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koide3 / small_gicp

Efficient and parallel algorithms for point cloud registration [C++, Python]
MIT License
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Question of Jacobian of ICP #56

Closed Wuqiqi123 closed 1 month ago

Wuqiqi123 commented 1 month ago

Thanks for your great works of ICP. I have fa few question about Jacobian matrix of ICP and PointToPlaneICP

$$ e_i=p_i-Rq_i-t. $$

$$ \frac{\partial e_i}{\partial R}=Rq_i^\wedge,\quad\frac{\partial e_i}{\partial t}=-I. $$

https://github.com/koide3/small_gicp/blob/5c6f13cfc94c1ab129d32b8554c8bd712dc76346/include/small_gicp/factors/icp_factor.hpp#L43-L45

Why the translation part of Jacobian is $-R$ , rather than $-I$ (Also the PointToPlaneICP)?

Wuqiqi123 commented 1 month ago

Sorry just find the https://github.com/koide3/small_gicp/issues/53