Doubt about the jacobian of the reprojection residual w.r.t. the control points
Thanks again for your work, personally it's being very helpful to understand better several concepts.
Reading section: 6.2. Camera-IMU Calibration I have the following doubt:
If the reprojection residuals are defined as:
\mathbf{r}_p(u) = \pi\left(T^{-1}_{ic}T_{wi}(u)^{-1}\mathbf{x} \right) - \hat{\mathbf{p}}
and knowing that the jacobian derived at Section 5.2. correspond to the matrix logarithm of the rotation matrix being interpolated:
\frac{\partial \boldsymbol{\rho}(u)}{\partial R_{i+j}} = \frac{\partial \log R(u)}{\partial R_{i+j}}
How is this jacobian included in the jacobian of the reprojection residuals?
I'm confused because using chain rule I get:
\frac{\partial \mathbf{r}_p(u)}{\partial R_{i+j}} = \frac{\partial \mathbf{r}_p(u)}{\partial R_{wi}(u)}\frac{\partial R_{wi}(u)}{\partial R_{i+j}}
Thereby the matrix logarithm does not appear in it, so I am struggling to see how is it possible to include \frac{\partial \log R(u)}{\partial R_{i+j}}
in the optimization.
Thanks in advance!
Edited by Javier Tirado