Information Technology Reference
In-Depth Information
Box 4.3
Two-dimensional smoothing
In some prints in this topic the pixel maps have been smoothed by sev-
eral passes of a binomial filter. In one dimension this can be written as
(1
and dissipates the intensity of a pixel with a value of 1 by
the following intensities after the first five passes:
1
4
,
/
4
,
1
/
2
,
1
/
4
)
1
2
,
1
4
1
16
,
1
4
,
3
8
,
1
4
,
1
16
1
64
,
3
32
,
15
64
,
5
16
,
15
64
,
3
32
,
1
64
1
256
,
1
32
,
7
64
,
23
128
,
35
128
,
23
128
,
7
64
,
1
32
,
1
256
1
1024
,
5
512
,
45
1024
,
5
128
,
95
512
,
29
128
,
95
512
,
5
128
,
45
1024
,
5
512
,
1
1024
The two-dimensional version of this filter is given by the following matrix
(after Tobler, 1969):
1
16
,
1
8
,
1
16
1
8
,
1
4
,
1
8
1
16
,
1
8
,
1
16
After approximately ten passes this filter is equivalent to the effect of a
normal kernel with variance
n
/4 (where
n
is the number of passes). This is
one of the simplest and most elegant forms of spatial smoothing. It is also,
interestingly, reversible (although this is only practical for low numbers of
passes). Its inverse could theoretically be used to sharpen an image.
and faulted. The pictures produced show the clear divisions between the sectors
and strong geographical patterns. These underlie many of the images already
presented and many of those still to be seen.
It may appear odd today to see maps in which transport and banking are put
within the same category. However, in the 1980s they were just seen as different
parts of the general business and domestic support infrastructure, mundane, run-
of-the-mill, industries. Later on banking came to be categorised separately and
seen as an activity that could somehow make money in its own right, not simply
by providing some basic services. This had many great adverse consequences.
Search WWH ::
Custom Search