Oracle Spatial, Raster Data
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Objects with Broad Boundaries E LISEO C LEMENTINI Department of Electrical and Information Engineering, University of L’Aquila, L’Aquila, Italy Synonyms Spatial objects; Spatial data types with indeterminate boundaries; Vague boundaries; Uncertain boundaries; 3-value indeterminacy; Fuzzy sets; Probability theory; Egg-yolk model
Definition Objects with broad boundaries are spatial objects, whose crisp boundaries are replaced by an area expressing the boundary’s uncertainty. There are two main interpretations for broad boundaries: (1) for positional uncertainty, the broad boundary represents the set of all possible positions among which the unknown boundary position is hidden; (2) for “fuzzy” boundaries, that is, boundaries that are by nature not crisp, the broad boundary represents their minimum and maximum extent. The main motivation for objects with broad boundaries is to record information about uncertainty together with the data. In this way, they represent a new geometric model that overcomes the limits of current spatial database models, which are a collection of lines (points, polylines and polygons). The geometric model of objects with broad boundaries takes into account a 3-valued indeterminacy of location (false, maybe, true), where “false” means that the point is not in the location, “true” means that the point is in the location and “maybe” means either that the point is with some probability in the location or that the point belongs, up to a certain membership value, to the location. Regions, lines and points with broad boundaries can be distinguished. In the case of lines, the broad interior can also be defined: a line with a broad boundary and broad interior is called an uncertain line. Historical Background To represent uncertainty in spatial data, many models suggested the introduction of broad boundaries replacing crisp ones in the case of regions [2,5,7,10,14] and lines [1]. The advantage of objects with broad boundaries is that they can be implemented on existing database systems at reasonable cost, being a direct extension of existing geometric models. Objects with broad boundaries corresponding to a 3-valued indeterminacy of a region’s location do not support any further hypothesis on the internal structure of the broad boundary. Other approaches utilize fuzzy sets [15] or probability theory [16], which describe the internal structure of the uncertain geometry with membership functions or probability distributions, respectively. These other
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Objects with Broad Boundaries
Objects with Broad Boundaries, Figure 1 Regions with a broad boundary
Objects with Broad Boundaries, Figure 2 Composite regions with broad boundaries
approaches require much effort to store data and also the operations become computationally
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