Jacobians with Local Parameterizations

[Edward Vadim]

Hi All,

I'm starting to use ceres solver, I just have a quick question about local parameterizations.  When computing the analytical Jacobians of the residual terms, what do I need to provide to Ceres?   The Jacobian with respect to the local parameterization parameters, or the Jacobian with respect to the "global" or ambient parameters?

For example, suppose I'm optimization over a rotation represented by a 3x3 rotation matrix.  Do I supply the Jacobian with respect to the three local parameters of the rotation matrix, or the Jacobain with respect to the "global" 9 rotation matrix elements?

Thanks for your help

[Sameer Agarwal]

jacobian w.r.t the global parameterization.

and a LocalParameterization object associated with the corresponding parameter block.

ceres will take care of composing the two.

--
You received this message because you are subscribed to the Google Groups "Ceres Solver" group.
To unsubscribe from this group and stop receiving emails from it, send an email to ceres-solver...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/ceres-solver/07459fdd-7fff-4ecd-a273-1814812df990%40googlegroups.com.
For more options, visit https://groups.google.com/d/optout.

[Edward Vadim]

Thanks for your quick reply Sameer!

One follow up question.  Is the composition of the Jacobians you're describing the one performed in the function

LocalParameterization::MultiplyByJacobian?

where in that function, it composes the jacobian wrt to the global parameters, and the jacobian of the boxplus operation, resulting in the jacobian wrt the local parameterization? 

[Sameer Agarwal]

Arun,

That happens inside residual_block.cc. We compute the two jacobian matrices and multiply them.

Sameer

To view this discussion on the web visit https://groups.google.com/d/msgid/ceres-solver/0c0dfe21-7da9-446d-8f42-d69e205a1a5f%40googlegroups.com.

[Tanner Schmidt]

Hi Sameer,

Are there any plans to add the ability to compute Jacobians directly in the local space without the need for two Jacobians? For a lot of SE(3) applications there are very simple analytical Jacobians in the local se(3) space, so in these cases it seems unnecessary and inefficient to apply the chain rule.

- Tanner

[Sameer Agarwal]

No there is no plan to do that right now, because the API changes required to do that are too intrusive.

Sameer

To view this discussion on the web visit https://groups.google.com/d/msgid/ceres-solver/93f2e205-3a23-4816-8aa1-5b241d0c90c3%40googlegroups.com.