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------Using GIS-Introduction to GIS
Lecture 14:
More Raster and Surface Analysis in
Spatial Analyst
Lecture notes by Austin Troy, University of Vermont
------Using GIS-Introduction to GIS
Converting vector to raster
Can convert raster to
vector or vice versa.
When converting vector
to raster, must specify an
attribute field upon
which raster z values
will be based. When just
yes/no, must often create
a new field. Example:
protected areas
©2005 Austin Troy
------Using GIS-Introduction to GIS
Converting vector to raster
Or you may be converting based on a
variable, like land use
©2005 Austin Troy
------Using GIS-Introduction to GIS
Proximity
Can use raster distance functions to create zones based on proximity
to features; here, each zone is defined by the highway that is closest
©2005 Austin Troy
------Using GIS-Introduction to GIS
Distance Measurement
Can create
distance
grids from
any vector
feature
based on
straight line
©2005 Austin Troy
------Using GIS-Introduction to GIS
Distance Measurement
Can also
weight distance
based on
friction factors,
like slope
©2005 Austin Troy
Introduction to GIS
Density Functions
•We can also use sample points to map out density raster surfaces.
This need to require a z value in each, it can simply be based on the
abundance and distribution of points.
©2005 Austin Troy
Introduction to GIS
Density Functions
•These settings would give us a raster density surface, based just on
the abundance of points within a “kernel” or data frame. In this
case, a z value for each point is not necessary.
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
• From last lecture: this
is a “local” method of
summarizing raster
data within a
neighborhood by a
statistical measure, like
mean, stdv, min
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
• In Arc GIS,
neighborhood statistics
command allows you to
specify statistic:
– Min, max, mean, standard
deviation, range, sum,
variety
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
• Neighborhood statistics creates a new grid
layer with the neighborhood values
• This can be used to:
–
–
–
–
Simplify or “filter down” the features represented
Emphasize areas of sudden change in values
Look at rates of change
Look at these at different spatial scales
©2005 Austin Troy
Introduction to GIS
Neighborhood Filters
• Generating neighborhood means is similar to
RS technique called low pass filtering:
– Low pass filtering: takes “tonally rough”
surfaces, with abrupt changes in cell values, and
makes those values vary more smoothly.
• The opposite is called a high-pass filter.
– High pass filtering: emphasizes detailed, abrupt
changes in cell values, deemphasizes areas of
gradual change.
©2005 Austin Troy
Introduction to GIS
Low Pass filtering
Usually in low-pass filtering, the median is used instead, but the
concept is similar.
Low-pass filters emphasize overall, general trends at the expense of
local variability and detail.
It serves to smooth the data and remove statistical “noise” or
extreme values that occur in isolation or small patches.
While lose feature detail, different from changing resolution;
Resolution of cells stays the same.
The larger the neighborhood, the more you smooth, but the more
processing power it requires.
A circular neighborhood has the effect of rounding the edges of
features a little more.
©2005 Austin Troy
Introduction to GIS
High Pass filtering
One way of obtaining this is by subtracting a low pass
filtered layer from the original.
This serves to emphasize and highlight areas of tonal
roughness, or locations where values change abruptly
from cell to cell.
The result is to emphasize local detail at the expense of
regional, generalized trends.
Summarizing a neighborhood by standard deviation is
another form of high pass filter.
©2005 Austin Troy
Introduction to GIS
Why do we care about this?
• Low pass filtering: filtering out anomalies
Bathymetry mass points:
sunken structures
©2005 Austin Troy
Introduction to GIS
Why do we care about this?
• After turning into raster grid
We see sudden
anomaly in grid
Say we wanted to “average”
that anomaly out
©2005 Austin Troy
Introduction to GIS
Why do we care about this?
• Try a low-pass filter of 5 cells
We can still see those anomalies but
they look more “natural” now
©2005 Austin Troy
Introduction to GIS
Why do we care about this?
• Try a low-pass filter of 25 cells
The anomalies have been “smoothed
out” but at a cost
©2005 Austin Troy
Introduction to GIS
What about high pass filters?
• Say we wanted to isolate where the wreck was
All areas of sudden change, including
our wrecks, have been isolated
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
• Example, using a DEM showing elevation
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
A low pass filter of the DEM done by taking the mean values for a
3x3 cell neighborhood: notice it’s hardly different
DEM
Low pass
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
But if we take the mean for a 10 unit square neighborhood…
Notice how
much
smoother it
is; note also
how much
less detail
there is in
this low
pass filter
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
Now, here’s one with a 20 unit square neighborhood
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
Here’s one with a 10 unit radius circular neighborhood
The only
difference
from 20 unit
square is that
edges are
more rounded
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
Here’s one with a 20 wide x 5 tall unit rectangular neighborhood
Note how there is
more detail in the
vertical axis
(features facing left
and right) than in
the horizontal axis
(features facing
down and up); so
horizontal feature
detail is resampled
to a lower
resolution than
vertical feature
detail
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
Here’s what it looks like the other way: 20 tall x 5 wide
Here note
better feature
definition for
features along
the horizontal
axis, with
more detail to
features
facing down
or up
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
In this high-pass filter the mean is subtracted from the original
It represents
all the local
variance that
is left over
after taking
the means for
a 3 meter
square
neighborhood
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
We do this using the map calculator
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
If we do a high-pass filter by subtracting from the original
the means of a
20x 20 cell
neighborhood,
it looks
different
because more
local variance
was “thrown
away” when
Dark areas represent
taking a mean
things like cliffs and
with a larger
steep canyons
neighborhood
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
Using standard deviation is a form of high-pass filter because it is
looking at
local variation,
rather than
regional
trends. Here
we use 3x3
square
neighborhood
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
• Note how similar it looks to a slope map.
• This is because it is showing standard deviation, or normalized
variance, in spot heights, which is similar to a rate of change.
• Hence it is emphasizing local variability over regional trends.
• The resolution of the slope is quite high because it is sampling
only every nine cells.
• When we go to a larger neighborhood, by definition, the
resulting map is much less detailed because the standard
deviation of a large neighborhood changes little from cell to cell,
since so many of the same cells are shared in the neighborhood
of cell x,y and cell x,y+1.
• Look at the following as an example.
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
• Here is the same function with 8x8 cell neighborhood.
Here, the
coarser
resolution due
to the larger
neighborhood
makes it so
that slope rates
seem to vary
more gradually
over space
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
Here’s what it looks like with a circular 4 unit radius neighborhood
You can see
that an 8 unit
diameter
circle gives
slightly more
detail and fine
resolution
than an 8 unit
square (if you
look closely)
©2005 Austin Troy
Introduction to GIS
Neighborhood Statistics
Later on we’ll look at filters and remote sensing imagery, but here is
a brief example
of a low-pass
filter on an image
that has been
converted to a
grid. This can
help in
classifying land
use types
©2005 Austin Troy