Stereo disparity ($d$)

Stereo disparity is the difference between the image positions of the same scene feature in two views. For an ideal horizontally aligned pair, use signed horizontal coordinates with matched principal points and defineWith the orientation and camera baseline convention of stereoscopic triangulation, a point in front of the cameras has $d=fB/Z$: stereo disparity measures inverse depth, rather than depth itself. Halving $d$ doubles $Z$ when the camera baseline and focal length stay fixed.

A disparity map assigns this difference to matched image locations. Finding the matches is a separate stereo correspondence problem. A repeated pattern can give several plausible matches; a feature hidden from one camera has no visible partner. A small measured stereo disparity is therefore not, by itself, proof of a distant object: the match and calibration must also be credible.^[ref]

The ideal relation also explains why far-away reconstruction becomes sensitive to measurement error. Differentiating $Z=fB/d$ gives $\mathrm{d}Z/\mathrm{d}d=-fB/d^2$; the first-order propagation of uncertainty is ${\sigma }_Z\simeq fB{\sigma }_d/d^2$. Thus equal disparity errors produce larger depth errors at greater depth. The example and curves under stereoscopy quantify this effect.