Direct sparse odometry
Variable
| Variable |
Formula |
Description |
JpJdF |
\(\begin{bmatrix} (\frac{\partial r_{ji}}{\partial \boldsymbol{\xi}_{ji}})^T\frac{\partial r_{ji}}{\partial \rho_{i}} \\ (\frac{\partial r_{ji}}{\partial \begin{bmatrix} -e^{a_{ji}} \\ -b_{ji}\end{bmatrix}})^{T}\frac{\partial r_{ji}}{\partial \rho_{i}} \end{bmatrix}\) |
|
Function
void fixLinearizationF()
/** \brief Fix a point's residual */
void fixLinearizationF(EnergyFunctional* ef);
- This function is usually called when we want to remove some point, so we need to fix the residual (not update it anymore).
- The formula to compute the residual is \(r_{ji} = r_{ji}^{0} + \begin{bmatrix} \frac{\partial r_{ji}}{\partial \mathbf{p}_{j}} & \frac{\partial r_{ji}}{\partial \mathbf{a}_{ji}}\end{bmatrix} \begin{bmatrix}\delta{\mathbf{p}_{j}} \\ \delta{\mathbf{a}_{ji}}\end{bmatrix}\), where
\[\delta \mathbf{p}_{j} = \begin{bmatrix}
\frac{\partial \mathbf{p}_{j}}{\partial \mathbf{C}} & \frac{\partial \mathbf{p}_{j}}{\partial \boldsymbol{\xi}_{ji}} & \frac{\partial \mathbf{p}_{j}}{\partial \rho_{i}}
\end{bmatrix}
\begin{bmatrix}
\delta \mathbf{C} \\
\delta \boldsymbol{\xi}_{ji} \\
\delta \rho_{i}
\end{bmatrix}\]
\[\delta{\boldsymbol{\xi}_{ji}} = \begin{bmatrix} \frac{\partial \boldsymbol{\xi}_{ji}}{\partial \boldsymbol{\xi}_{iw}} & \frac{\partial \boldsymbol{\xi}_{ji}}{\partial \boldsymbol{\xi}_{jw}}\end{bmatrix} \begin{bmatrix}\delta{\boldsymbol{\xi}_{iw}} \\ \delta{\boldsymbol{\xi}_{jw}}\end{bmatrix}\]
\[\delta{\mathbf{a}_{ji}} = \begin{bmatrix} \frac{\partial \mathbf{a}_{ji}}{\partial \mathbf{a}_{i}} & \frac{\partial \mathbf{a}_{ji}}{\partial \mathbf{a}_{j}}\end{bmatrix}\begin{bmatrix} \delta{\mathbf{a}_{i}} \\ \delta{\mathbf{a}_{j}}\end{bmatrix}\]
