and http://www.cs.dartmouth.edu/farid/downloads/tutorials/fip.pdf.
The limit of ScaledSigmoidal as a->0 is the identity, but a=0 gives a
division by zero. This is fixed above by exiting immediately when
- contrast is small. This would appear to be safe because the series
- expansion of the logistic sigmoidal function around x=b is
- 1/2-a*(b-x)/4+... so that s(1)-s(0) is about a/4. (With tanh, it's a/2.)
+ contrast is small, leaving the image (or colormap) unmodified. This
+ appears to be safe because the series expansion of the logistic
+ sigmoidal function around x=b is 1/2-a*(b-x)/4+... so that the key
+ denominator s(1)-s(0) is about a/4 (a/2 with tanh).
*/
#define ScaledSigmoidal(a,b,x) ( \
(Sigmoidal((a),(b),(x))-Sigmoidal((a),(b),0.0)) / \