Computation of the translation synchronization about sghr HOT 3 CLOSED

Hi @qsisi ,
Sorry for the late reply and thanks for your interest!
In SGHR, the relative transformation aligns point cloud $P_j$ to point cloud $P_i$ , here $j>i$, i.e., $P_i = R_{ij} * P_j + t_{ij}$ s.t. $j>i$. (For consistence with FCGF/YOHO/SpinNet/GeoTrans.)
In LTS, the basic relative transformation is formulated as: $P_j = R_{ij} * P_i + t_{ij}$, s.t. $j>i$.
Thus, $R_{ij}^{LTS} = (R_{ij}^{SGHR})^T$ and $t_{ij}^{LTS} = -(R_{ij}^{SGHR})^T * t_{ij}^{SGHR}$.
Such a difference causes the differences of rotation and translation synchronization formulations. Specifically, for rotation synchronization, LTS uses $R_{ij}^T$ in its Eq.(1) while SGHR using $R_{ij}$ in Eq.(8).
For translation sychronization, I have not derived LTS‘s formulation carefully, but I believe it can be derived with the basic least square method or its variants: https://en.wikipedia.org/wiki/Least_squares, where the translation solution of SGHR comes from.

Yours,

from sghr.

Thanks for your prompt reply, I did notice the "inverse" relations on rotations between LTS and SGHR, but I still could not derive the translation synchronization of your implementation. So may I ask did the code scripts come from other code bases?

Thank you so much for your help.

from sghr.

Hi @qsisi,
Sorry for the late reply!
This code snippet is original and is implemented based on Linear Least Square Algorithm and the following formulas:

yours,

from sghr.