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[AMR] Fix errors pointed out to me

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janishutz
2026-08-09 08:30:17 +02:00
parent cc5f111813
commit a8b3bd7b20
24 changed files with 50 additions and 47 deletions
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electives/amr/parts/04_vision/00_keypoints.tex
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@@ -20,8 +20,8 @@ $\mat{M} = \sum_{x, y \in P}
\shade{gray}{Blob Detection} ($I$ is the image)
\bi{Laplacian of Gaussian} (LoG): $L = g(x, y, t) \cdot I(x, y)$.
Then apply Laplacian Operator $\nabla_\text{norm}^2 L = t\left( \frac{\partial^2 L}{\partial x^2} + \frac{\partial L}{\partial y^2} \right)$
\bi{Laplacian of Gaussian} (LoG): $L = g(x, y, t) * I(x, y)$.
Then apply Laplacian Operator $\nabla_\text{norm}^2 L = t\left( \frac{\partial^2 L}{\partial x^2} + \frac{\partial^2 L}{\partial y^2} \right)$
\bi{Diff. of Gaussians} (DoG): $\Delta L = L(x, y, t) - L(x, y, kt)$
electives/amr/parts/04_vision/01_bootstrapping.tex
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@@ -14,7 +14,7 @@ Find good point in 3D. Fast sol: \bi{Midpoint Method}:
\bi{1} Find p. along ray w/ min. dist (Lin. Least Squares)
\[
\vec{\lambda}\! =\! [\lambda_1 \; \lambda_2]^\top\! = \! \argmin{} ||({_W}\vec{t}_{C_2} + \lambda_2 {_W}\vec{e}_2) - ({_W}\vec{t}_{C_1} + \lambda_1 {_W}\vec{e}_2)||^2
\vec{\lambda}\! =\! [\lambda_1 \; \lambda_2]^\top\! = \! \argmin{} ||({_W}\vec{t}_{C_2} + \lambda_2 {_W}\vec{e}_2) - ({_W}\vec{t}_{C_1} + \lambda_1 {_W}\vec{e}_1)||^2
\]
\rmvspace
@@ -38,4 +38,4 @@ Find good point in 3D. Fast sol: \bi{Midpoint Method}:
\quad C_i \text{ cam}
\]
\bi{3} Pick midp. ${_W}\vec{t}_P \! = \! 0.5(\tau_1 \! + \! \tau_2)$; $\tau_n \! = \! {_W}\vec{t}_{C_n} + \lambda_n{_W}\vec{e}_n)$
\bi{3} Pick midp. ${_W}\vec{t}_P \! = \! 0.5(\tau_1 \! + \! \tau_2)$; $\tau_n \! = \! {_W}\vec{t}_{C_n} + \lambda_n {_W}\vec{e}_n$
electives/amr/parts/04_vision/03_mapping.tex
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@@ -35,9 +35,9 @@ $\displaystyle s_k = \frac{w_{k - 1} s_{k - 1} + \tilde{s}_k}{w_{k - 1} + 1}$ wi
\subsubsection{Iterative Closest Point}
Build \textit{correspondences}: associate all live scan points $l_i$ to closest map points $m_i$. Error term:
$\vec{e} = \vec{T}_{W L_l L_l} m_i - {_W}\vec{l}_i$.
$\vec{e} = \vec{T}_{W L_l} {_{L_l}}m_i - {_W}\vec{l}_i$.
Minimize this via Gauss-Newton, then re-associate, iterate.
\bi{Photometric}: $u_{KF} = \pi(\mat{T}_{WC_{KF}}^{-1} \mat{T}_{WC_l} \pi^{-1}(\vec{u}_{KF}, \mat{D}_{KF}[\vec{u}_{KF}]))$,
\bi{Photometric}: $u_{L} = \pi(\mat{T}_{WC_{KF}}^{-1} \mat{T}_{WC_l} \pi^{-1}(\vec{u}_{KF}, \mat{D}_{KF}[\vec{u}_{KF}]))$,
error term $\vec{e} = \mat{I}_{KF}[\vec{u}_{KF}] - \mat{I}_L[\vec{u}_{L}]$,
where all subscript $L$ are from live image, all subscript $KF$ key frame.