This is the approach I would take assuming there is no software for it, basically you can extrapolate all the yellow points that are the same color, within a given area of pixels (tolerance).

So the steps would be,

1) import image into allegro
2) use a function that allows the user to click on that yellow line ( anywhere on it)
3) create another function that can check if there are contiguous points of the same color, basically it would check the perimeter of the point (based on tolerance,which means the number of square pixels around the point, I'd say 3 at the most), and save that coordinate into a vector. The function would need to keep track of directions that are found also. Like the first point would notice there are two directions to run across (if you choose the center of the yellow line as the starting point).
*You could ideally just figure out the coordinate of the left most yellow pixel and not worry about that though, I'd take that approach.

4) you created a vector that has the points extrapolated and you go into GNUplot and fit the thing with a polynomial. But you can just Google for a gnuplot polynomial fit and you'll find the formula.

I used The Gimp to make the image I attached, its a gif.
to make it
1) Import your image into The Gimp.
2) Zoom to about 200% under the view toolbar.
3) Under select toolbar use select by color. Shift+O.
4) Select the yellow line.
5) Once its highlighted, CTRL+C,and and paste as a new image or just press SHIFT+CTRL+V

and save as somename.gif

This should make it easier to extrapolate the coordinates cause now you should have a transparent gif.

EDIT: You need to find ImageMagick and download it, you can convert the gif I uploaded into a jpeg and follow these instructions