Coherent point drift registration does not end up in global minimum

I am trying to perform a rigid cpd registration of two point sets (~500 points each). The point sets initially lie apart from each other. I preprocess the data by converting them to point cloud, downsampling and increasing the number of iterations and the tolerance parameter (as explained in the documentation of pcregistercpd). However, the registration ends up in a local minimum. Therefore, I figured I had to initially translate the point sets to the same origin. This lead to a better result, but still did not reach the global minimum (as I could tell with my eyes).

I now suspect that I also have to rotate the moving point set prior to registration. What else could be reasons for the registration not ending up in the global minimum? If prerotation can help, how can I perform it (I cannot use pctransform with rigid3d since rigid3d is only available from R2020a. I am using R2019a.).

Looking forward to your suggestions. Thank you!

[Qu Cao]

Chris, have you tried other registration methods, for example pcregisterndt?

https://www.mathworks.com/help/vision/ref/pcregisterndt.html