9 - MAP ALGEBRA, SURFACE DERIVATIVES AND SPATIAL PROCESSES

Summary

Introduction: point and spatial operations

In this chapter we introduce a number of point and spatial operations that can be performed on continuous field data. We begin with the use of map algebra, before moving on to the calculation of derivatives (e.g. slope and aspect) and spatial filtering (e.g. smoothing and edge detection), all of which are widely used by archaeologists. In the final section we introduce more specialised techniques that have archaeological potential.

Map algebra is a point operation, whereas the other techniques discussed in this chapter are spatial operations. Point operations compute the new attribute value of a location with coordinates (x, y) from the attribute values in other maps at the same location (x, y), (Fig. 9.1b). In contrast, spatial operations compute the new attribute value of a location from the attribute values in the same map, but at other locations – those in the neighbourhood (Fig. 9.1a). The neighbourhood used in a spatial operation may or may not be spatially contiguous. For example, slope is usually calculated using the elevation values in a neighbourhood comprising the four or eight map cells immediately adjacent to the location in question (see below), but we saw in Chapter 6 how inverse distance weighting interpolates elevation values from some number of nearest spot heights, irrespective of how far away those spot heights actually are.