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I need to explain why ArcGIS offers the function "standard deviation" when symbolizing rasters with the Stretch method.

The Standard Deviation is a measure of how spread out numbers are and is calculated by the square root of the Variance. The variance in the Squared differences from the mean and the "n" in the ArcGIS Setting refers to the population.

So what is really happening? Is ArcGIS replacing each Height value with a StdDev value calculated by neighbouring "n" pixels? That would mean the colours represent the average "spread" of heights and not the actual height values themselves.

Am I on the right track here?

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    If it works in a similar they than in programs I know it goes like in this example: - Average is 200 and std dev is 50 -> - After sdt dev stretch original pixel value 150 is mapped to 0 and value 250 is mapped to 255 - Other pixel values are mapped by linear interpolation. This stretch is a good guess for making any imagery visible on screen with a usable contrast. – user30184 Nov 25 '14 at 7:35
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If your values are Normally distributed then approximately 68%, 95% & 99.7% of the values lie within 1, 2 & 3 Standard Deviations respectively, see here, so if you are stretching your values of the colour map using SD(2) all of the values that are below 2.5% will be black and all over 97.5% will be white, (depending on your colour scale of course) - this will allow you to see the variation of the more common values without being swamped by the absolute max and min.

Say you are looking at a height map that includes structures and you have a single very high chimney and a single vary deep well included in the map, this might lead to a colour step of 50 ft when the rest of your structures are all in this range, SD will clip those two features allowing you to see the variation of the rest.

  • DEMs are also often of 16 bit or 32 bit type and the high end of scale is unused which makes DEM to appear all black without stretching. – user30184 Nov 25 '14 at 7:54
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    Please note however that for the reasons described here: gis.stackexchange.com/questions/123350/… the elevations in most DEMs are not normally distributed and therefore clipping the tails using a percentile method is generally more suited. – WhiteboxDev Nov 25 '14 at 14:45
  • @WhiteboxDev please also note that I gave elevations as as example & specifically mentioned that any SD based method is only really valid for normaly distributed data. – Steve Barnes Nov 25 '14 at 21:39
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    @SteveBarnes I know I just wanted to reiterate the fact that this is a condition that rarely if ever applies to DEMs. So the take-home message is, this is how the SD clipping method works but you probably shouldn't apply it to a DEM. You have the right answer and that's why I upvoted ;) – WhiteboxDev Nov 25 '14 at 21:48

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