Qiao Wang

Fuzzy description of topological relations I: a unified fuzzy 9-intersection model

First, the impacts of uncertainty of position and attribute on topological relations and the disadvantages of qualitative methods in processing the uncertainty of topological relations are concluded. Second, based on the above point, the fuzzy membership functions for dividing topology space of spatial object and for describing uncertainty of topological relations are proposed. Finally, the fuzzy interior, exterior and boundary are defined according to those fuzzy membership functions, and then a fuzzy 9-intersection model that can describe the uncertainty is constructed. Since fuzzy 9-intersection model is based on fuzzy set, not two-value logic, the fuzzy 9-intersection model can describe the impacts of position and attribute of spatial data on topological relations, and the uncertainty of topological relations between fuzzy objects, relations between crisp objects and fuzzy objects, and relations between crisp objects in a united model.

Reasoning about topological relations between regions with broad boundaries

Uncertain regions can be represented as having broad boundaries (BBRs) and their topological relations can be modeled by the extended 9-intersection. In order to satisfy the need for querying, managing, and processing BBRs, this study presents a 4-tuple representation of topological relations between BBRs, and a method in which the relations between simple regions with broad boundaries (SBBRs) are used to infer new topological information. The 4-tuple representation can distinguish the same topological relations as identified by the extended 9-intersection. Since the 4-tuple uses combinations of the basic topological relations between crisp regions to describe the relations between uncertain regions, the reasoning of topological relations between SBBRs can be obtained by combining the results of those between crisp regions. The reasoning mechanism can be used in several applications, such as to evaluate the consistency of topological relations between uncertain regions in multi-resolution spatial databases and to assess the consistency of a complete or incomplete symbolic description of a spatial scene.

Evaluating structural and topological consistency of complex regions with broad boundaries in multi-resolution spatial databases

Multi-resolution or multi-scale spatial databases store and manage multiple representations of spatial objects in the same area, so consistency among multiple representations of the same objects should be evaluated and maintained. Although many approaches have been proposed to check inconsistencies in multi-resolution databases, there is still a lack of effective approaches working for complex objects, especially for regions with broad boundaries which is a general model for representing various types of uncertainties. This paper presents approaches for evaluating structural and topological consistency among multiple representations of complex regions with broad boundaries (CBBRs) based on map generalization operators: merging, dropping, and hybrid of these two. For evaluation of structural consistency, all possible multiple representations of a CBBR are generated automatically and organized into a structured neighborhood graph, and then correspondences and equivalences among the multiple representations are defined to determine whether two representations at different levels of detail are structurally consistent. For evaluation of topological consistency, the topological relations between all pairs of regions in two CBBRs are considered, and their variation with change of spatial scale is analyzed. Since the approaches in this paper are built on a hiearchical representation of CBBRs with arbitrarily complex structure, they will also work well for evaluating consistency among multiple representations of complex objects.

Fuzzy description of topological relations II: computation methods and examples

The unified fuzzy 9-intersection model of topological relations can describe the uncertainty of topological relations introduced by the uncertainty of spatial data. In this article, first, the raster algorithm for computing fuzzy 9-intersection model is presented, and the vector algorithms for computing fuzzy 9-intersection model of point/point, point/line, point/region, line/line, line/region, region/region topological relations are also provided. Second, based on the software developed by us, the examples for computing fuzzy 9-intersection matrix between two crisp objects, between two fuzzy objects and between a crisp object and a fuzzy object are listed. The results and analysis show that the unified fuzzy 9-intersection model is effective to describe the uncertainty of topological relations.

Modeling the scale dependences of topological relations between lines and regions induced by reduction of attributes

The scale dependences of topological relations are caused by the changes of spatial objects at different scales, which are induced by the reduction of attributes. Generally, the detailed partitions and multi-scale attributes are stored in spatial databases, while the coarse partitions are not. Consequently, the detailed topological relations can be computed and regarded as known information, while the coarse relations stay unknown. However, many applications (e.g., multi-scale spatial data query) need to deal with the topological relations at multiple scales. In this study new methods are proposed to model and derive the scale dependences of topological relations between lines and multi-scale region partitions. The scale dependences of topological relations are modeled and used to derive the relations between lines and coarse partitions from the relations about the detailed partitions. The derivation can be performed in two steps. At the first step, the topological dependences between a line and two meeting, covered and contained regions are computed and stored into composition tables, respectively. At the second step, a graph is used to represent the neighboring relations among the regions in a detailed partition. The scale dependences and detailed relations are then used to derive topological relations at the coarse level. Our methods can also be extended to handle the scale dependences of relations about disconnected regions, or the combinations of connected and disconnected regions. Because our methods use the scale dependences to derive relations at the coarse level, rather than generating coarse partition and computing the relations with geometric information, they are more efficient to support scale-dependent applications.

A scale-explicit model for checking directional consistency in multi-resolution spatial data

Multi-resolution spatial data always contain the inconsistencies of topological, directional, and metric relations due to measurement methods, data acquisition approaches, and map generalization algorithms. Therefore, checking these inconsistencies is critical for maintaining the integrity of multi-resolution or multi-source spatial data. To date, research has focused on the topological consistency, while the directional consistency at different resolutions has been largely overlooked. In this study we developed computation methods to derive the direction relations between coarse spatial objects from the relations between detailed objects. Then, the consistency of direction relations at different resolutions can be evaluated by checking whether the derived relations are compatible with the relations computed from the coarse objects in multi-resolution spatial data. The methods in this study modeled explicitly the scale effects of direction relations induced by the map generalization operator – merging, thus they are efficient for evaluating consistency. The directional consistency is an essential complement to topological and object-based consistencies.

Multi-scale qualitative location: A direction-based model

Abstract Qualitative locations describe the locations of spatial objects by relating them to a reference frame with qualitative relations. Existing models concerned with regional partitions are mainly topology-based and do not consider the effects of scale changes on locations. This study develops a direction-based multi-scale qualitative location (DMQL) model to fill this gap. First, a cell partition is defined by extending the borders of the minimum bounding rectangles of the regions in a regional partition. Relating spatial objects to all regions by a set of directions is equal to representing the objects as a set of cells in a cell partition. Second, due to the multiple cell representations of spatial objects and the changes in direction relations across scales, some approaches are presented to derive the direction changes between regions in different frames, between spatial objects and regions, and between spatial objects at different scales. Third, the location and relation consistencies of qualitative locations are evaluated based on the cell representations of spatial objects at multiple scales through a case study. The results indicate that the DMQL model can locate objects more precisely than the topology-based models.

Multi‐Scale Qualitative Location: A Topology‐Based Model

Qualitative locations describe spatial objects by relating the spatial objects to a frame of reference (e.g. a regional partition in this study) with qualitative relations. Existing models only formalize spatial objects, frames of reference, and their relations at one scale, thus limiting their applicability in representing location changes of spatial objects across scales. A topology-based, multi-scale qualitative location model is proposed to represent the associations of multiple representations of the same objects with respect to the frames of reference at different levels. Multi-scale regional partitions are first presented to be the frames of reference at multiple levels of scale. Multi-scale locations are then formalized to relate multiple representations of the same objects to the multiple frames of reference by topological relations. Since spatial objects, frames of reference, and topological relations in qualitative locations are scale dependent, scale transformation approaches are presented to derive possible coarse locations from detailed locations by incorporating polygon merging, polygon-to-line and polygon-to-point operators.