Transformations - Spatial Mathematics: Theory and Practice through Mapping - page 74

to the 4th power, or 16 values, would be available, and the resulting image
would have less radiometric resolution. A Landsat band is typically 8-bit
data, while a GeoEye IKONOS band is typically 11-bit data and therefore has
a higher radiometric resolution.
To select an appropriate spatial resolution, just as when considering other
spatial data for use, there is no perfect solution. One guideline is to choose a
resolution that is a factor of ten times finer than the size of the features you
need to identify. For example, if you want to visually delineate features with
a minimum size (referred to as the “minimum mapping unit”) of one square
kilometer (1 kilometer × 1 kilometer on each side, which is 1,000,000 square
meters, or 1000-meter resolution), a 1000/10, or 100-meter spatial resolution
is probably sufficient. To identify tree crowns that are three meters by three
meters in size, you would need to select a one meter or finer resolution. A
mathematical relationship exists between the map scale and the image reso-
lution. The rule is to divide the denominator of the map scale by 1000 to
get the detectable size in meters. The resolution is one half of this amount.
“Of course the cartographer fudges. He makes things which are too small to
detect much larger on the map because of their importance. But this cannot
be done for everything so that most features less than resolution size get left
off the map. This is why the spatial resolution is so critical” (Tobler, 1987,
1988).
To determine an appropriate mapping scale from a known spatial resolution,
use the following formula: Map Scale = Raster resolution (in meters) × 2 × 1000.
The number “2” in this equation is the minimum number of pixels required
to detect something. Thus, if you have an image of 1-meter resolution, you
can detect features at a map scale of 1:2000 using this formula: 1 × 2 × 1000.
The spatial resolution needed to detect features at a map scale of 1:50,000 is
approximately 25-meter [50000/ (1000*2)] resolution. This may be helpful if
you need to acquire satellite imagery to digitize vector data layers against, or
you already have imagery and need to know the scale of map in which it can
be used.
3.4.4 Determining if a data set is fit for use
Fundamental to the effective integration of geography and mathematics is
how to determine whether a data set is fit for use in addressing a problem
or issue. Five measures of accuracy exist that should be considered when
determining whether the spatial data are fit for one's own use. The first is
positional accuracy: How close are the locations of the objects to their cor-
responding true locations in the real world? Will this be sufficient for your
needs? The second is attribute accuracy: How close are the attributes to their
true values? The third, logical consistency, asks such questions as: If you used
this data set with other data sets, will its spatial characteristics and attributes
cause strange juxtapositions or illogical associations, such as a road that is
also a canal? Does every area have a label point? Is the data set consistent with