Beginner’s Guide of Camera Calibration
Starting with Pinhole Model
Camera calibration herein is about “geometric” camera calibration, which estimates the parameters of an image or video camera consisting of a lens system and sensor. Camera parameters describe how an image is mapped through the camera system from the world coordinates. One may use these parameters to correct the image distortion, measure the size of the object in world units and calculate the location of the object relative to the camera. These tasks are widely used in applications, specifically for robotics related to navigation or 3-D scene reconstruction.
The word “camera model” is an assumption that describes how the object in the real world is projected onto the image plane. The “pinhole model” describes the lens as an aperture so it assumes that the rays pass through the aperture and form an inversed real image on the image plane. Apparently, pinhole model neglects the refraction caused by the material and the geometry of the lens, so it is applicable only when the “negligible refraction” holds.
Camera Parameters
In pinhole model, the camera parameters are represented in a 3-by-4 matrix called “camera matrix”, which maps the 3-D world into the image plane:
Camera matrix is composed by extrinsic and intrinsic parameters. The extrinsic parameters represent the location of the camera in the 3D scene by translation and rotation and the intrinsic parameters describes the optical center and the focal length of the camera.
The extrinsic parameters are to transform the world points from 3D-scene to camera
coordinates, and the camera coordinates are then mapped into image plane according to the intrinsic parameters. We may summarize: the extrinsic parameters describe the relative position between the camera system and the 3D world while the intrinsic parameters could define the optical features of the camera.
Distortion
Pinhole model does not account for the lens distortion; however, utilizing pinhole model without taking distortion into consideration is very unpractical. To well describe the projection from the world to image plane, a camera model includes both radial and tangential distortion. Fig SEQ Fig \* ARABIC 3 Radial distortion Radial distortion occurs due to the curvature of a lens, and it is more serious near the edge of a lens than it is at the optical center. This can be easily explained by Snell’s law because light rays bend more at the edge of a lens as the normal of the incident plane deviates from the optical axis more. The relationship between radially distorted point () and undistorted points ()can be represented as:
