[AMR] Add gauss newton from NumCS summary

electives/amr/parts/02_Sensors-Actuators/04_depth-range.tex

@@ -7,8 +7,10 @@ Typ. derive D.M. with sensor dir param (as vec line eq)
 
 
 \subsubsection{Classic Stereo}
-Both images: same plane, focal length, centre, $x$-axis. Given corresponding pixels $[u_l, v]$ and $[u_r, v]$,
-$z = \frac{b \cdot f}{u_r - u_l}$ with $u_l = f\cdot \frac{x}{z} + c_u$ and $u_r = f \cdot \frac{x - b}{z} + c_u$
+Both images: same plane, focal length $f$, centre, $x$-axis. Given corresponding pixels $[u_l, v]$ and $[u_r, v]$: disparity (pixel offset) $d = u_r - u_l$;
+$z = \frac{b \cdot f}{d}$, then projected into left (right) cam, $u_l = f\cdot \frac{x}{z} + c_u$ or $u_r = f \cdot \frac{x - b}{z} + c_u$, $b$ distance between cameras.
+Then often apply pinhole camera projection (to e.g. get 3D point coords, comp ${_C}\vec{r}$, then point $z \cdot {_C}\vec{r}$).
+Uncertainty introduced with 1.-order error propag. $\Delta z = \pardiff{d}z \Delta d$, with $\Delta d$ error of $d$
 
 
 \subsubsection{Time of Flight, Projection}
@@ -31,6 +33,7 @@ $z = \frac{b \cdot f}{u_r - u_l}$ with $u_l = f\cdot \frac{x}{z} + c_u$ and $u_r
                 d \vec{x'} \\d
             \end{bmatrix}
         }$
+This $x'$ is obtained from pinhole cam projection.
 
 
 \subsubsection{Range Sensors}