Camera Intrinsics

The parameters describing how a camera itself forms an image, determining which pixel a 3D point lands on.

Camera intrinsics are usually written as a 3×3 matrix K, containing the focal lengths fx and fy in pixels and the principal point cx, cy (where the optical axis meets the image plane, generally near the image center); lens distortion coefficients are typically listed separately. Intrinsics describe how a 3D point in the camera's own coordinate frame projects onto a pixel, and depend only on the camera and lens, not on what's being photographed — so they stay valid as long as the focal length doesn't change. They can be found by calibrating against a checkerboard (Zhang Zhengyou's method), and depth cameras such as the RealSense ship factory-calibrated, with intrinsics readable straight from the SDK. A common pitfall: if an image is resized or cropped before being fed to a model, the intrinsics must be adjusted by the same scale and offset, or any point cloud reprojected from it will come out misaligned.

ExampleFor a 640×480 image with fx = fy = 600, cx = 320, cy = 240: a pixel at (420, 240) with a measured depth of 1 meter corresponds to a camera-frame point of X = (420 − 320) × 1/600 ≈ 0.17 m, Y = 0, Z = 1 m.

Also called

Intrinsic Parameters, Intrinsic Matrix, K Matrix, Focal Length and Principal Point

Related

Camera Extrinsics · Pinhole Camera Model · Lens Distortion · Projection / Back-Projection · Camera Calibration · Calibration Board

Sources

OpenCV calib3d.hpp：camera intrinsic matrix（fx、fy、cx、cy）
RealSense SDK rs_types.h：rs2_intrinsics 结构体 (Chinese)
Wikipedia: Camera resectioning