How to scale f(x) when covariance of observation is not Identity?

[zheng rong]

Hi All,

I am using ceres-solver to solving bundle-adjustment problem.
Today I read the "covariance estimation" part in API reference and read the following paragraph:

So, if it is the case that the observations being fitted to have a covariance matrix not equal to identity, then it is the user’s responsibility that the corresponding cost functions are correctly scaled, e.g. in the above case the cost function for this problem should evaluate S−1/2f(x) instead of just f(x), where S−1/2 is the inverse square root of the covariance matrix S.

1. Does this means that scaling cost function is necessary even I don't use the covariance estimation?
2. How to do the scaling? scale the residual in functor structure?

Any help would be greatly appreciated.

Thanks,

Zheng

[Sameer Agarwal]

if you are not using a covariance, then there is nothing to do. have a look at simple_bundle_adjuster.cc in the example code.

you can scaled the residuals in the functor, or you can scale it using a loss function.

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[Zheng Rong]

Hi Sameer,

Got it!
I am going to use covariance estimation to evaluate the quality of the solution.

Thank you very much!

Zheng

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