Qualitative Spatial Reasoning: Extracting and Reasoning with Spatial Aggregates

Article excerpt

The ability to perceive spatial objects and reason about their relations seems effortless for humans but has proved so difficult for computers that they have yet to attain the capabilities of a five-year-old child. Part of the computational problem lies in the difficulty of identifying and manipulating qualitative spatial representations. For example, although the pixels in a digital image implicitly define the locations of spatial objects, the task at hand might require a more qualitative characterization of the configuration of these objects, say, whether one object will soon occlude another. Handling spatial data is a key task in many applications, including geographic information systems (GISs), meteorological and fluid flow analysis, computer-aided design (CAD) systems, and protein structure databases (figure 1) (Zhao et al. 1999). For example, a GIS system might have large amounts of numeric information about spatial features such as highways and terrain but require query mechanisms to efficiently determine qualitative relationships such as those between a proposed route and wetlands regions.

Qualitative spatial reasoning (QSR) addresses these problems with representational primitives (a spatial "vocabulary") and inference mechanisms. QSR approaches can be characterized by two important and complementary classes of problems. Problems in the first class are data poor, and the goal is to design representations that can answer qualitative queries without much numeric information. The goal of answering qualitative queries addresses an important aspect of commonsense reasoning by humans and can be found in many practical applications such as computer-aided tutoring or diagram understanding. Because of the lack of detailed numeric information, representations used by the approaches to data-poor problems are often carefully designed by hand with respect to a task at hand. Problems in the second class (for example, scientific and engineering applications from fluid-flow analysis to distributed control design) are data rich, and the goal is to derive and manipulate qualitative spatial representations that efficiently and correctly abstract important spatial aspects of the underlying data and can be used for subsequent tasks. The approaches to data-rich problems are complementary to those for data-poor problems in that they can automatically construct spatial representations. Computational efficiency in reasoning arises from appropriate qualitative spatial representations; for example, a qualitative description of a temperature distribution as a configuration of iso-contours focuses the search for good thermal control designs. Similarly, qualitative representations allow efficient access and manipulation of data, for example, correlating maps (for example, a road map, a utilities map, and a forestry map) in a GIS system, determining the interaction of parts in a CAD design, and planning paths for a robotics application. An important feature of qualitative spatial representations is their ability to relate reasoning results to underlying data (rich or poor) and domain knowledge provided by the user.

In this article, we first review the representative work on QSR for data-poor scenarios. We then turn to the data-rich case and focus on how a particular QSR system, SPATIAL AGGREGATION, can help answer spatial queries for scientific and engineering data sets. Finally, we present a particular application that illustrates the effective representation and reasoning supported by both forms of QSR.

Qualitative Spatial Reasoning for Data-Poor Problems

Qualitative reasoning research uses high-level representations of physical systems and domain knowledge for tasks such as prediction, diagnosis, reconfiguration, and tutoring (de Kleer and Brown 1984; Falkenhainer and Forbus 1991; Forbus 1984; Kuipers 1986; Weld and de Kleer 1990) without requiring significant amounts or quality of data. Classical qualitative reasoning work deals primarily with temporal aspects of a system, abstracting away its spatial properties. …


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