[AMR] More fixes

electives/amr/parts/04_vision/00_keypoints.tex

@@ -1,11 +1,14 @@
 \subsection{Keypoints}
-\bi{Corner det.} $SSD(\Delta_x, \Delta_y) \approx [\Delta_x \; \Delta_y] \mat{M} [\Delta_x \; \Delta_y]^\top$
-with $\mat{M} = \mat{R}^\top \text{diag}(\lambda_1, \lambda_2) \mat{R}$; $\lambda_i$ E.V. of $M$;
-$\mat{R} = \det(M) - \kappa \cdot \text{trace}(M)^2 = \lambda_1\lambda_2 - \kappa(\lambda_1 + \lambda_2)^2$;
-$\displaystyle M = \sum_{x, y \in P} \begin{bmatrix}
-        I_x^2   & I_x I_y \\
-        I_x I_y & I_y^2
-    \end{bmatrix}$
+\bi{Corner det.} $SSD(\Delta x, \Delta y) \approx [\Delta_x \; \Delta_y] \mat{M} [\Delta_x \; \Delta_y]^\top$
+with $\mat{M} = \mat{R}^\top \text{diag}(\lambda_1, \lambda_2) \mat{R}$; $\lambda_i$ E.V. of $M$; $\kappa$ const 0.04-0.15;
+$\mat{R} = \det(M) - \kappa \cdot \text{TR}(M)^2 = \lambda_1\lambda_2 - \kappa(\lambda_1 + \lambda_2)^2$;\\
+$M = \sum_{x, y \in P}
+    {\scriptsize
+        \begin{bmatrix}
+            I_x^2   & I_x I_y \\
+            I_x I_y & I_y^2
+        \end{bmatrix}
+    }$
 
 
 \shade{gray}{Blob Detection} ($I$ is the image)

electives/amr/parts/04_vision/01_bootstrapping.tex

@@ -1,9 +1,11 @@
 \subsection{Bootstrapping}
 
-\bi{PnP Problem} {\scriptsize Persp. n-P.}
+\bi{PnP Problem} {\scriptsize Persp. $n$-P.}
 Find sol. for camera pose \textit{directly}
 
 \bi{RANSAC} {\scriptsize RANdom SAmpling Consensus} for find. outliers \& correct
+% TODO: Do we need to know this algorithm / be able to implement it?
+% -> likely not
 
 \bi{Stereo Triang.} Given two rays (known poses for points in 2D).
 Find good point in 3D. Fast sol: \bi{Midpoint Method}:
@@ -16,15 +18,22 @@ Find good point in 3D. Fast sol: \bi{Midpoint Method}:
 \rmvspace
 \bi{2} Solve normal equation $\mat{A} \vec{\lambda} = \vec{b}$ with $\vec{q} = -{_W}\vec{e}^\top_1 {_W}\vec{e}_2$:
 \[
-    \mat{A} = \begin{bmatrix}
+    \mat{A} =
+    {\scriptsize
+    \begin{bmatrix}
         1       & \vec{q} \\
         \vec{q} & 1
     \end{bmatrix}
+    }
     \quad
-    \vec{b} = \begin{bmatrix}
+    \vec{b} =
+    {\scriptsize
+    \begin{bmatrix}
         \vec{e}_1^\top \cdot ({_W}\vec{t}_{C_2} - {_W}\vec{t}_{C_1}) \\
         -\vec{e}_2^\top \cdot ({_W}\vec{t}_{C_2} - {_W}\vec{t}_{C_1})
     \end{bmatrix}
+    }
+    \quad C_i \text{ cam}
 \]
 
 \bi{3} Pick midp. ${_W}\vec{t}_P \! = \! 0.5(\tau_1 \! + \! \tau_2)$; $\tau_n \! = \! {_W}\vec{t}_{C_n} + \lambda_n{_W}\vec{e}_n)$