Peter F. Fisher

The pixel: a snare and a delusion

The pixel is an explicit feature of remotely-sensed imagery, and a primary concept of the raster GIS (Geographical Information System) which is the usual vehicle for integration. This Letter addresses the underlying spatial conceptualization of the pixel, which is the parallel of the grid cell in spatial analysis, and the regular grid in sampling. It is argued that integration of remote sensing and GIS can only possibly advance if we develop methods to address the conceptual short-comings of the pixel as a spatial entity, and stop pretending that it is a true geographical object. Three major strands of research which address this issue are highlighted, including mixture modelling, geostatistics and fuzzy classification.

Causes and consequences of error in digital elevation models

All digital data contain error and many are uncertain. Digital models of elevation surfaces consist of files containing large numbers of measurements representing the height of the surface of the earth, and therefore a proportion of those measurements are very likely to be subject to some level of error and uncertainty. The collection and handling of such data and their associated uncertainties has been a subject of considerable research, which has focused largely upon the description of the effects of interpolation and resolution uncertainties, as well as modelling the occurrence of errors. However, digital models of elevation derived from new technologies employing active methods of laser and radar ranging are becoming more widespread, and past research will need to be re-evaluated in the near future to accommodate such new data products. In this paper we review the source and nature of errors in digital models of elevation, and in the derivatives of such models. We examine the correction of errors and assessment of fitness for use, and finally we identify some priorities for future research.

Sorites paradox and vague geographies

Abstract The sorites paradox is ranked among the top five paradoxes of philosophy (Sainsbury, Paradoxes, 2nd ed., Cambridge University Press, Cambridge, 1995). It is simply stated as ‘what is a heap’. Deriving from the paradox is a definition of vagueness, which is contrary to the Boolean concept of the world implicit in much geographical teaching and thought, and the representation of geographical information in modern geographical information system. The argument of Sorites Paradox is suggested as a test of whether a concept is vague. If that concept is sorites susceptible, then it should be modelled as a vague concept, otherwise a Boolean model may be appropriate. The recognition of whether or not a particular concept is sorites susceptible does not have to influence the methods of analysis. It should merely inform the interpretation, and the investigator and reader should be aware that the outcome of the analysis is only one of a set of possible outcomes, which depends on how the vague concept is crispened. Furthermore, it is argued here that very many geographical phenomena (relations, objects and processes) can be shown to be sorites susceptible, and so vague, both generically and genetically. Vagueness can be addressed by multi-valued logic and applications of fuzzy set theory (the most common method of implementing multi-valued logic) to geography are reviewed. A formal recognition of vagueness in geographical phenomena is long overdue, and should be welcome in geographical analysis and, certainly, in geographical information systems.

Modelling the errors in areal interpolation between zonal systems by Monte Carlo simulation

Areal interpolation involves the transfer of data (often socioeconomic statistics and especially population data) from one zonation of a region to another, where the two zonations are geographically incompatible. This process is inevitably imprecise and is subject to a number of possible errors depending on the assumptions inherent in the methods used. Previous analysts have had only limited information with which to compare the results of interpolation and so assess the errors. In this paper a Monte Carlo simulation method based on modifiable areal units is employed. This allows multiple interpolations of population to be conducted from a single set of source zones to numerous sets of target zones. The properties of the full error distribution associated with a particular interpolation model can then be examined. The method based on dasymetric mapping consistently gave the highest accuracy of those tested, whereas the areal weighting method gave the lowest. More important than the results presented is the potential for future testing of other methods in increasingly complex situations.

Algorithm and implementation uncertainty in viewshed analysis

Abstract In most documentation of geographical information systems (GIS) it is very rare to find details of the algorithms used in the software, but alternative formulations of the same process may derive different results. In this research several alternatives in the design of viewshed algorithms are explored. Three major features of viewshed algorithms are examined: how elevations in the digital elevation model are inferred, how viewpoint and target are represented, and the mathematical formulation of the comparison. It is found that the second of these produces the greatest variability in the viewable area (up to 50 per cent over the mean viewable area), while the last gives the least. The same test data are run in a number of different GIS implementations of the viewshed operation, and smaller, but still considerable, variability in the viewable area is observed. The study highlights three issues: the need for standards and/or empirical benchmark datasets for GIS functions; the desirability of publica...

Improved Modeling of Elevation Error with Geostatistics

The elevations recorded within digital models are known to be fraught with errors of sampling, measurement and interpolation. Reporting of these errors according to spatial data standards makes several implicit and unacceptable assumptions about the error: it has no spatial distribution, and it is statistically stationary across a region, or even a nation. The approach explored in this paper employs actual elevations measured in ground and aerial survey at higher precision than the elevations in the DEM and recorded on standard paper maps. These high precision elevations are digitized and used to establish the real statistical and spatial distribution of the error. Direct measurements could also have been taken in the field by GPS or any other means of high precision data collection. These high precision elevations are subtracted from values stored in the DEM for approximately the same locations. The distribution of errors specific to the DEM can then be explored, and can be used in the geostatistical method of conditional stochastic simulation to derive alternative realizations of the error modeled and so of the DEM. Multiple versions of the derived products can also be determined. This paper compares the results of using different methods of error modeling. The best method, which gives widely implementable and defensible results, is that based on conditional stochastic simulation.

Assessing interpolation accuracy in elevation models

Methods that identify the spatial variation in elevation model accuracy and highlight relative variation are proposed. Visualization within the geographic resources analysis support system (GRASS) is used to identify the accuracy preserved in interpolation digital contour data to produce elevation models. The interpolation routines are inverse distance weighting, contour flood filling, simultaneous over-relaxation, and one-dimensional spline fitting. The results of the interpolation process are presented as colored contours, shaded relief maps, aspect maps, and products of Laplacian filtering, profile and plan convexity, and visualizing root mean square error methods.<<ETX>>

Multivariate texture¿based segmentation of remotely sensed imagery for extraction of objects and their uncertainty

In this study, a segmentation procedure is proposed, based on grey‐level and multivariate texture to extract spatial objects from an image scene. Object uncertainty was quantified to identify transitions zones of objects with indeterminate boundaries. The Local Binary Pattern (LBP) operator, modelling texture, was integrated into a hierarchical splitting segmentation to identify homogeneous texture regions in an image. We proposed a multivariate extension of the standard univariate LBP operator to describe colour texture. The paper is illustrated with two case studies. The first considers an image with a composite of texture regions. The two LBP operators provided good segmentation results on both grey‐scale and colour textures, depicted by accuracy values of 96% and 98%, respectively. The second case study involved segmentation of coastal land cover objects from a multi‐spectral Compact Airborne Spectral Imager (CASI) image, of a coastal area in the UK. Segmentation based on the univariate LBP measure provided unsatisfactory segmentation results from a single CASI band (70% accuracy). A multivariate LBP‐based segmentation of three CASI bands improved segmentation results considerably (77% accuracy). Uncertainty values for object building blocks provided valuable information for identification of object transition zones. We conclude that the (multivariate) LBP texture model in combination with a hierarchical splitting segmentation framework is suitable for identifying objects and for quantifying their uncertainty.

What is land cover

Much geographic information is an interpretation of reality and it is possible for multiple interpretations to coexist. This is unproblematic for the research community but, as the numbers of users increase through initiatives resulting in data integration on an unprecedented scale, such as E-science and GRID, issues of information meaning and conceptualisation become more important. We explore these issues through the mapping of land cover and the variety of conceptions of land-cover features that may be held by actors in the creation, distribution, and use of the information. Current metadata do not report the wider meaning of the information categories in terms of the decisions that were made and by whom in specifying class conceptualisations.

Landscape metrics with ecotones: pattern under uncertainty

Landscape metrics are in widespread use, but previous research has highlighted problems over scale and error in the reliability of the metric values. This paper explores the variation of metric values when it is hard to distinguish exactly where one land cover type changes into another; when the ecotone is not an abrupt transition, but has a spatial extent in its own right. The values of metrics are explored in a landscape classified, using satellite imagery and the fuzzy c-means classifier, into fuzzy sets so that every location has a degree of belonging to all classes. The result is that any ecotone can be characterised by a variety of metric values depending on the degree to which a location is in any particular land cover class. The values recorded show some similarities, however, to those for an interpretation of the same landscape with abrupt changes, but the nature of that similarity varies unpredictably between metrics and classes. This analysis provides a limited degree of reassurance for those using metric analysis where the boundaries may have spatial extent, but much further work is required to establish an improved description of metrics under this condition.