Camera calibration terms,defined plainly.

The process of estimating the parameters that describe how a camera maps a 3D point in the world to a 2D pixel in an image — its intrinsics (focal length, principal point) and lens distortion. The result lets you undistort images and recover real geometry from pixels.

The camera-internal parameters that map a point in the camera frame to a pixel: the focal lengths (fx, fy) and the principal point (cx, cy), collected in the intrinsic matrix K. They do not depend on where the camera is in the world.

The rotation and translation that describe where the camera sits in the world relative to the calibration target. Unlike intrinsics, extrinsics change every time the camera or scene moves.

A 3×3 upper-triangular matrix holding the focal lengths (fx, fy) on the diagonal and the principal point (cx, cy) in the last column. K converts a normalised camera-frame coordinate into a pixel coordinate.

In calibration, the focal length (fx, fy in pixels) encodes how strongly the lens magnifies the scene onto the sensor. Larger values mean a narrower field of view and more zoom.

The pixel coordinate (cx, cy) where the camera’s optical axis intersects the image plane — usually near, but not exactly at, the image centre. It is part of the intrinsic matrix K.

The deviation of a real lens from an ideal pinhole, which bends straight world lines into curves in the image. The most common forms are radial distortion (barrel and pincushion) and tangential distortion, modelled by the Brown–Conrady coefficients.

The numbers (typically k1, k2, p1, p2, k3, …) that quantify how a lens distorts the image. Estimated during calibration, they are used to undistort images so that straight world lines become straight again.

The standard rectilinear projection model where a 3D point projects through a single optical centre onto the image plane. With Brown–Conrady distortion it covers most normal lenses up to roughly a 90° field of view.

An extension of the pinhole model with additional denominator terms (k4, k5, k6) that fits wide-angle and action-camera lenses up to about 120° field of view, where the basic pinhole model breaks down.

A projection model for very wide lenses approaching 180°, where image radius grows roughly linearly with the incoming ray angle (the equidistant, or Kannala–Brandt, model). Fisheye lenses need this model rather than the pinhole model to calibrate well.

The pixel distance between a detected target point and where the calibrated model predicts that point should appear. It is the quantity calibration minimises, and the primary measure of how well a calibration fits the data.

The root-mean-square of reprojection errors over all observed points — a single-number quality score in pixels. Below 0.5 px is excellent and above 2 px usually signals weak frames, wrong board parameters, or a model mismatch.

Using the estimated distortion coefficients to remap a distorted image into one that obeys the ideal pinhole model, so that straight world lines appear straight. A prerequisite for accurate measurement and rectification.

Warping one or more images onto a common ideal image plane — for a single camera, removing distortion; for a stereo pair, aligning the two views so corresponding points share the same image row.

A printed board of known geometry — checkerboard, circles grid, ArUco, or ChArUco — captured from many angles so the calibration has accurate 3D-to-2D correspondences to solve from.

A black-and-white chessboard pattern whose inner corners are detected with sub-pixel accuracy. The classic, simplest calibration target, though it must be fully visible in every frame.

Square fiducial markers, each encoding a unique binary ID, that can be detected individually. Because each marker is identifiable, ArUco boards tolerate occlusion and partial views better than a plain checkerboard.

A hybrid target that places ArUco markers in the white squares of a checkerboard, combining the sub-pixel corner accuracy of a checkerboard with the per-marker identification of ArUco — so it stays robust even when partially out of frame.

The angular extent of the scene a lens captures. FOV is the quickest signal for choosing a camera model: ≤90° suits the pinhole model, ~120° the wide-angle model, and approaching 180° the fisheye model.