, Tarski 1941, Maddux 1991) Properties of relations are described as the outcome of the ....

M. Egenhofer (1994) Deriving the Composition of Binary Topological Relations. Journal of Visual Languages and Computing 5(2): 133-149.

....to set of locations dictated by the different manners in which a the shape definition can be fitted into the prescribed location space. ffl If the object is a shapeless object the required location is the location space (as defined in the script) within which the object is known to exist. space([5,5]) class(equals, fixed) class(blob, shapeless) class(plus, free, 256. 256, 1. 1) instance(e1, equals, 0. 2, 512. 514) instance(b1, blob, 1. 1027) instance(p1, plus, 257. 1028) constraint( e1) intersects, p1, offset( 256. 256) constraint( b1) complement, e1, offset( 257. 257) ....

M.J. Egenhofer, Deriving the composition of binary topological relations, Journal of Visual Languages and Computing 5 133-149 (1994).

.... has not been removed. An alternative approach is to consider only topological relations. Egenhofer defines such relations as follows: those spatial relations that are invariant under topological transformations and, therefore, preserved if the objects are translated, rotated or scaled. [21]) Egenhofer uses a 9 Intersection model (Egenhofer [21] Papadias et al. 44] founded on an earlier 4 Intersection model (Egenhofer [20] to identify and manipulate such relations. In this model spatial objects are considered to have three parts (a) an interior, b) a boundary and (c) an ....

....is to consider only topological relations. Egenhofer defines such relations as follows: those spatial relations that are invariant under topological transformations and, therefore, preserved if the objects are translated, rotated or scaled. 21] Egenhofer uses a 9 Intersection model (Egenhofer [21], Papadias et al. 44] founded on an earlier 4 Intersection model (Egenhofer [20] to identify and manipulate such relations. In this model spatial objects are considered to have three parts (a) an interior, b) a boundary and (c) an exterior. The topological relation between two point sets ....

M.J. Egenhofer, Deriving the composition of binary topological relations, Journal of Visual Languages and Computing 5 (1994) 133-149.

....first of the above allows us to define spaces (say) within another object or at some location outside an object. The second allows us to expand an object in all or some direction(s) In this manner all the standard multi dimensional topological relations such as those identified by (say) Egenhofer [8], Hern andez [11] or Cohn [6] can be defined. Of course it is only appropriate to apply such offsets to shaped objects applying offsets to shapeless objects will result in unpredictable conclusions. Thus a constraint definition has an operator and two operands plus possibly two offsets to be ....

M.J. Egenhofer, `Deriving the Composition of Binary Topological Relations', Journal of Visual Languages and Computing, 5, 133-149, 1994.

....Some notes concerning the constraint satisfaction mechanism are then given in Sections 6. In the following two sections the approach is illustrated firstly (Section 7) with respect to Allen s interval calculus [8] and secondly (Section 8) with respect to Egenhofer s 9 Intersection mechanism [9] . It should be noted that these two illustrations are of necessity brief and therefore only serve to give a flavour of the full power of the approach. Finally in section 9 some concluding remarks are presented. 1.1 NOTE ON SPATIAL REASONING Spatial reasoning can be defined, very broadly, as the ....

....are processed, i.e. the sequence in which constraints are presented becomes significant. Using the above filters and mappings it is possible to express many of the standard relations encountered in spatial reasoning applications (such as those discussed by Retz Schmidt [17] Egenhofer [9] and Cohn [18] amongst many others) However, to increase the expressiveness of these constraints an offset can be applied to the location associated with an identifier prior to satisfaction of the constraint. An offset is some subset of UD which is applied (using the f translate function) to ....

[Article contains additional citation context not shown here]

M.J. Egenhofer, Deriving the composition of binary topological relations, Journal of Visual Languages and Computing 5 133-149 (1994).

.... (Lakoff and Johnson 1980, Johnson 1987) The formalization of spatial relations has, therefore, been an active area of research at least since 1989 (Mark et al. 1995) Topological relations between simply connected regions were treated in (Egenhofer 1989) and extensive work has followed from this (Egenhofer 1994). Metric relations between point like objects, especially cardinal directions (Frank 1991b, Frank 1991a, Freksa 1991, Hern ndez 1991) and approximate distances (Frank 1992, Hern ndez et al. 1995, Frank 1996b) were discussed. Other efforts dealt with orderings among configurations of points ....

....frame problem, which makes succinct definition for changes impossible (Hayes 1977, McCarthy 1985) McCarthy (1980, 1986) proposed situation calculus with circumscription as an extension of the logical theory to overcome this limitation. 4. 2 Relations Calculus The behavior of topological relations (Egenhofer 1994, Papadias and Sellis 1994) but also cardinal directions and approximate distances (Hern ndez et al. 1995, Freksa 1991, Frank 1992, Frank 1996b) can be analyzed using the relations calculus (Schroeder 1895, Tarski 1941, Maddux 1991) Properties of relations are described as the outcome of the ....

M. Egenhofer (1994) Deriving the Composition of Binary Topological Relations. Journal of Visual Languages and Computing 5(2): 133-149.

.... and Johnson 1980; Johnson 1987) The formalization of spatial relations has, therefore, been an active area of research at least since 1989 (Mark et al. 1995) Topological relations between simply connected regions were treated in (Egenhofer 1989) and extensive work has followed from this (Egenhofer 1994). Metric relations between point like objects, especially cardinal directions (Frank 1991b; Frank 1991a; Freksa 1991; Hernandez 1991) and approximate distances (Frank 1992; Hernandez et al. 1995; Frank 1996b) were discussed. Other efforts dealt with orderings among configurations of points ....

....using predicate calculus. In theory, predicate calculus has all the expressive power necessary, but it is practically limited by the frame problem, which makes succinct definition for changes impossible (Hayes 1977; McCarthy 1985) 3.4. 2 Relations Calculus The behavior of topological relations (Egenhofer 1994; Papadias and Sellis 1994) but also cardinal directions and approximate distances (Frank 1992; Frank 1996b) can be analyzed using the relations calculus (Schroeder 1895; Maddux 1991) Properties of relations are described as the outcome of the combination (the ; operator) of two relations. ....

M. Egenhofer (1994) Deriving the Composition of Binary Topological Relations. Journal of Visual Languages and Computing 5(2): 133-149.

.... relations are able to describe all aspects of the scene which are invariant with respect to common linear transformations (translation, rotation, rubber sheeting) and therefore provide a description of important characteristics of the objects involved in the scene (Randell, Cui, and Cohn 1992; Egenhofer 1994; Clementini and Di Felice 1996) However, topological relations alone, being independent of the position and extension of objects, are not sufficient to provide a full description of a scene. Orientation relations describe where objects are placed relative to one another, and can be defined in ....

Egenhofer, M. J. (1994). Deriving the composition of binary topological relations. Journal of Visual Languages and Computing, 5 (1), 133--149.

....a new set of cells. 1. Example filters: equals, subset, superset, disjoint, intersects. 2. Example mappings: complement, intersection. Using these relations many of the standard topological relations encountered in spatial reasoning can be expressed, e.g. within, contains, overlaps, disjoint ([4, 5, 6, 7, 8]) The expressiveness of these relations can be increased by allowing offsets to be applied to the locations before the relation is processed. For example we may have two objects L1 and L2 whose locations are given by the sets f257: 514g and f514: 771g and a subset relation: L1 subset L2 to ....

M.J. Egenhofer, Deriving the composition of binary topological relations, Journal of Visual Languages and Computing 5 133-149 (1994).

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Egenhofer, M.: Deriving the Composition of Binary Topological Relations. Journal of Visual Languages and Computing. 5:(2) (1994) 133-149.

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Egenhofer, M. (1994). Deriving the composition of binary topological relations. Journal of Visual Languages and Computing, 5:133--149.

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