Re: Seeking Clarification of Procedure for Averaging Images


Gerald Bakker
 

On Thu, Jul 9, 2020 at 12:01 AM, Rick Gordon wrote:
Based on the maxim that "the median is affected by outliers and skewed data than the mean, and is usually the preferred measure of central tendency when the distribution is not symmetrical" <https://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-+measures+of+central+tendency#:~:text=In%20a%20distribution%20with%20an,value%20is%20the%20middle%20value.&text=Advantage%20of%20the%20median%3A,the%20distribution%20is%20not%20symmetrical.>, that brings up an interesting note: as to whether doing this with Median as opposed to Mean would mitigate the damage of "one bad apple spoiling the apple cart."
That's an interesting thought for sure. I couldn't resist trying this out on one of the exercise images, the Panama photo, the only for which I had downloaded 5 versions. Well, the result surprised me, as the two procedures give quite different results. Different color ("mean" version somewhat more saturated) and different weight ("median" version a bit lighter).

I don't want to draw many conclusions from just one example, but I noticed something that may be typical. Zooming in to 100%, the "mean" version looks smoother, whereas the "median" shows a bit more color noise and is slightly more splotchy. I think the reason is that averaging pixel values has a smoothing effect. Taking the median however implies that one pixel may come from version A and a nearby pixel from version B, causing a more rough appearance. The more differences between the base versions, the stronger this effect.
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Gerald Bakker
http://geraldbakker.nl

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