twist parametrization terminology / strange results when using pt2pl in filterreg about probreg

[cmatija]

No I mean the original c++ filterreg code by the authors

[neka-nat]

Hi @cmatija ,

Thank you for the some suggestions.
In my opinion, there are two methods when converting from a twist to a transformation matrix.
One is a linear approximation and the other is Rodrigues' rotation formula.

I think your first opinion is correct. In the function I made, the rotation is computed using Rodrigues' formula, but the translation is a linear approximation. So, as you say, I think it's better to make the translation also Rodrigues' formula.

In the second opinion, eq.5 uses the linear approximation. However, to improve accuracy I have replaced it with Rodrigues' formula.

Finally, regarding the results of pt2pl, in general, pt2pl doesn't work well for objects with many curved surfaces. And I also found it difficult to set the sigma2 parameter when using the pt2pl filterreg.
If a stable solution is not obtained when using ICP's pt2pl, it is considered to be difficult even for filterreg.

[neka-nat]

I also had a question that came up.
The definition of twist described in your link seems to relate to a robot joint, so is that the formula that can apply to the twist calculation in this case?

[cmatija]

I would think so. If you for instance look at the first chapter of 'An Invitation to 3-D Vision' by Ma et al. you will find the same formula.

That being said, I have also checked out the original code (which you probably did also) and they do it the same way, i.e. use Rodrigues formula for R but leave t untouched, so I guess I'm still missing something here.

[neka-nat]

Thank you for the good reference!
Is this the original code you're referring to?
https://github.com/sunglok/3dv_tutorial
I'll check it out as well.