History for Sigmoid filter

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I found the following text at:

http://public.kitware.com/pipermail/insight-users/2007-January/020625.html

It is very helpful in understanding how to set alpha and beta values for the sigmoid filter.


Page 150 has a nice illustration of the parameters.  The Beta 
value can be thought of the offset on the pixel value that you are 
trying to isolate.  E.g., if the object you are trying to isolate is at 
a pixel intensity above 150, you would choose a Beta value that is 
around that value.  The Alpha value can be thought of as the scaling or 
variance of the sigmoid.  Lower alpha values will make the pixel range 
of your intensity sharper.   There are quite a few examples in the Level 
Set  chapter on  the use of the sigmoid function.  Here it is applied to 
the  mapping of the  gradient of the image.  In this case you would want 
to choose a Beta value near  the intensity of the gradient that you are 
trying to isolate.  E.g., the gradient you are trying to find occurs at 
an intensity of 5 or more.  Perhaps you would notice that most gradients 
that have an intensity of less than 2 are noise/nonsense objects.  You 
might choose a Beta value that is near your gradient, but would account 
for some variability, say, 4.  Your alpha value would decide how much of 
the noise you would want to include in your transformation.  Smaller 
alpha values (0.25, 0.5) would zero out most of the noise, but it might 
make your actual signal thicker and not specific enough.  Conversely, 
larger alpha values (e.g. 3+) might have a smoother signal but might 
include more noise.  Negative alpha values can be thought of as using a 
positive alpha value and then inverting the image.