Non Linear Remapping of the Pixel Values Suppose you take a photo of a beautiful scene of mountains and a lake. The representation devotes half of the scale between black and white to the bright surface of the lake, and the other half to the subtle shadings of the mountains. Is it possible to change the mapping so that only ¼ of the scale is devoted to the lake's colors, and ¾ to the mountains shades? If so, how would you do it?
Yes, using a non-linear mapping function on the intensity. Let us for the moment suppose you have a grayscale image (because of the words "black and white", "shadings"), with luminance $0\leq p_{i,j} &lt;1$. 

The piecewise linear mapping: $f( p_{i,j}) = \frac{p_{i,j}}{2}$ if $p_{i,j}&lt;\frac{1}{2}$, and  $f( p_{i,j}) = \frac{3}{2} (p_{i,j}-\frac{1}{2})+\frac{1}{4}$ if $p_{i,j}\geq\frac{1}{2}$ can do the job. 

This is a simple example of "Non-linear Contrast Enhancement". If that works for you, you can try with smoother functions.