= Stereoscopy
{wiki}
<Stereoscopy> uses images from different viewpoints to convey or recover depth. In scientific <photography>, identifying the same feature in two calibrated views permits <stereoscopic triangulation>: intersecting the directions inferred from the two images.<What Is Stereo Reconstruction? by MathWorks>[How Does Stereo Reconstruction Work? and Stereo Camera Calibration]{ref}
Consider ideal <cameras> with parallel axes, separated by a baseline $B$. With matching forward-projection coordinates and common <focal length> $f$ in image-coordinate units, a point at $(X,Z)$ projects to
$$
x_L=\frac{fX}{Z},\qquad x_R=\frac{f(X-B)}{Z}.
$$
Subtracting gives the <stereo disparity> $d=x_L-x_R=fB/Z$, hence $Z=fB/d$. If $f$ and $d$ are measured in <pixels>, $Z$ has the same length unit as $B$.
For an original example, $B=0.12\,\mathrm m$, $f=800$ <pixels> and $d=24$ <pixels> give $Z=4\,\mathrm m$. First-order <propagation of uncertainty> gives $\sigma_Z\simeq fB\sigma_d/d^2$. Thus fixed disparity precision produces increasing depth uncertainty for more distant objects. Correctly matching the same feature is also essential; ambiguous or hidden features can defeat the reconstruction even when the geometry is known.
\Image[/stereoscopy-depth-from-disparity.png]
{title=Depth and uncertainty in an ideal <stereoscopy> model}
{description=Original model curves with stipulated calibration and disparity uncertainty. These are analytical predictions, rather than observations or a camera performance specification.}
Back to article page
