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49 lines
2.3 KiB
TeX
49 lines
2.3 KiB
TeX
\subsection{Depth and Range sensing}
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Typ. derive D.M. with sensor dir param (as vec line eq)
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\subsubsection{Triangulation-based}
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\bi{Struct. Light} Single cam, single projector: {\color{ForestGreen}Spatial acc}, {\color{red} no worky in bright light, interference with other IR depth cams}
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\bi{Active Stereo} 2 cams, 1 proj: {\color{ForestGreen} worky in bright light}, {\color{red} need stereo matching, less accurate, error grows with distance}
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\subsubsection{Classic Stereo}
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\label{sec:classic-stereo}
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Both images: same plane, focal length $f$, centre, $x$-axis. Given corresponding pixels $[u_l, v]$ and $[u_r, v]$: \bi{disparity} (pixel offset) $d = u_r - u_l$;
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$z = \frac{b \cdot f}{d}$, 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.
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Then often apply pinhole camera projection (to e.g. get 3D point coords, comp ${_C}\vec{r}$, then point $z \cdot {_C}\vec{r}$).
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Uncertainty introduced with 1.-order error propag. $\Delta z = \pardiff{d}z \Delta d$, with $\Delta d$ error of $d$.
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Too large $b$ disables depth estimations, too small increases error
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\shorttheorem[Intercept] $f \div Z = u_l \div X$, with $Z$ and $X$ the $z$ and $x$ coordinates of tracked object
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\subsubsection{Time of Flight, Projection}
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{\color{ForestGreen}No occlusions/shadows}, {\color{red}Interference with other dev, multipath leading to larger distances sensed}
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\bi{Proj.} $\vec{z} =
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{\scriptsize
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\begin{bmatrix}
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\vec{u} \\ d
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\end{bmatrix} =
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\begin{bmatrix}
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\vec{k}(\vec{d}(\vec{p}({_C}\vec{t}_P))) \\
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[0, 0, 1] {_c}\vec{t}_P
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\end{bmatrix}
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}$
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\bi{Back}: ${_C}\vec{t}_P
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=
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{\scriptsize
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\begin{bmatrix}
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d \vec{x'} \\d
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\end{bmatrix}
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}$
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This $x'$ is obtained from pinhole cam projection.
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\subsubsection{Range Sensors}
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\bi{Ultrasonic} Typ. freq: 40kHz - 180kHz, Range: 12cm - 5m, Acc: $\approx$ 2cm, rel error $\approx$ 2\%
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{\color{ForestGreen} meas. for transp. surf., cheap(ish)}, {\color{red} Cone wider, reflect. angle dep, wind / currents}
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\bi{LiDAR} Time-of-Flight-based, {\color{ForestGreen}Accuracy, range, works in bright light}, {\color{red} Complex, expensive, one timestamp per measurement}.
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Typical Ranges: up to 100m
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