Find out the optimal points (best fitted points) using optimization technique based on contour plot

I have data set such as attached figure (true contour).

This data have no function (just only have value).

The thing what I want to do is that find the best points to represent the true contour.

For example, I find 10 best fitted points and interpolate it. Then, I want to compare interpolated contour with true contour which is similar each other.

To do this, I would like to apply the optimization technique such as coordinate descent method (steepest descent method).

Could you guys let me know how to find the best fitted points using optimization technique (coordinate descent etc.) in matlab.

Thank you.