Uncertainty

Geography refers literally to representations of phenomena on the earth's surface and near surface. Traditionally, geographic information is communicated with paper maps that depict various spatial entities and phenomena. Using computers, geographic information systems (GIS) have revolutionized the way in which maps are produced and used, thereby permitting great efficiency in processing a large quantity of spatial data for numerous applications.

However, maps in both analog and digital formats may disguise unseen generalization, selection, and approximation typical in the process of mapmaking. Moreover, due to measurement error, the input data sources themselves are subject to inaccuracy, as exemplified in photogrammetric plotting and classification of remotely sensed images. In a GIS environment where map overlaying and predictive modeling are performed, errors in input map layers will be propagated to the resultant maps, usually in complex ways. Thus, spatial data and their derivatives are subject to error, raising questions as to whether map users are willing to accept map data at their face value and what confidence limits should be placed on information products derived from imperfect data. As GIS applications are expanding at an unprecedented scale, answers to such questions are needed more urgently than ever before, and decades of research into error issues have produced some constructive results.

It is important to consider how the real world is conceptualized and, for the purpose of digital geoprocessing, made discrete. Conceptually, the real world can be considered as populated by discrete entities or as consisting of single-valued functions defined everywhere in space, known as objects and fields, respectively, in geographic information science (GIScience). The object-based models clearly are suited to represent well-defined features, such as human-made structures, human settlements, and transportation infrastructure, and have played an important role in cartography. On the other hand, the field-based models are better geared to represent spatially varied phenomena such as land cover, where class labels can be assigned at pixels or patches of land, and elevation, which can be defined for every location on the terrain surface. Clearly, fields are important data models in physical geography, and many phenomena about humans, human activities, and the space and/or structures used to conduct human activities are making greater use of fields as well as objects for representation and geoprocessing.

In object models, spatial entities are represented by position and attributes. Often it is the positional data that are examined with respect to error in objects, whereas attribution is assumed to be the responsibility of specialists such as census workers. There are three types of objects in terms of geometry: points, lines, and areas. Positional errors in points and lines usually are described by error ellipses and epsilon error bands, respectively, whereas positional errors in area objects are described by their boundary inaccuracy, which is effectively a combination of errors in lines constituting areas' boundaries. In field models, errors in variables measured at a continuous scale are described by standard deviations, and on the assumption of Gaussian distribution it is possible to state that the true value is within the interval of measured or estimated values plus or minus twice the standard[Page 506] deviation with a probability of 95%. For field variables that represent discrete labels, probability can be used to describe the accuracy of labeling at certain locations. For continuous data, including positional data and discrete data, accuracy assessment is commonly performed on the basis of independent reference data, which usually are of higher accuracy, to act as ground truth to benchmark the discrepancy of a test data set from it. Root mean squared errors (RMSEs) usually are calculated to measure the closeness of a data set to the reference, whereas percentage correctly classified (PCC) pixels that result from summarizing a confusion matrix measure the likelihood that a randomly chosen pixel classified as a certain class actually belongs to that class according to reference classification.

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