DSO

DSO - EnergyFunctional

Posted by Tong on April 17, 2020

Direct sparse odometry

Variable Type Size Formula Description
nFrames int     Number of frames
adHost Mat88* nFrames x nFrames \(\begin{bmatrix} (\frac{\partial \boldsymbol{\xi}_{ji}}{\partial \boldsymbol{\xi}_{iw}})^{T} & \\ & (\frac{\partial \begin{bmatrix} -e^{a_{ji}} \\ -b_{ji}\end{bmatrix}}{\partial \mathbf{a}_{i}})^{T}\end{bmatrix} = \begin{bmatrix} (\frac{\partial \boldsymbol{\xi}_{ji}}{\partial \boldsymbol{\xi}_{iw}})^{T} & \\ & (\frac{\partial \mathbf{a}_{ji}}{\partial \mathbf{a}_{i}})^{T}\end{bmatrix}\) For a pair of frames (host, target), the corresponding index is (host id + target id * nFrames)
adTarget Mat88* nFrames x nFrames \(\begin{bmatrix} (\frac{\partial \boldsymbol{\xi}_{ji}}{\partial \boldsymbol{\xi}_{jw}})^{T} & \\ & (\frac{\partial \begin{bmatrix} -e^{a_{ji}} \\ -b_{ji}\end{bmatrix}}{\partial \mathbf{a}_{j}})^{T}\end{bmatrix}= \begin{bmatrix} (\frac{\partial \boldsymbol{\xi}_{ji}}{\partial \boldsymbol{\xi}_{jw}})^{T} & \\ & (\frac{\partial \mathbf{a}_{ji}}{\partial \mathbf{a}_{j}})^{T}\end{bmatrix}\)  
adHTdeltaF Mat18f* nFrames x nFrames \(\begin{bmatrix}\delta{\boldsymbol{\xi}_{ji}} & \delta{\mathbf{a}_{ji}} \end{bmatrix} = \begin{bmatrix}(\frac{\partial \boldsymbol{\xi}_{ji}}{\partial \boldsymbol{\xi}_{iw}} \delta{\boldsymbol{\xi}_{iw}})^{T} + (\frac{\partial \boldsymbol{\xi}_{ji}}{\partial \boldsymbol{\xi}_{jw}} \delta{\boldsymbol{\xi}_{jw}})^{T} & (\frac{\partial \mathbf{a}_{ji}}{\partial \mathbf{a}_{i}}\delta{\mathbf{a}_{i}})^{T} + (\frac{\partial \mathbf{a}_{ji}}{\partial \mathbf{a}_{j}}\delta{\mathbf{a}_{j}})^{T} \end{bmatrix}\) Increment of relative pose and relative photometric parameters