alignment using Procrustes again

Hello, I am rewriting the question. Procrustes analysis is a method to align one shape against another . Say I have a 3D matrix which looks like:- A=[ 1 2 100 2 3 200]; and B =[3 4 566 4 7 899]; Now, My question is I have got 2 mesh-grids by interpolating A and B using Z = griddata(xi,yi,zi,X,Y,'cubic') where xi,yi and zi are the coordinates from the above matrices. And X,Y are 1:100 coordinates for setting up the mesh grid. .The problem is that I want to align perfectly A with B using the following code: [d Z tr] = procrustes(C,B,'scaling',true);

          axis([ 0 100 0 100 0 100]);
          figure(1),plot3( B(:,1),B(:,2),B(:,3),'rx');
          figure(2),plot3( C(:,1),C(:,2),C(:,3),'gx');
          figure(3),plot3( Z(:,1),Z(:,2),Z(:,3),'bx');
The problem is that when finally I AM PLOTTING Z it is not at all showing the perfect alignment. Any help would be appreciable.

[Matt J]

I find the rewritten question much more confusing than your previous version.

• Firstly, there is nothing 3D-looking about A and B. They are both vectors. Are they supposed to have 3 columns [xi(:), yi(:), zi(:)]?
• Secondly, the new information about the two mesh grids doesn't seem to play a role. You're registering A to B, right? The output of griddata does not provide any input to the registration.
• Thirdly, you haven't told us what C is and you're using Z to represent both the output of griddata() and the output of procrustes()

Answer 1

[Matt J]

Aside from my comments above, what you said about GRIDDATA suggests that the zi data in A and the zi data in B might be from totally different functions of the (xi,yi) data in A and the (xi,yi,) data in B respectively.

Therefore, you should probably be doing 2D registration between the (xi,yi) coordinates, not 3D registration between the (xi,yi,zi) coordinates. So maybe the following is what you want:

   [d Z tr] = procrustes(A([1,2],:),B([1,2],:),'scaling',true);