Another useful class of maps expands the grayscale in one particular range. The prototype might look like this:

The slope of the flatter segments

Here, the values around 't' are stretched and the others are correspondingly compressed. A restriction will be imposed on the stretched section: it must be positioned so that the compressed sections have the same slope, this makes the arithmetic a bit more complicated. Here, it's easier to work directly with the gray values in the range [0..255]. We will use a range of 10 on either side of 't' and expand to 40 on either side. If 'p' is the height of the graph @ x=t the condition of equal slope is:

The mapping function is:

Try changing 't' to numbers between [10..245] and see how the mapping function adjusts.

Now, experiment with expanding the scale in different ranges of the camera image by changing the definition of 't' below. For example, you'll find that t=20 brings out the details in the coat and glove, while t=182 stretches the values in the taller building in background.

Plug in SmathFile