Lecture 14:More Raster and Surface Analysis in

Spatial Analyst

------Using GIS--Introduction to GIS

Lecture notes by Austin Troy, University of Vermont

©2005 Austin Troy

Converting vector to raster

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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

Converting vector to raster

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Or you may be converting based on a variable, like land use

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Proximity

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Can use raster distance functions to create zones based on proximity to features; here, each zone is defined by the highway that is closest

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Distance Measurement

Can create distance grids from any vector feature based on straight line

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Distance MeasurementCan also weight distance based on friction factors, like slope

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Density Functions

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•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

Density Functions

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•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

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

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Neighborhood Statistics• In Arc GIS,

neighborhood statistics command allows you to specify statistic:– Min, max, mean, standard

deviation, range, sum, variety

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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

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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.

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Low Pass filteringUsually 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.

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©2005 Austin Troy

High Pass filteringOne 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.

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Why do we care about this?• Low pass filtering: filtering out anomalies

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Bathymetry mass points: sunken structures

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Why do we care about this?• After turning into raster grid

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We see sudden anomaly in grid

Say we wanted to “average” that anomaly out

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Why do we care about this?• Try a low-pass filter of 5 cells

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We can still see those anomalies but they look more “natural” now

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Why do we care about this?• Try a low-pass filter of 25 cells

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The anomalies have been “smoothed out” but at a cost

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What about high pass filters?• Say we wanted to isolate where the wreck was

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All areas of sudden change, including our wrecks, have been isolated

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Neighborhood Statistics• Example, using a DEM showing elevation

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Neighborhood StatisticsA low pass filter of the DEM done by taking the mean values for a

3x3 cell neighborhood: notice it’s hardly different

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DEM Low pass

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Neighborhood StatisticsBut if we take the mean for a 10 unit square neighborhood…

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Notice how much smoother it is; note also how much less detail there is in this low pass filter

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Neighborhood StatisticsNow, here’s one with a 20 unit square neighborhood

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Neighborhood StatisticsHere’s one with a 10 unit radius circular neighborhood

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The only difference from 20 unit square is that edges are more rounded

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Neighborhood StatisticsHere’s one with a 20 wide x 5 tall unit rectangular neighborhood

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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

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Neighborhood StatisticsHere’s what it looks like the other way: 20 tall x 5 wide

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Here note better feature definition for features along the horizontal axis, with more detail to features facing down or up

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Neighborhood StatisticsIn this high-pass filter the mean is subtracted from the original

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It represents all the local variance that is left over after taking the means for a 3 meter square neighborhood

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Neighborhood StatisticsWe do this using the map calculator

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Neighborhood StatisticsIf 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 taking a mean with a larger neighborhood

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Dark areas represent things like cliffs and steep canyons

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Neighborhood StatisticsUsing 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

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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.

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Neighborhood Statistics• Here is the same function with 8x8 cell neighborhood.

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Here, the coarser resolution due to the larger neighborhood makes it so that slope rates seem to vary more gradually over space

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Neighborhood StatisticsHere’s what it looks like with a circular 4 unit radius neighborhood

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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

Neighborhood StatisticsLater 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

Introduction to GIS