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Jul
15
comment Functional equations of (S-shape?) curves
Thanks again for that suggestion. However, will it overcome the "going out of range" and "not soft behavior" problems, which are being considered in Rahul's answer below?
Jul
15
comment Functional equations of (S-shape?) curves
And thanks for the Hermite suggestions.
Jul
15
comment Functional equations of (S-shape?) curves
Thanks, the idea seems to be nice, although the so called "overshooting" is a major problem. I want the curve to behave as it behaves in Curves tool in image processing software (Gimp, Photoshop etc.) - generally speaking it behaves in a far softer way. Here is another example (with x and y in [0,255]), on a verge of acceptance: ubuntuone.com/2GtSMuciatWC99P1EhsMWS - note that the curve leans gently to the edges.
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Jul
15
comment Functional equations of (S-shape?) curves
@Rahul well, I don't have any specified needs except those listed above. I'm looking for the simplest possible idea (the 2 last options I mentioned don't sound friendly to me) - to express the function and to calculate its values. Its application involves image processing; not sure yet how I will implement it - I consider storing precalculated values and calculating them on the fly as well.
Jul
15
comment Functional equations of (S-shape?) curves
@Leonid the curves should be used for image processing so I guess it would be better to avoid corners? Anyway, thanks for suggestion, that's pretty simple idea.
Jul
15
comment Functional equations of (S-shape?) curves
Yes, I'm looking for curves for image processing. Thanks for the suggestion, I will take a closer look at it!
Jul
15
comment Functional equations of (S-shape?) curves
That's right. It shouldn't go outside the range [0,1] for any x from [0,1].
Jul
15
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Jul
15
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15
asked Functional equations of (S-shape?) curves