I'd like to brighten one of my own images for printing purposes, using a program I made.
When I use the formula: pixelBrightness^0.6 to brighten an image (0.6 being an example, and where pixelBrightness is in the normalized range 0..1), I find the very dark colours (black or near black) contrast too much with the somewhat dark colours. This is standard gamma correction.
Mathematically this makes sense, because the (b^0.6) curve 'hugs' the left wall for a bit on the graph, and only eases out half way through. See here to show what I mean. However, unfortunately, this makes the near blacks too 'contrasty'. I want the very beginning of the curve to be more like 20-30 degrees off from pure vertical.
Is there a simple formula (e.g: like pixelBrightness^0.6) which is better than gamma correction for my purposes? After the two points (start (0,0) and end (1,1)) have been defined, I preferably want a single degree of freedom to determine how 'curvy' (for want of a better word please?) the curve is (i.e.: how dissimilar to a line it is). So bezier curves (with their two degrees of freedom) are possibly out.