MATLAB: Problems fitting a plane using cftool

Question

I'm having an issue fitting a plane to a 3d data set using the cftool. I have lots of these data sets, and every once and a while, the plane fit it gives me is clearly way off, and I have no idea why.

Here is the piece of code I'm using, its pretty basic:

    X = data(:,1);
    Y = data(:,2);
    Z = data(:,3);
    fitobject = fit( [ X, Y], Z, fittype('poly11'));
    Fitted_plane = [ fitobject.p00 , fitobject.p10 , fitobject.p01 ];

And to give you an idea of what the fit looks like:

http://imgur.com/yOVSmmp

http://imgur.com/BGe2SXV

And the fit is clearly not correct, but I cannot for the life of me figure out how to fix it. This happens for maybe 1/10 of the fits I'm doing, and I was wondering if maybe there is a problem with the toolbox? I can definitely send out the data set, I just didnt want to post the whole thing here.

Thanks in advance.

Answer 1

From your plots, it looks like the 3D plane containing your data could be of the form

 a*X + b*Y + c*Z = d

but with c=0. Obviously, when c=0, this cannot be rewritten as a function Z(X,Y), as you are trying to do.

The following is a way to fit the plane without CFTOOL and it works for all plane orientations,

 m=mean(data,1);
 [~,~,v]=svd(  bsxfun(@minus, data, m) ,0);
 abc=v(:,end); %plane normal vector
 d=dot(abc,m); %distance from origin
 a=abc(1); b=abc(2); c=abc(3);