[AMR] Finished update

electives/amr/parts/04_vision/03_mapping.tex

@@ -30,4 +30,14 @@ $l(o_j | \vec{x}_{R, 1 : k}, \vec{z}_{1 : k})$ =
 \shade{gray}{In 3D} 3D voxel $j$ as signed dist. $s$ and weight $w$, update:
 $\displaystyle s_k = \frac{w_{k - 1} s_{k - 1} + \tilde{s}_k}{w_{k - 1} + 1}$ with $w_k = \min(w_{\max}, w_{k - 1} + 1)$
 
-\bi{Impl.} Using HashTables or octree
+\bi{Implementation} Using Hash maps or octree (dense grid inefficient)
+
+
+\subsubsection{Iterative Closest Point}
+Build \textit{correspondences}: associate all live scan points $l_i$ to closest map points $m_i$. Error term:
+$\vec{e} = \vec{T}_{W L_l L_l} m_i - {_W}\vec{l}_i$.
+Minimize this via Gauss-Newton, then re-associate, iterate.
+
+\bi{Photometric}: $u_{KF} = \pi(\mat{T}_{WC_{KF}}^{-1} \mat{T}_{WC_l} \pi^{-1}(\vec{u}_{KF}, \mat{D}_{KF}[\vec{u}_{KF}]))$,
+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.