How can I do a homogeneous transform of data to a different coordinate system?

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Nicolai Sanders 2017-3-8

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评论： GAldos 2018-7-26

Hello

I have two 3D data arrays, A and B, that contain spatial measurement data of the same real world object. A and B are not the same size. There are XYZ coordinate systems attached to both arrays. In array B the object is rotated, scaled and translated relative to the data in array A. I do have the transformation matrix for the affine transformation between the two coordinate systems, thanks to fiduciary points in the object which show up in the data.

I would like to interpolate the data in the B array into the coordinate system for the A array, but I am unsure how to do this?

The end result would be a new array, C, that contains the interpolated data from the B array, but with the same size as the A array.

Thank you for your help.

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Answer 1

Nicolai Sanders 2017-3-10

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https://ww2.mathworks.cn/matlabcentral/answers/328737-how-can-i-do-a-homogeneous-transform-of-data-to-a-different-coordinate-system#answer_258156

在 MATLAB Online 中打开

To answer my own question: I ended up using imwarp when i realized it can handle 3D arrays.

I defined spatial references for the A and B coordinate systems with

 RA = imref3d(size(A),[min(xA), max(xA)],[min(yA), max(yA)],[min(zA), max(zA)]);
 RB = imref3d(size(B),[min(xB), max(xB)],[min(yB), max(yB)],[min(zB), max(zB)]);

Then i defined an affine transformation AT with my transformation matrix TM

AT=affine3d(TM);

Now i could transform B into the coordinate system of A with

[C,RC]=imwarp(B,RB,AT,'OutputView',RA);

On a sidenote, i acquired the transformation matrix with absor

 [rp,Bfit,ErrorStats]=absor(PA,PB,'DoScale',1);
 TM=rp.M.';

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GAldos 2018-7-26

Thanks for posting your solution! Just wondering why did you take the transpose of the rotation matrix to get the transformation matrix with absor? i.e. TM=rp.M.' ?

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