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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]

The camera center is the center of projection in an ideal perspective camera model: the common origin of its viewing rays. It is a point in scene space, distinct from a principal point, which is an image-plane coordinate. Two distinct camera centers define the camera baseline used by stereoscopy.

For the calibrated perspective projection model $q\sim K(RP+t)$, where $R$ is a rotation matrix, the camera center $C$ satisfies $RC+t=0$. HenceThis follows by applying the inverse rotation to the zero camera-space position.^[ref] For $R=I$ and $t=(-0.1,0,0)$ metres, $C=(0.1,0,0)$ metres: the translation parameter is not directly the world-space camera center. Rotating about that center changes viewing directions without creating a new triangulation baseline.

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.

In an ideal camera model, the principal point is the intersection of the optical axis with the image plane, expressed in image pixel coordinates $(c_x,c_y)$. It supplies the coordinate offset in perspective projection. For a scene point $(X,Y,Z)$ expressed relative to the camera, the model iswhere $f_x,f_y$ are focal lengths in pixel units. Thus the principal point belongs to the camera's internal geometry; the camera's position and orientation in the world are separate parameters.^[ref]

For $f_x=800$, $c_x=320$, $X=0.1$ metres and $Z=2$ metres, the horizontal coordinate is $u=360$ pixels. A point on the optical axis instead has $X=Y=0$ and projects to $(c_x,c_y)$. The principal point is often near the image center, but camera calibration estimates it rather than establishing that it must be exactly centered. Cropping an image also changes the principal point's coordinate values: removing 20 columns from the left changes $c_x=320$ to $300$, without physically moving the optical axis.

Scale ambiguity of perspective projection means that image coordinates alone cannot determine absolute scene size and distance. In an ideal camera with focal length $f$ and centered image coordinates,Replacing $(X,Y,Z)$ by $(sX,sY,sZ)$ for any positive $s$ leaves $(u,v)$ unchanged. A geometrically similar scene twice as large and twice as far away therefore produces the same projection.^[ref]

For example, a $0.10\mathrm{m}$ object at depth $1\mathrm{m}$ and a $1\mathrm{m}$ object at depth $10\mathrm{m}$ subtend the same image height under this model. Extra metric information, such as a known object length or a measured camera baseline, supplies a scale. In stereo vision, scaling the reconstructed scene and the assumed baseline together preserves the image observations; measuring the baseline breaks that freedom. Camera calibration of focal length alone does not provide an absolute length for an otherwise unknown scene.

Stereo rectification transforms a pair of images so that corresponding epipolar lines become aligned scan lines. In a horizontal stereo arrangement, a scene point visible in both rectified views should have the same vertical image coordinate. This turns a two-dimensional matching search into a one-dimensional search along a row.^[ref]

For example, a feature initially at left row 100 and right row 104 can be mapped to the same row in virtual aligned views. Camera calibration supplies geometry for the transforms, and image resampling evaluates the transformed images on a new pixel grid. The new images need not retain every border region. Stereo rectification aligns the geometric search; it does not identify the correct partner among repeated patterns or restore a feature hidden in one view. The rectified focal length and coordinate offsets must also be used when converting stereo disparity to depth.

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]