Intersection between surface and planes

Hi,

I have an image and I want to select a specific part on it. The part of interest on the image is a valley. My idea in order to extract it is to make intersections between planes - in all directions - and the surface of the image. Then, I will conserve the plane whose intersection values are minimal.

This is the 3D representation of the image :

My question : how can I make intersection with that surface which I defined as follows ?

x = 1:size(image,1);
y = 1:size(image,2);
[X,Y] = meshgrid(x,y);
surf(X,Y,image');

Thanks for any help.