How to fit largest ellipsoid for 3d data points such that it covers all points?
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Hi, I have search a lot for ellipsoid fit to 3d data and come up with some answer but I want some improvement in my method such that it covers all the data points. My code is here.
Y=data; % data in non-principle coordinate
X = data;
X= bsxfun(@minus,X,oldmu); % mean-centered data
[pc val] = eig(X'*X );
nC = X*pc; % data in principle coordinate
a2=(max(nC(:,1))-min(nC(:,1)))/2; %range of data in X
b2=(max(nC(:,2))-min(nC(:,2)))/2; %range of data in Y
c2=(max(nC(:,3))-min(nC(:,3)))/2; %range of data in Z
[x, y, z] = ellipsoid(0,0,0,a2,b2,c2,40);
% fit ellipsoid in principle coordinate
tt=[x(:) y(:) z(:)]*inv(pc);%ellipsoid in non-principle coordinate
% plot ellipsoid in non-principle coordinate
hSurface=surf(nx+oldmu(1), ny+oldmu(2), nz+oldmu(3), 'FaceColor','r','EdgeColor','none','FaceAlpha',0.6);
%plot data in non-principle coordinate
The data file is here.
Image Analyst on 8 Aug 2017
I think it's pretty difficult. John did the same thing in 2-D here http://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects If it were easy he'd probably have done it already.