Pinhole Camera Model

A mathematical model treating a camera as an ideal tiny hole, projecting 3D points onto an image plane along straight lines.

The pinhole camera model is computer vision's standard model for how a 3D point becomes a pixel: it assumes every ray of light passes through an ideal tiny hole, the optical center, and a point (X, Y, Z) in the camera's coordinate frame lands at u = fx·X/Z + cx, v = fy·Y/Z + cy. Here fx and fy are the focal lengths in pixels, and (cx, cy) is the principal point — together these four numbers are the camera's intrinsics. Dividing by Z produces perspective — near things look big, far things look small. The model ignores lens distortion and defocus blur, so it's only a first-order approximation; in practice, distortion coefficients are calibrated first to undistort the image, and the pinhole model is applied afterward. Turning a depth map into a point cloud, converting a pixel position into a 3D grasp point, and doing hand-eye calibration are all built on this formula.

ExampleA camera has fx = fy = 600 pixels and principal point (320, 240). A point 1 meter directly ahead and 0.1 meters to the right lands at column 600 × 0.1/1 + 320 = 380; moving that same point to 2 meters away lands it at column 350, closer to the center of the image.

Also called

Pinhole Model, Perspective Projection Model

Related

Camera Intrinsics · Camera Extrinsics · Lens Distortion · Projection / Back-Projection · Camera Calibration · Camera Coordinate Frame

Sources

Wikipedia: Pinhole camera model
Intel RealSense Wiki: Projection in RealSense SDK 2.0