In my experience, the sigmoid tends to stay in the limits of the first
schema in your pdf. A very small deviation has a huge impact so that
if you are not looking for strange-looking results, you tend to stay
close to the diagonal, especially with jpegs where doing too much
correction triggers banding. For example, here are the 3 curves I used
on o1 for lowering contrast, increasing contrast, and the third
D-shaped curve which gives the results closest to faux-bracketing.

2012/12/21, JohnPW <[email protected]>:
> I mean that as the contrast factor increases, the curve trends to be more
> like a step function (where all pixels to the left of the midpoint become
> black and all to the right become white.)
> Attached a horrible pdf drawing (sorry I had no handy vector drawing tool
> and had to draw with the trackpad too!)
>
> I assume the inflection point of the sigmoid curve only shifts along the
> diagonal as the contrast factor is changed. Is this correct? If so, at 100%
>
> the invlection point is at the white point and the slope of the curve
> coming out of the white point is is very steep (essentially straight down.
> If instead, the inflection point stays at the same level (only moves left
> and right,) it would be even steeper. No, I guess this is impossible as the
>
> curve would emerge from the middle of the right side of the graph (and the
> white point would not be anchored at the top right.) Yup, I'm just letting
> my thoughts wander here.  :-)
>
> Anyway, with such a steep curve coming out of the white point, surely this
> would effectively blow out the highest of the highlights a good way down
> the scale, wouldn't it? Which would make details in the extremes disappear.
>
> John
>
>
> On Thursday, December 20, 2012 3:47:51 PM UTC-6, Frederic Da Vitoria wrote:
>>
>> 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] <javascript:>>
>>
>>> 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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-- 
Frederic Da Vitoria
(davitof)

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

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