Nearest Neighbor Interpolated data

If you are give a matrix,zi, generated using griddata where:

x=5 unknown values;
y=5 unknown values;
xq=linspace(0,25,26);
yq=linspace(0,25,26);
z=[1:5];
zi=gridata(x,y,z,xq,yq,'nearest');

How do you approximate/calculate the original 5 (x,y) points?

Answer 1

[Image Analyst]

There is no unique solution. There could be millions of x and y that could give the shape. Just look at the example in the help. x and y (the blue dots on their colored wire grid surface) could be anywhere along any of the wires, and you'd still have the same surface. You can't tell where they came from just by having the surface.

[Jahangir]

http://www.therightstuff.amatyc.org/voronoidiagrams.pdf page 3