Interpolate a function according to an image

Question

I have in this image 3 "lines".

I would like to interpulate 3 functions from the data in the picture something like the second picture,

any ideas?

Answer 1

First I'll assume you have a mapping of color to intensity. You really want to work with the intensity as a grayscale image.

Use a blurring function to reduce the noise in the image and help make the output continuous.

Use a vertical difference to find the line. Where the difference switches from positive to negative is the place to put your line.