I have a problem where I have a binary image stack which I process with regionprops3. I can recover the principle axes directions and scaling from this function but when I plot them the output does not appear to be related to the ellipsoid at all. I have tried plotting both the rows and columns of the eigenvector matrix from regionprops3 but nothing seems to work.
As an example:
%%Example Code
x = 0:1:100
y = 0:1:100
z = 0:1:100
dx = .1
[X,Y,Z] = meshgrid(x,y,z);
%Define an ellipse
ell = 1*(X-50).^2 + 100*(Y-50).^2 + 3*(Z-50).^2 + 3*(Z-50).*(X-50) < 500 ;
T = regionprops3(ell ,'PrincipalAxisLength', 'Orientation' , 'centroid','EigenVectors','EigenValues')
c=T.Centroid
%Principle axes ?
axis_mat= ( (T.EigenVectors{1}) *(diag( (T.PrincipalAxisLength) ) ) )
%plot principle axis vectors
figure(1)
quiver3(c(1),c(2) ,c(3) , axis_mat(1,1),axis_mat(2,1),axis_mat(3,1))
hold on
quiver3(c(1),c(2) ,c(3), axis_mat(1,2),axis_mat(2,2),axis_mat(3,2))
quiver3(c(1),c(2) ,c(3), axis_mat(1,3),axis_mat(2,3),axis_mat(3 ,3))
xlim( [0,100] )
ylim( [0,100 ] )
zlim( [0,100 ] )
xlabel('X')
ylabel('Y' )
zlabel('Z')
%plot ellipsoid
isosurface(X,Y,Z,(ell),1 - 1e-6)
alpha(.2)
