Consistency among parts and aggregates: A computational model

Abstract

Heterogeneous geographic databases contain multiple views of the same geographic objects at different levels of spatial resolution. When users perceive geographic objects as one spatial unit, although they are physically separated into multiple parts, appropriate methods are needed to assess the consistency among the aggregate and the parts. The critical aspect is that the overall spatial relationships with respect to other geographic objects must be preserved throughout the aggregation process. We developed a systematic model for the constraints that must hold with respect to other spatial objects when two parts of an object are aggregated. We found three sets of configurations that require increasingly more information in order to make a precise statement about their consistency: (1) configurations that are satisfied by the topological relations between the two parts and the object of interest; (2) configurations that need further information about the topological relation between the object of concern and the connector in order to be resolved unambiguously; and (3) configurations that require additional information about the topological relation between the aggregate's boundary and the boundary or interior of the object of interest to be uniquely described. The formalism extends immediately to relations between two regions with disconnected parts as well as to relations between a region and an arbitrary number of separations.

Spatial Relations Using High Level Concepts

“…Despite the huge body of work on modeling spatial relations all existing models do not consider that different concepts may exist on different levels in a hierarchy. A number of authors have previously considered the effect splitting or merging of objects has on spatial relations [3][4][5]. However these works do not consider that different concepts exist on different levels in a hierarchy and in turn that the spatial relations in a given scene are a function of the specific concepts considered.…”

A framework for dynamic updates of map data in mobile devices

“…A number of work has been done to maintain the consistency between multi-scale or multiple LOD spatial databases. But few of them deal with the topological consistency except [5,6,15]. Several methods have been proposed for maintaining topological consistency depending on the operation type of generalization.…”

“…In order to make it consistent, the aggregation must be re-computed as shown by figure 5(b)-B3. The derivation method of topology for aggregation is proposed [6], and it can be used to recompute the aggregation with updated or newly inserted objects.…”

“…Several methods have been proposed for maintaining topological consistency depending on the operation type of generalization. In [6], a method to assess the topological integrity has been proposed for aggregation operator. A similar work has been carried out for collapse operator in [13].…”

“…a. assessment of topological consistency: For each LOD derived from LOD 0 , neighboring objects are checked to assess topological consistency with LOD 0 . The methods for assessment of topological consistency [5,6,13] will be explained in the next section.…”