M. Egenhofer, R. Franzosa, On the Equivalence of Topological Relations, International Journal of Geographical Information Systems, 9(2), pp.133-152 (1995)  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... have not missed a condition (an adhoc style of analysis might easily identify a sufficient condition but might not identify all sufficient conditions) This analysis is rather in the style of the 4 and 9 intersection model of Egenhofer [Egenhofer and Franzosa, 1991; Egenhofer and Herring, 1994; Egenhofer and Franzosa, 1995] where from a 2 x 2 and 3 x 3 matrix which determine whether various topological parts of two regions share points or not, then by imposing a variety of conditions (such as regularity or one pieceness) the or 2 possibilities are whittled down to just eight possibilities (corresponding to ....

M J Egenhofer and R D Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9(2):133--152, 1995.

....of connection through fiat boundaries [59] Yet another notion of connection is given by a pair of linked (interlocked) tori [27, 65] 34 b g a b c d Figure 14. Further connection relations with multi piece regions. It is also worth pointing to the work of Egenhofer and Franzosa [28, 29], who present a calculus that allows, at the cost of arbitrary complexity, the possibility of classifying any topological distinct situation. Compare [18] for a related proposal. The variety of mereotopological connection relations is very rich indeed. We hope to have gone some way in the ....

Egenhofer M. J., Franzosa R. D., 1995, `On the Equivalence of Topological Relations ', International Journal of Geographical Information Systems 9, 133--152.

....intersection of A with B, and in certain other regions determined by A and B. The investigation of this use of connected components is due to Galton [Gal98] Another way of extending the 4 intersection model, which provides for still finer distinctions than in Galton s technique, is described in [EF95] The RCC schemes have been extended to systems such as RCC15 and RCC23 [CB 97] which take account of the convex hulls of the regions involved. Another direction for extension is to vague regions. Two approaches based on the 9 intersection model, are the work of Clementini and Di Felice ....

M. J. Egenhofer and R. Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9:133--152, 1995.

.... object based [7] While the former deals with spatial distributions over a geographical region, the latter deals with discrete, identifiable entities on the geographical space [8] These two approaches have led to two separate areas of research: definition of spatial operations on discrete objects [9], and definition of operations on fields (the map algebra of Tomlin [10] Furthermore, most current GIS implementations provide different sub systems for map algebra, spatial queries and image processing. To improve upon this situation, there is a need for a comprehensive approach which unifies ....

M.J. Egenhofer and R.D. Franzosa, On the equivalence of topological relations. International Journal of Geographical Information Systems, 9(2), 133-152 (1995).

....determined by A and B. The investigation of this use of connected components is due to Galton [Gal98] Another way of describing the relationship of A to B, which provides for ner distinctions than in Galton s technique, is a re nement of the 4 intersection model also by Egenhofer and Franzosa [EF95] Some recent work in this area includes the investigation of relations between three dimensional regions [Zla99] Since it is possible to regard time as the third dimension, this is likely to provide one way of treating relationships between two dimensional spatial regions which vary over a one ....

M. J. Egenhofer and R. Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9:133-152, 1995.

.... have not missed a condition (an adhoc style of analysis might easily identify a sufficient condition but might not identify all sufficient conditions) This analysis is rather in the style of the 4 and 9 intersection model of Egenhofer [Egenhofer and Franzosa, 1991; Egenhofer and Herring, 1994; Egenhofer and Franzosa, 1995] where from a 2 x 2 and 3 x 3 matrix which determine whether various topological parts of two regions share points or not, then by imposing a variety of conditions (such as regularity or one pieceness) the 2 4 or 2 9 possibilities are whittled down to just eight possibilities (corresponding ....

M J Egenhofer and R D Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9(2):133--152, 1995.

.... of the forms such as: Given that a region a is in relation R 1 to region b, and region b is in relation R 2 to region c; what relations may or must hold between a and c Of course, it might be possible to adapt the conventional mathematical formalisms, and indeed this strategy has been adopted [60, 64, 184]. One existing approach to topology which has been espoused by the QSR community is the work to be found in the philosophical logic community [181, 51, 183, 23, 24, 13] This work has built axiomatic theories of space which are predominantly topological in nature, and which take regions rather ....

....of dimensions. Other theories which introduce the notion of boundaries of regions explicitly include [166, 175, 152, 167] 4.2.2. Topology via n intersections An alternative approach to representing and reasoning about topological relations has been promulgated via a series of papers [57, 60, 58, 26, 61, 64]. Three sets of points are associated with every region its interior, boundary and complement. The relationship between any two region can be characterized by a 3x3 matrix 7 called the 9 intersection. Although it would seem 5 Note, however, that this task becomes almost trivial once the ....

Egenhofer, M. J. and Frenzosa, R.: \On the equivalence of topological relations", International Journal of Geographical Information Systems, 9(2), 1995, pages 133-152

....induced by the FOL data model, a finite structure which is an abstraction that captures all the topological properties of the spatial database. The strategy of maintaining such a finite structure (from now on called topological invariant) is very useful and has been addressed in the literature [7, 8, 19, 23]. Different abstractions of topological properties have been considered, and each of them can be viewed as an augmentation of the model proposed by the U.S. Census Bureau, which contains topological properties on points, lines and areas [6, 20] Different classes of continuous topological ....

M. J. Egenhofer and R. D. Franzosa. On the equivalence of topological relations. International Journal of Geographic Information Systems, 9(2):133--152, 1995.

....intersection of A with B, and in certain other regions determined by A and B. The investigation of this use of connected components is due to Galton [Gal98] Another way of extending the 4 intersection model, which provides for still finer distinctions than in Galton s technique, is described in [EF95] The RCC schemes have been extended to systems such as RCC15 and RCC23 [CB 97] which take account of the convex hulls of the regions involved. Another direction for extension is to vague regions. Two approaches based on the 9 intersection model, are the work of Clementini and Di Felice ....

M. J. Egenhofer and R. Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9:133--152, 1995.

....where no spatial indeterminacy is admitted. For example, the relation between two regions may be that they are disjoint or that they meet only at their boundaries. The two principal approaches to these topological relations are those based on the RCC formalism [6] and on Egenhofer s 4 intersection [11, 12] and 9 intersection models [13] The relations that can be de ned on regions in the RCC approach are often grouped into sets of relations that are pairwise disjoint and jointly exhaustive (JEPD) meaning that for any two regions, one and only one of a particular JEPD set of relations will hold ....

....us a function: F : R R fDR; PO; PP; PPi; EQg; 1) where R is the set of regions, and F (a; b) takes a given one of the ve values if and only if the corresponding relation holds between the regions a and b. The approach to relations between crisp regions due to Egenhofer and his colleagues [11, 12, 13] is based on a treatment of regions constructed from sets of points, making it a topological rather than mereological approach. It takes into account the interior and boundary (and exterior in the case of the 9 intersection model) of pairs of crisp regions, and looks at the intersections of these. ....

M. J. Egenhofer and R. Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9:133{ 152, 1995.

.... detailed survey of mereotopology which also deals with the RCC and related systems can be found in the recent book by Casati Varzi (1999) Schemes for classifying relationships between spatial regions have arisen from the needs of geographic information systems (GIS) Egenhofer Franzosa 1991, Egenhofer Franzosa 1995, Galton 1998) The majority of all this work has been concerned with space which is in nitely divisible and continuous. For example, the RCC axioms stipulate (Cohn et al. 1997, p283) that every region has a non tangential proper part, thus ensuring that space is in nitely divisible. The ....

Egenhofer, M. J. & Franzosa, R. (1995), `On the equivalence of topological relations', International Journal of Geographical Information Systems 9, 133-152.

....search and retrieval therefore allows for raw imagery to be queried on line. Currently, we are extending our queries to include configurations of objects. We employ the well known concept of 9 intersection, describing the major topological relations between areal, linear, and point features [5]. According to this model, the topological relationships between two objects is described by a 3x3 matrix whose elements express whether the mutual relationships between the interior, exterior and outlines of two features are empty or non empty sets. Individual objects are queried separately, and ....

Egenhofer M. & R. Franzosa. On the Equivalence of Topological Relations. Int. Journal of Geographical Information Systems, Vol. 9, No. 2, pp. 133-152, 1995.

....introduce boundaries of regions explicitly (e.g. 119, 120, 125, 109] but which did not explicitly introduce dimensional reasoning. Topology via n intersections An alternative approach to representing and reasoning about topological relations has been promulgated via series of papers (e.g.[23, 39, 41, 41, 40, 46, 42]) In the most recent calculus three sets of points are associated with every region its interior, boundary and complement; the relationship between two regions can be characterized by a 3x3 matrix, 6 called the 9 intersection, each of whose elements denotes whether the intersection of the ....

M J Egenhofer and R D Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9(2):133--152, 1995.

....imprecise information by abstracting away from metrical details. However, specific formalisms have also been developed to facilitate representing and reasoning with indefinite information. For example, 10] and, independently, 6] have developed extensions of two related formalisms (i.e. 9] and [13] respectively) for representing and reasoning about mereological relations between spatial regions. Common to both these formalisms is the notion of an egg yolk 1 : intuitively, 1 In fact [6] do not use the term egg yolk ; however the concept is essentially the same. this is a pair of ....

M J Egenhofer and R D Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9(2):133--152, 1995.

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M. Egenhofer and R. Franzosa, On the Equivalence of Topological Relations. International Journal of Geographical Information Systems 9(2): 133-152, 1995.

.... In order to establish topological relationequivalencebetween two regions (i.e. to decide whether or not two pairs of objects have the same topological relations) it is sufficient to describe topological invariants for the components (or separations) of the boundary boundary intersection [14] and the approach generalizes to line line and line region relations. The necessary invariants to consider for region region relations are: Journal of Visual Languages and Computing, Vol. 8, No. 4, pp. 403 424, 1997. the sequence of components counted in a consistent orientation of the plane ....

.... Detailed topological relations between two regions are expressed by the componentinvariant table for non empty boundary boundary sequences, which lists the sequence of boundaryboundary components and each component s dimension, type, crossing direction, boundedness, and complement relationship [12, 14]. Journal of Visual Languages and Computing, Vol. 8, No. 4, pp. 403 424, 1997. 4.3 Metrical Refinements Occasionally, topology per se is insufficient to characterize the essence of spatial relations. For instance, in order to capture the semantics of the spatial relation between Interstate I 95 ....

M. Egenhofer and R. Franzosa, "On the Equivalence of Topological Relations," International Journal of Geographical Information Systems, vol. 9, no. 2, pp. 133-152, 1995.

.... between two regions (i.e. to decide whether or not two pairs of objects have the same topological relations) it is sufficient to describe such invariants for the components (or separations) of the boundary boundary intersection only, since the other intersections can be inferred from them [7]. The necessary invariants to consider are the sequence of components counted along the boundaries; the dimension of each component; the type of boundary boundary component intersection (touch or cross) where crossing may be further refined depending on whether the component crosses into or ....

M. Egenhofer and R. Franzosa, "On the Equivalence of Topological Relations," International Journal of Geographical Information Systems, vol. 9, no. 2, pp. 133-152, 1995.

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M. Egenhofer, R. Franzosa, On the Equivalence of Topological Relations, International Journal of Geographical Information Systems, 9(2), pp.133-152 (1995)

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M. Egenhofer and R. Franzosa. On the Equivalence of Topological Relations. International Journal of Geographical Information Science, 9(2):133--152, 1995.

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M. Egenhofer and R. Franzosa, "On the Equivalence of Topological Relations," International Journal of Geographical Information Systems, vol. 9, pp. 133-152, 1995.

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M. J. Egenhofer and R. D. Franzosa. On the equivalence of topological relations. International Journal of Geographic Information Systems, 9(2):133-152, 1995.

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M. Egenhofer, R. Franzosa, On the Equivalence of Topological Relations, International Journal of Geographical Information Systems, 9(2), pp.133-152 (1995)

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M. J. Egenhofer and R. Franzosa. On the equivalence of topological relations. International Journal of Geographical Information Systems, 9:133-152, 1995.

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Egenhofer M J and Franzosa R D. On the equivalence of topological relations. Int. J. Geographical Information Systems, 9:133--152, 1995.

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M J Egenhofer and R D Franzosa, `On the equivalence of topological relations ', International Journal of Geographical Information Systems, 9(2), 133-- 152, (1995).

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