Thank you for sharing the great work! I want to ask a question of the Gauss-Newton method used in your paper.
You used Gauss-Newton method in the 6D space of \xi. The assumption is that the residual is linearly varying around the current \xik. By \delta\xi = H^{-1}b, it is basically saying that \xi{k+1} = \delta\xi + \xi_k is locally the best point (derivative of the energy = 0). However, you didn't update \xi_k in this way, but updated it via exp(\delta\xi)exp(\xi_k) (Equation 2 in paper). However, this composition doesn't necessarily end up with the same SE(3) point (or se(3)) as the additive updating step.
My feeling is that there is a mismatch between the assumption of the Gauss-Newton method and your updating step. Could you provide more detailed reasoning about this?
Thank you for sharing the great work! I want to ask a question of the Gauss-Newton method used in your paper.
You used Gauss-Newton method in the 6D space of \xi. The assumption is that the residual is linearly varying around the current \xik. By \delta\xi = H^{-1}b, it is basically saying that \xi{k+1} = \delta\xi + \xi_k is locally the best point (derivative of the energy = 0). However, you didn't update \xi_k in this way, but updated it via exp(\delta\xi)exp(\xi_k) (Equation 2 in paper). However, this composition doesn't necessarily end up with the same SE(3) point (or se(3)) as the additive updating step.
My feeling is that there is a mismatch between the assumption of the Gauss-Newton method and your updating step. Could you provide more detailed reasoning about this?
Thank you very much!