question about ObjectPoseGraph.h

[zpwithme]

hello, in function linearizeOplus() ObjectPoseGraph.h. Does the variable _jacobianOplusXj lack to multiply _measurement.inverse().adj() ?

[JingwenWang95]

Hi @zpwithme, actually for _jacobianOplusXj you don't need to multiply with the adjoint. Here the error residual is defined as log(Tij^-1 * Ti * Tj^-1). Since we apply the perturbation to the left, to compute _jacobianOplusXi, you will have to get rid of the part on its left, which is T_ij^-1. And to do so you need to multiply the adjoint of Tij^-1 to the right of the expression, which is why the adjoint term exists in _jacobianOplusXi. But for _jacobianOplusXj, you can simply inverse the whole expression inside the bracket and negate the log value, which will make Tj already appear on the left.

For more detailed derivation you can refer to this thesis (Appendix B.6): https://www.doc.ic.ac.uk/~ajd/Publications/Strasdat-H-2012-PhD-Thesis.pdf