how to detrend data in multiple dimensions

Hey all,

I am stuck on a detrending data problem. I have the following matrix Z:

    [X,Y] = meshgrid(-2:.2:2);
    Z = X .* exp(-X.^2 - Y.^2) + 0.1*X+0.2*Y;
    surf(X,Y,Z)

Which consists of function X .* exp(-X.^2 - Y.^2) plus a plane 0.1*X+0.2*Y. Now I want to detrend matrix Z such that only the first function remains. Basically I need to fit a non curved plane trough Z(x,y) and then subtract that from Z(x,y).

In 1d that is easy using detrend(Z) but if I put a matrix in detrend() it will detrend all columns separately.

Any ideas on how to detrend in 2d?

[Takfarinas]

Try this file exchange function which is a 2d equivalent of the detrend function: https://uk.mathworks.com/matlabcentral/fileexchange/33192-flatten-a-data-in-2d/content/detrend_2d.m

Answer 1

[Star Strider]

For a relatively simple solution, this comes close to completely detrending your surface:

[X,Y] = meshgrid(-2:.2:2);
Z = X .* exp(-X.^2 - Y.^2) + 0.1*X+0.2*Y;

B = [ones(size(X(:))) X(:) Y(:)]\Z(:);

Zdm = ones(size(X))*B(1) + B(2)*X + B(3)*Y;                         % Z-Detrending Matrix

figure(1)
surfc(X,Y,Z)
grid on

figure(2)
surfc(X,Y,Z-Zdm)
grid on