Jiro Doke has a tool (GRABIT) on File Exchange that allows you to pick points along the curve of a jpeg and then import them to ML. You could start there. You could use those points, fit them and/or interpolate them to get your 100 points along the curve.
If you wanted to go and do it yourself, you could take the image and turn it into a logical matrix of ones and zeros based on color. Then you could use region properties to find your line and get the indices. From the indices, you could then pull out the x and y coordinates according to your axes scale.
