[EM] interpolated median

rob brown rob at karmatics.com
Wed Dec 21 22:58:34 PST 2005


I mentioned I'd dig up the way I have done a median with interpolated values
to "smooth" out the quantized values.

Since I'm of the "picture paints a thousand words" persuasion, I think you
can figure out what I'm getting at from this image as opposed to a long
description:

http://karmatics.com/stuff/median.gif

This shows getting a median of the values 3,3,3,3,4,4,4,4,4,5,5,5,6,6,7.
The top image is a graphical representation of a standard median.  The lower
image shows how we can draw lines from the midpoints of each group of
identical values, and project the overall midpoint onto that resulting curve
to get our "interpolated median".  The purple square is the result, 4.25.

To do this programmatically is fairly trivial.

-r
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