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In ArcGIS 10, users can define the neighborhood in the Focal statistics tool. The moving window shape can be set to any of the following: Wedge, annulus, circle, rectangle, irregular, and weight. For example purposes, let's assume we want to calculate the mean tree canopy area from a binary classified canopy raster (i.e. 0 = no canopy and 1 = canopy present) at 1 m spatial resolution. Given this example:

Are there any rules of thumb to determine which moving window shape should be used?

Once you determine the moving window shape, is there way to quantitatively determine the optimal neighborhood settings, or is this entirely subjective?

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I'm not really sure of the correct answer, and I'm curious to see what answers people will post. But, since tree canopies are, in general, roughly circular, then it seems reasonable that a circle would be appropriate. Maybe even a square, but probably not a wedge or an annulus. –  Fezter Dec 17 '12 at 23:41
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The neighborhood shape is not typically chosen based on a feature's shape, @Fezter, but based on what kind of analysis is intended and how it will be interpreted. For instance, to create a summary of all landcover to the northeast of each point, you would need to use a southwest-pointing wedge terminating at the center of the neighborhood. Annuli are used to summarize conditions at various buffer distances from each point. A square differs from a circle by being closely tied to the coordinate system (making it a somewhat artificial (but handy) shape), whereas the circle is not so tied. –  whuber Dec 18 '12 at 8:08
    
@whuber, that makes sense. Thanks for the info. –  Fezter Dec 18 '12 at 9:02
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I would always visualise the data, look for trends then then make sure that your moving window does not align with any of them. For this reason a circle often makes sense.

To take your tree canopy example. If your trees are arranged in rows in a plantation, a rectangle oriented with the rows would be a bad idea .. unless you are interested to capture the row effect.

I would also try more than one to establish the sensitivity of the test to the shape used.

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