There are a number of tools for transcribing graphs from images. This post lists a few.
Doing that would get you a set of x,y vectors for each curve. You could interpolate from there.
I have a feeling that trying to do this automatically via image processing is going to be a complete mess. The jpg compression is going to mess up line extraction significantly enough that the close-packed sections are going to need to be manually transcribed anyway. Trying to extract the heatmap by relying on the colorbar is similarly defeated by the gross chroma distortion in the image. Anything extracted that way would be very noisy and likely distorted in ways that are less obvious than extracting the level curves.
If it were me, I'd probably try to use one of the digitizer webapps, or I'd throw it into a vector graphics program, trace it out with bezier curves, and then export each curve as an image, import that image into Matlab, and run [x,y]=find(thiscurve) or somesuch.
