Assessing positional and modelling uncertainties in vector-based spatialprocesses and analyses in geographical information systems

Abstract

This study assesses and models uncertainties in vector-based spatial processes and analyses in a Geographical Information System (GIS), including buffering, point-in- polygon query, overlay, and line simplification. GIS is a tool for spatial-related data processing and decision making. Handling decision making under uncertainty is a further extension of GIS functions. Therefore, it is of vital importance to study uncertainties in GIS and to decide the fitness of data to user's particular applications. Uncertainty in a vector spatial analysis is mainly introduced from (a) uncertainty of raw spatial data, (b) uncertainties propagated through various spatial analyses, and (c) uncertainty arising from a mathematical representation of the spatial analysis. Each spatial analysis has its own mathematical model to describe its mechanism. It is, therefore, impossible to obtain a generic uncertainty model for all spatial analyses. In this study, uncertainty models for vector buffer analysis, for vector overlay analysis, for point-in-polygon query, and for line simplification have been proposed, in order to provide uncertainty measures for the associated analyses. Uncertainty in vector buffering is due to uncertainty of the spatial data itself and uncertainty of the buffer width. Current uncertainty models for vector buffering are analysed and are found to be oversimplified. More complete uncertainty models for the process, therefore, are proposed in which three uncertainty measures are defined: discrepancy, error of commission, and error of omission. These uncertainty measures can show the uncertainty in the analysis in different situations. In vector overlay, uncertainty of original spatial features leads to two main uncertainty problems: silver polygons and uncertain overlaid polygons. Some current uncertainty models for the overlay propose some methods to eliminate silver polygons regarclmg tile ratio between an area anu a perimeter or tnese poiygons systematically. Some assess uncertainty of an area measurement of the overlaid polygons. They are most likely to make an assumption that there is no correlation among points of original polygons. Considering the limitations of the current uncertainty models, we propose more complete uncertainty models for the overlay. A set of uncertainty measures is derived to describe uncertainty of overlaid polygon's measurements: variances of the polygon' perimeter, area and gravity canter point. hi addition, a covariance matrix and an uncertainty interval for the overlaid polygon are proposed to describe its overall uncertainty. These uncertainty measures can assess the uncertainty in the vector overlay to various GIS applications. Uncertainty in point-in-polygon query is caused by uncertainty of an original point and an original polygon. Existing methods provide solutions for several special cases only. We propose uncertainty models by considering the following two points: (a) error ellipse should be used to describe uncertainty of a point rather than error circle; and (b) uncertainty of polygon's points should be auto-correlated and cross- correlated. In the proposed models, a probability of an uncertain point inside an uncertain polygon is defined and estimated. The models proposed in this study aims to relax the assumption in previous research and provide a more general uncertainty analysis for point-in-polygon query. Current uncertainty models for line simplification are able to quantify uncertainty of the simplified line in a special case where the original line is free from uncertainty. The uncertainty of the initial line always exists; it is likely appropriate to consider an effect of the uncertainty of the original line on uncertainty of a simplified line. In order to overcome the problem of the current uncertainty model, we propose uncertainty models in a case where the uncertainty of the initial line exists and classify the uncertainty in line simplification into three types: propagated uncertainty, model uncertainty and overall processing uncertainty. Uncertainty measures for each uncertainty types can assess the uncertainty in line simplification in different situations. These uncertainty measures are potentially used to determine an optimal weed threshold ot the Douglas-Peucker line simplitication algontnm sudn tuat tue simplified line satisfies a predefined acceptable level of accuracy. The significances of this research lie on two aspects: (a) contributing to the development of GIS by providing uncertainty analyses for vector-based spatial processes and analyses, and (b) contributing to the applications of GIS by providing data quality indices for GIS users. The first aspect can be exhibited in our theoretical uncertainty models while the second one can be demonstrated in our examples. Users can thus much efficiently decide the fitness of spatial data to their GIS applications according to the uncertainty level.