Rigid transformation matrix units of measure?

[adrianom]

I have a rigid transformation matrix generated after using the ICP registration between two different point clouds. When visualizing the shift between the non-registered and registered point clouds, it is obvious that there wasn't much of a shift (at least in the x and y coordinates). However, when looking at the transformation matrix, the translation vector is very large which leads to my main question. What units does the matrix use? I'd except the matrix to use the same units as my point cloud (which would be meters in my case). I am assuming there is some information I am missing about how transformation matrices work in CloudCompare.

The matrix generated:
0.999282360077 -0.002026880626 -0.037824779749 428.433746337891
-0.001172434655 0.996433913708 -0.084369190037 783.407348632813
0.037860892713 0.084352985024 0.995716392994 -15207.101562500000
0.000000000000 0.000000000000 0.000000000000 1.000000000000

I attached a picture of my point clouds before and after registration. Not the best I could provide, but it should be enough to see that not much of a shift occurred in comparison to what the matrix says.

[daniel]

It's probably because the coordinates are quite large, and there's a small rotation here. As the 'translation' part is applied after the rotation (which is implicitly applied about the origin (0, 0, 0)), the translation is also a correction factor to cope with the de-centering of the cloud after the rotation.

[adrianom]

Thanks for the reply! So the rotation vector rotates the point cloud based the origin point (0, 0, 0), which would in turn make the translation vector larger? Is this correct? I was trying to determine if it would be possible to take the transformation matrix generated and apply it to a shapefile, though I am starting to think it is more difficult than I thought.

[adrianom]

Another question. My rotation is pretty small in my example, no? Assuming it is small, it would still make that big of a difference to the translation vector? Thanks in advance.

[daniel]

If the coordinates are large, yes!