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Intrinsic parameters
Set of a camera's internal optical characteristics including focal length, principal point, and distortion coefficients, which determine how 3D points are projected onto the 2D image plane. These parameters are independent of the camera's position and orientation in space.
Extrinsic parameters
Parameters describing the position and orientation of a camera relative to a world coordinate system, including the rotation matrix and translation vector. They allow transforming real-world coordinates into camera frame coordinates.
Calibration matrix
3x3 matrix containing the camera's intrinsic parameters, including focal lengths fx and fy, the principal point (cx, cy), and skew coefficients. It is essential for correcting distortions and performing accurate measurements in image space.
Radial distortion
Type of optical distortion caused by the non-ideal shape of the lens, causing points to move away from or closer to the optical center. It is modeled by coefficients (k1, k2, k3) and must be corrected for accurate geometric reconstruction.
Tangential distortion
Optical distortion resulting from misalignment between the camera's optical elements, causing points to shift perpendicular to radial rays. It is generally modeled by two coefficients (p1, p2) in the Brown-Conrady model.
Principal point
Intersection point between the camera's optical axis and the image plane, generally located at the theoretical center of the sensor but offset in practice. It is noted as (cx, cy) in the calibration matrix and is crucial for correct projection.
Focal length
Distance between the optical center of the lens and the image plane, expressed in pixels in the calibration context (fx, fy). It determines the field of view and the scale of the projection of 3D points onto the image.
Calibration pattern
Physical tool with known geometric patterns (chessboard, symmetric circles, dot grid) used to determine calibration parameters. The precision of its dimensional characteristics directly influences the quality of calibration.
Homogeneous coordinates
Mathematical representation extending Cartesian coordinates by an additional dimension, allowing for a unified representation of projective transformations and points at infinity. Essential for calibration and computer vision.
Image rectification
Process of geometric transformation correcting image distortions to make straight lines in the real world also straight in the image. It uses calibration parameters to produce an undistorted and geometrically correct image.
Pinhole model
Simplified geometric camera model representing perspective projection through a simple hole, serving as the basis for calibration. It ignores optical aberrations but provides the fundamental framework for understanding 3D-2D transformations.
Reprojection error
Quantitative measure of calibration quality, calculated as the distance between observed points in the image and their theoretical projections using the calibrated parameters. A low error indicates an accurate and reliable calibration.
Stereo calibration
Simultaneous process of calibrating two or more cameras to determine their intrinsic parameters and their relative extrinsic position. Essential for stereoscopic vision, 3D reconstruction, and depth measurement.
Barrel distortion
Specific type of radial distortion causing an image to bulge outwards, where straight lines appear curved outward. More common with wide angles and wide-angle lenses.
Pincushion distortion
Form of radial distortion opposite to barrel distortion, causing an image to contract where straight lines appear curved inward. Typical of telephoto lenses.
Self-calibration
Calibration technique that does not require a physical calibration target, using geometric constraints inherent to the scene or camera movements. Less precise but more flexible than calibration with a target.
Bundle Adjustment
Non-linear optimization algorithm that simultaneously refines calibration parameters and camera poses by minimizing global reprojection error. Considered the state-of-the-art for calibration optimization.