In ArcGIS 10, users can define the neighborhood in the [Focal statistics][1] 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?**


  [1]: http://resources.arcgis.com/en/help/main/10.1/index.html#//009z000000qs000000