VIIIth International Congress of Photogrammetry: Proceedings of the Congress

Fagerholm, P. O.; Ternryd, C. O.

Bibliographic data

Multivolume work

Persistent identifier:: 1048861678

Title:: VIIIth International Congress of Photogrammetry

Sub title:: Stockholm, Sweden, July 17 - 26, 1956

Year of publication:: 1957

Place of publication:: Stockholm

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 1048861678

Language:: English

Other Title:: Paralleltitel: VIIIe Congrès International de Photogrammétrie

Editor:: Fagerholm, P. O.

Corporations:: International Congress of Photogrammetry, 8., 1956, Stockholm; Board of the VIIIth International Congress of Photogrammetry

Adapter:: International Congress of Photogrammetry, 8., 1956, Stockholm; Board of the VIIIth International Congress of Photogrammetry

Founder of work:: International Congress of Photogrammetry, 8., 1956, Stockholm; Board of the VIIIth International Congress of Photogrammetry

Other corporate:: International Congress of Photogrammetry, 8., 1956, Stockholm; Board of the VIIIth International Congress of Photogrammetry

Document type:: Multivolume work

Volume

Persistent identifier:: 1048862747

Title:: Proceedings of the Congress

Sub title:: VIIIe Congrès International de Photogrammétrie

Scope:: 399 Seiten

Year of publication:: 1957

Place of publication:: Stockholm

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 1048862747

Illustration:: Illustrationen

Signature of the source:: ZS 312(12,1)

Language:: French

Other Title:: Paralleltitel: Compte rendu du Congrès

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Contributor:: Ternryd, C. O.

Editor:: Fagerholm, P. O.

Corporations:: International Congress of Photogrammetry, 8., 1956, Stockholm; Board of the VIIIth International Congress of Photogrammetry

Adapter:: International Congress of Photogrammetry, 8., 1956, Stockholm; Board of the VIIIth International Congress of Photogrammetry

Founder of work:: International Congress of Photogrammetry, 8., 1956, Stockholm; Board of the VIIIth International Congress of Photogrammetry

Other corporate:: International Congress of Photogrammetry, 8., 1956, Stockholm; Board of the VIIIth International Congress of Photogrammetry

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2019

Document type:: Volume

Collection:: Earth sciences

Chapter

Title:: COMMISSION III [compte-rendu]

Document type:: Multivolume work

Structure type:: Chapter

ISPRS, Vol.34, Part 2W2, "Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 interaction among whole objects, Voronoi regions of spatial objects are utilised. The remainder of this paper is structured as follows: Section 2 introduces the basic strategies of the new approach. In Section 3, spatial components are introduced to set algebra to form a spatial algebra for spatial relations. In Section 4, Voronoi regions are employed to make this spatial algebra more generalised. Section 5 and Section 6 examine possible spatial relations described and distinguished by this spatial algebra. Some conclusions are made in Section 7. 2. THE STRATEGIES USED IN THIS STUDY In order to develop an appropriate strategy of study, a critical examination of existing models seems appropriate. As mentioned in the previous section, in the decomposition-based approach, a spatial object is decomposed into several topological components such as the interior and boundary. The interaction between these components of objects determines the relations between spatial objects. Most of existing models are based on point-set topology. The typical examples are the 4-intersection model by Egenhofer and Franzona (1991) and its extension to 9-intersection model (Egenhofer and Herring 1991). However, there are some imperfections associated with this model (Clementini et al. 1993, Molenaar et al. 1994, Chen et al. 2001). For example, 9-intersection model results in too many relations for humans to use and the list of cases resulting from this approach is not directly related to the users' interpretation of topological facts (Clementini et al. 1993, 1995). More seriously, the use of complement as exterior in the 9-intersection model makes the three components linearly dependent (Li et al. 2000, Chen et al. 2001). Now let's turn to the whole-based approaches. The whole-based approach directly uses spatial objects instead of their components for the description of spatial relations, thus the problems associated with decomposition-based approach can be avoided. However, it is not sufficient to consider only objects themselves for distinguishing spatial relations (Egenhofer et al. 1993). Indeed, many relations cannot be distinguished if only the objects themselves are used. As a consequence of these reasons, in this study, the whole-based approach will be used as a basis. In order to overcome the shortcomings with the whole-based approach, an additional parameter should be introduced and this parameter must be insensitive to the dimensionality of space. On the hand, it must be closely related to the object as so to have functions similar to those of boundary and exterior. As a result, the Voronoi region of an object is selected, because Voronoi regions have many good properties (Gold 1992, Li et al. 1999). [A Voronoi region (or Thiessen polygon) for a point is the locus of points closer to that point than to any other given one]. Another observation arising from the analysis of existing literature is that only the ‘intersection’ operator out of the many Set operators are in use. This is perhaps the most expensive one in terms of computation. There is no reason why other operators cannot be used. Therefore, it is attempted to explore the full range of set operators to constitute a spatial algebra for the spatial relations. In summary, the basic strategies adopted here are: (1) (2) a spatial object is treated in a whole; Voronoi region of an object is employed to enhance its interconnection with neighbours; appropriate operators from set operators are utilised to distinguish the spatial relations between neighbouring spatial objects; and several types of values are used for the computational results of set operations, e.g. content, dimension and number of connected components and so on. 3. SPATIAL ALGEBRA FOR SPATIAL RELATIONS: AN INTEGRATION In the previous section, the basic strategies employed in this study are outlined. From this section on, the development of spatial algebra using such strategies will be described. In this section, a number of set operators will be employed and spatial concepts are embedded into the algebra. 3.1 Set operators for spatial relations Spatial objects are often regarded as sets in space in the context of GIS. This is very important as it means that objects can be manipulated by ordinary set operators: union, intersection, set difference and symmetrical difference and so on. At the same time, spatial relations can be considered as the result for handling these "sets". In fact, the theory of sets is the basis of the description and determination of spatial relations, especially, topological relations can be regarded as detailed relations between sets (Worboys, 1995). Figure 1 illustrates working principles of set operators, using line and area objects as examples.

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