Preliminary findings
I am pretty sure that sigmoidization is dead as a general purpose resampling method.
The simple version of what works better is to use mapping through a gamma space (with a matching pair of -gamma commands, like
Code: Select all
-gamma 3 -distort Resize 800% -gamma .33333333333333
) to reduce the most offensive of the halos, namely the dark ones, varying gamma until the light and dark halos are equally offensive

Converting whatever into linear light before passing things through "gamma resizing" is almost certainly a very good idea. For example
Code: Select all
-set colorspace sRGB -colorspace RGB -gamma 3 -distort Resize 800% -gamma .33333333333333 -colorspace sRGB
if both your input image and your output image are sRGB.
(So far, I have tested with XYZ instead of RGB using a different software program.)
Generally, gamma 1 leads to offensive dark halos with filters that have negative lobes. On the other hand, large gammas lead to exaggerated light halos and, possibly, to color artifacts, esp. if a non-HDRI version of ImageMagick is used.
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I have developed a more robust way of doing the above, which I am investigating as time permits.