Correcting Radial Distortion of Cameras with Wide Angle Lens Using Point Correspondences

Most algorithms in 3-D Computer Vision rely on the pinhole camera model because of its simplicity, whereas video optics, especially wide-angle lens, generates a lot of non-linear distortion. In some applications, for instance in stereo vision systems and robotic systems, this distortion can be critical. Camera calibration consists of finding the mapping between the 3-D space and the camera plane. This mapping can be separated in two different transformations: first, the relation between the origin of 3-D space (the global coordinate system) and the camera coordinate system, which forms the external calibration parameters (3-D rotation and translation), and second the mapping between 3-D points in space (using the camera coordinate system) and 2-D points on the camera plane, which forms the internal calibration parameters (Devernay & Faugeras, 1995). Fig. 1 shows two types of distortion due to lens: barrel and pincushion distortions and a rectangle without any distortion like reference (e.g. the image taken by an ideal pinhole camera) (Weng et al. 1992). The pincushion distortion is due to zoom lens and the barrel distortion is due to wide angle lens. In commercial cameras with wide angle lens the most important component of the barrel distortion is the radial distortion and this chapter introduces a method to find the internal calibration parameters of a camera, specifically those parameters required to correct the radial distortion due to wide-angle lens.