Apart from the "and a sigmoidal (s) shape between perfectly straight and
infinitely steep (essentially a step function)" (my English is not good
enough to understand your meaning, so I can't say if this is correct or
not), yes, this is correct. In the Gimp curves filter, the sigmoidal curve
could be inflected as a printed "S", in which case the results are
accentuated (by increasing the dynamic range in the middle tones and losing
details in the extremes), or like a rounded "Z" and this results
subjectively in a loss of contrast but should improve the details in the
extremes.

2012/12/20 JohnPW <[email protected]>

> I'm glad this is stimulating discussion. This is the kind of thing I enjoy
> reading here (especially when somebody can explain things they know.)
>
> Anyway, I'd like to figure out some things about sigmoidal contrast. Is a
> "sigmoidal contrast" simply an approach to setting the contrast curve we
> all know from photography and digital imaging? In other words, is it a
> subset of  possible contrast curves that could be uses which follow a
> sigmoidal shape as described in the formula?
> From what I can understand, this means it is a typical contrast curve but:
> • with the endpoints locked down at blackest black and and whitest white
> • with a single inflection point somewhere in the middle
> • and a sigmoidal (s) shape  between perfectly straight and infinitely
> steep (essentially a step function)
> • presumably this function always has a positive slope and the 's' shape
> is never inverted into a backward 's' shape.
> Are my assumptions correct?
>
>
>
> On Wednesday, December 19, 2012 5:09:02 PM UTC-6, Bruno Postle wrote:
>>
>> On Wed 19-Dec-2012 at 12:13 +0100, Frederic Da Vitoria wrote:
>> >
>> > But now that I think of it more closely, I understand that
>> > JohnPW's question is still unanswered and that my answers
>> > completely missed the point. I expect the faux-bracketing to keep
>> > the lightest parts of the darkest exposure and the darkest parts
>> > of the lightest exposure.
>>
>> I'm not entirely sure what you are trying to do, but Hugin will
>> extract 'bracketed' exposures from any photo.  By default it uses a
>> 'sigmoidal' camera response curve to map the data to linear space,
>> multiply and then map back again - This curve will be quite accurate
>> if you have calibrated your camera photometric parameters.
>>
>> All you have to do is load your photo and increment Eev for the
>> input or output.
>>
>> You can then enfuse these brackets, but this process only really
>> makes sense if you start with 16bit per channel data created from
>> RAW.
>>
>> --
>> Bruno
>>
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-- 
Frederic Da Vitoria
(davitof)

Membre de l'April - « promouvoir et défendre le logiciel libre » -
http://www.april.org

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