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values stored in a rectangular grid or raster, each element of which is the average elevation of the ground area represented by that element or cell of the grid. This representation of terrain height variation is known as a digital elevation model or DEM.

In the same way, variations in geology in a study region are stored in raster format as a set of labels. Each cell in the data array is given a numeric label that is linked to a description. For example, pixels with the label ‘1’ may be described as ‘carboniferous limestone’ while pixels given the label ‘2’ might be described as ‘Silurian grit’. In this book, we are concerned with spatial data (specifically, remotely sensed images) that are represented in terms of rectangular rasters.

In the examples given in the preceding paragraphs, each cell of the raster stores either a physical value (such as elevation in metres above a given datum) or a label (such as ‘1’ or ‘2’, indicating rock types such as granite and basalt). In practice, rasters (and particular raster data sets containing images for display) are generally stored in the form of integer rather than floating-point numbers, in order to conserve storage space. Thus, a DEM may be represented in terms of integers in the range 0–255, with each integer value representing a range of land surface elevations. The idea is similar to the use of a key in a printed map in which elevation is generally shown in shades of green and brown, with the map key showing the relationship between these hues and specific elevation ranges. In the same way, the values 0–255 contained in the DEM are connected to a range of real elevation values by the use of a table rather than a key. The table, known as a lookup table or LUT, allows the user to determine the actual range of elevations denoted by a particular label, such as 215. In some applications, the physical elevation value is required (for instance, if slope angle is to be calculated). Other questions can be answered by using the counts or labels directly. If label ‘18’ is used to represent land with a surface elevation between 200 and 205 metres, then the locations of such areas can be achieved by searching the raster for all values of 18 rather than converting the raster labels back to physical values and searching for cells holding numbers in the range 200–205.

Remotely sensed images are stored and manipulated in raster form. Each element of the raster is known as a pixel, and the value contained in any pixel location is simply a quantised count or a label, rather than a physical value. For some applications, such as pattern recognition, these counts can be used directly as we are interested in inter-pixel similarities and differences. In other applications, such as sea-surface temperature determination, the pixel counts must be converted to physical values of radiance or reflectance, with corrections applied for such factors as sensor calibration changes and atmospheric influences. The range of quantised counts used in a raster representation of an image ranges from 0–255 (8-bit representation, for images derived from sensors such as Landsat ETM+ and SPOT

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