MATLAB: Get transformation matrix from 3D points

matrixtransoformations

I have two plots of 3D reconstruction of a cup from 2 points of view. I need to find the transformation matrix that rotates the cup from the position of plot1 to the position of plot2. I fixed 3 point in plot1 (p1,p2,p3) with their respective coordinates and manually found the same point in plot2 (t1,t2,t3) with the transformed coordinate. I collected p1,p2,p3 in matrix P and t1,t2,t3 in matrix T, then I simply divided T/P=M. To check if I did good I tried to do p1*M hoping to find t1, but unfortunately I didn't succeed.

What should I do? Thanks

Best Answer

You should use more than 3 points to get better noise/error-resistance. Also, if your transformation is a rotation/translation, you need to constrain M to be of this form. This can be done with ABSOR ( Download ),

   reg=absor(P,T)

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The point is being plotted at right position. Try rotating the plot to make sure the point is at right position

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You can use this equations:

T=[4:4:24]';
P=[1e-4;2.5e-4;6e-4;1e-3;1.6e-3;2.25e-3];
plot(T,P,'o')
n=length(P);
A=[ones(n,1) T T.^2];
C=inv(A'*A)*A'*P;
P2=C(1)+C(2)*T+C(3)*T.^2;
hold on
plot(T,P2)

Best Answer

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