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The camera baseline is the separation between the camera centers of two views. For centers $C_L,C_R$, its length is $B=\Vert C_R-C_L\Vert$. It measures translation, so turning a stationary camera without moving its camera center does not create a nonzero camera baseline. A known camera baseline supplies the length scale in stereoscopic triangulation.^[ref]

In the ideal aligned model with matched coordinate origins, stereo disparity satisfies $d=fB/Z$. For focal length 800 pixels and depth 5 metres, a camera baseline 0.10 metres gives 16 pixels; doubling the camera baseline gives 32 pixels. With unchanged disparity precision, the larger separation improves depth sensitivity. It can also increase occlusion in stereo vision and reduce overlap of the views. Finally, multiplying both $B$ and all reconstructed lengths by the same factor leaves the projections unchanged: a small reprojection error alone cannot certify the metric scale.

Camera calibration estimates the parameters relating points in a scene to measured image coordinates. In the ideal pinhole model,where $K$ contains focal lengths and the principal point, while the rotation matrix $R$ and translation $t$ locate the camera relative to the scene. Lens distortion requires additional parameters.^[ref]

A calibration experiment photographs a flat board with a known grid from several orientations. Detected grid corners provide image measurements; their known spacing supplies geometric constraints and a length scale. Parameters are fitted by minimizing reprojection error. Multiple orientations help separate camera geometry from board pose. For an ideal camera with focal length 1000 pixels, a point displaced $0.1\mathrm{m}$ sideways at depth $2\mathrm{m}$ projects 50 pixels from the principal point.^[ref]

A checkerboard calibration target is a planar pattern of alternating dark and light squares with known geometry, used to estimate camera calibration parameters. Image measurements of internal corner intersections are paired with known target coordinates. Several tilted views constrain the image projection and distortion model.^[ref]

For a board with nine squares across and six down, the internal-corner grid has eight columns and five rows. If square spacing is 20 millimetres, one can assign corner coordinates $(20i,20j,0)$ millimetres for $i=0,\dots ,7$ and $j=0,\dots ,4$. Supplying only unit grid spacing instead yields translation estimates in square-size units. A useful experiment varies the target's orientation and image position, then examines reprojection error. Repeated identical views provide less geometric information; a warped board or inaccurate corner measurements can also bias the fitted camera model.

OpenCV is a software library for computer vision and image processing. Its camera-geometry tools connect observed pixel coordinates to models of imaging, including camera calibration, correction of lens distortion, stereo rectification and three-dimensional reconstruction.^[ref]

A checkerboard calibration target supplies known geometry that can be observed from several camera positions. Fitting the model compares detected image points with projected target points. The resulting reprojection error measures agreement in the image, rather than independently confirming every physical dimension of the reconstructed scene.

A simple perspective projection illustrates the distinction: in $u=fX/Z$, replacing $X$ and $Z$ by $kX$ and $kZ$ for $k>0$ leaves $u$ unchanged. This scale ambiguity of perspective projection means that image agreement alone cannot verify a chosen unit of length. A camera baseline or a target of known size supplies additional metric information. Using the library well therefore includes checking geometric assumptions and units, alongside the numerical fit.

A reprojection error compares an observed image point with the position predicted by projecting a reconstructed scene point through a camera model. If $q_i$ is an observed position and ${\pi }_i(P)$ its prediction, the residual is $e_i=q_i-{\pi }_i(P)$. One possible aggregate is the per-point root mean square Euclidean norm:Coordinates in pixels give an error in pixels. Least squares instead minimizes the associated sum of squares; normalization conventions should be stated when reporting a summary.^[ref]

For an observation $(100,50)$ and prediction $(103,54)$, the Euclidean norm of the residual is 5 pixels. Camera calibration can adjust model parameters to reduce many such residuals, while stereoscopic triangulation can adjust a reconstructed point with the camera parameters fixed. Low reprojection error tests agreement with observations under that model; incorrect stereo correspondence or an incorrect camera baseline can still produce wrong scene geometry.

Stereoscopic triangulation reconstructs a scene point from corresponding image positions and known camera geometry. Each image position determines a viewing direction. Two correctly matched views constrain the point to lie on both viewing rays; one view alone leaves its position along a ray undetermined.

For an ideal aligned pair, put the left camera at the origin and the right one at $(B,0,0)$ in a Cartesian coordinate system, with their axes pointing in the positive $Z$ direction. Assume a common focal length $f$, square pixels, corrected distortion and image coordinates measured from aligned principal points. Forward perspective projection givesThe stereo disparity $d=u_L-u_R$ therefore determines all three coordinates:Here $Z$ is depth along the camera axis; the Euclidean distance from the left camera is instead $\sqrt{X^2+Y^2+Z^2}$. If $f,u_L,v_L,d$ use pixels and the camera baseline $B$ uses metres, the recovered coordinates use metres. Without a known length scale, the images alone do not determine metric size.^[ref]

Real cameras require calibration before these simplified equations apply. Stereo rectification transforms the images to an aligned geometry. With noisy measurements, viewing rays need not intersect exactly; minimizing reprojection error instead seeks a point whose projected positions agree as closely as possible with the observations. Reconstruction also depends on stereo correspondence: a mathematically precise intersection of mismatched viewing directions can still describe the wrong scene point.^[ref]