Geography Reference
In-Depth Information
comparison of grids for dif erent time periods. If digital elevation models (DEMs, as
illustrated in Figure 10.5), for example, are available for two time periods, one could
be subtracted from the other to assess rates of erosion. However, it is, of course, neces-
sary to ensure that data sets compared in this way are compatible (e.g. they have the
same spatial resolution and the data were collected with instruments which make
measurements with a comparable level of accuracy). Matrix algebra is a key tool in
multicriteria decision analysis (see Section 5.3).
Image processing
10.3
h e analysis of images has, in comparison to GIS, a long history. h e need to remove
'noise' from raster grids (or images; e.g. remotely sensed images) or to identify features
contained in images has led to the development of a wide range of sophisticated tools.
Tools for spatial segmentation and classii cation are widely used to deal in dif erent
ways with the grouping together of pixels that have, in some respect, similar charac-
teristics. Such methods are outside the remit of this account. h is section begins by
dei ning dif erent classes of grid operators. Grid operators can be divided into four
groups (Chou, 1997):
•
local functions: work on every single cell (a cell is treated as an individual
object)
focal functions: derive a new value based on the neighbourhood of a pixel
•
•
zonal functions: work on each group of cells of identical values
•
global functions: work on a cell based on the data in the entire grid.
h e addition of two grids is a local function since the values in overlapping indi-
vidual cells are combined. Moving window functions (such as spatial i lters, described
in the following section) are examples of focal operators. Zonal operators deal with
values that fall within particular zones, and an example is given below. A common
example of a global function is the computing of Euclidean (straight line) distance
from one or more source locations to all cells in a grid (see Section 4.2).
With zonal operators, values from one input grid that fall within zones indicated
by a second input grid are combined in some way. h e zonal mean is illustrated in
Figure 10.3. h e zonal minimum or maximum, for example, could be computed
instead. Note that the boundaries of the individual cells in the zones layer and the
zonal means layer are not shown—the values in both cases would be written to all cell
locations indicated in the values grid. As an example, for zone 1: (45 + 44 + 44 + 43 +
42 + 43 + 42)/7 = 43.286.
h ere are many potential applications areas for zonal operations, for example aver-
age erosion in construction zones. Any application which makes use of zones repre-
sented as rasters might make use of operators like those just described.
h e focus of the following sections is spatial i lters for image smoothing or
enhancing edges of features.
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