Tone curve and its calculation

Question

I am trying to calculate the tone curve to compliment my histogram. I am running into some confusion on what the tone curve actually is and how it would be calculated.

From what I have searched, the tone curve shows the original (input) value along the x axis against the resulting (output) value along the y axis.

The tone curve for the original image is a straight line from the bottom left to the bottom right.

Am i correct in thinking along the x axis is just the histogram of the image, when the image is adjusted then the tone curve for each x position is the difference between the original histogram and the current histogram?

So to calculate the tone curve:

• Calculate original histogram
• Calculate histogram for adjusted image
• Calculate difference between histograms for each value 0-255
• Plot the difference + or - the original tone curve line (from bottom left to top right)

Answer 1

A tone curve (or more generally a response curve) is essentially an input/output function which tells you how each value in X is mapped to Y. I think what you are looking for is what is called Histogram Matching. That being said, histogram to histogram might not give the exact curve, since there would be more than one possible way to reach a value.