Is there a standard sigmoidal function used to increase the contrast in a gray level bitmap?
Currently I am using the following. This would be applied to gray levels represented at values between 0 and 1 inclusive.
static double ContrastCurve(double val, double k = 1)
{
Func<double,double> logistic_func = (double x) => 1.0 / (1.0 + Math.Exp(-k * (x - 0.5)));
var low = logistic_func(0);
var high = logistic_func(1);
var range = high - low;
var value = logistic_func(val);
return (value - low) / range;
}
This is the logistic function applied to a value between 0 and 1 with the output normalized so that the output is also in [0...1]. This function works but it is completely arbitrary, something I just made up, so the k param has no official name or meaning in image processing literature and so forth.
If there is a function that is standard I would prefer that but haven't found anything that seems definitive. Code such as this link seems as ad hoc to me.
As Mark Setchell's comment notes, ImageMagick uses the following function citing "Fundamentals of Image Processing", Hany Farid:
g(u) = 1 / [1 + exp(-α*u + β)]
scaled such that for domain [0..1] its range is [0..1].
This is essentially a two parameter version of the function defined in the code in the question above i.e. the code in the question implements the same function but makes the substitution α = k and β = -k/2 which yields a one parameter function f where f(0.5) = 0.5 when scaled such that f(0) = 0 and f(1) = 1.