Do you always want 0,0 and 1,1 on your curve? How many other points do you want to specify--just one?
Hi all, I am doing some tests about local/global contrast algorithms and need a simple equation to define an arbitrary S-shaped contrast curve. It's simple if the turning point is assumed to be (0.5, 0.5), but couldn't find a straight equation if the turning point has to be arbitrarily set.
These are the typical contrast curves I achieved for turning point in the middle (0.5, 0.5):
(http://www.guillermoluijk.com/misc/contrast.gif)
And the simple equations follow this rule:
y = x^2*2 for x<=0.5
y = 1-(1-x)^2*2 for x>0.5
I would like to be able to allocate the turning point to any (x,y) position and still have a smooth S-shaped curve where the slope is continuous on both sides of the turning point. If would like to keep the equation as simple and straightforward as possible, avoiding the use of splines or any other more complex math.
turning point — "point of inflection"
What is the advantage of having an entire curve, if one is only adjusting the value of the pixel relative to its neighborhood average? Perhaps I am just misinterpreting your figure: