The anycentric camera: A unifying pinhole model for ento-, hyper- and telecentric lenses using Geometric Algebra

Camera calibration is a crucial task when working with camera-based optical imaging and metrology systems. The widely used pinhole camera model has proven itself useful for this purpose, as it has a comparatively small number of parameters, yet accurately describes the desired system behavior. However, if non-entocentric lenses are to be calibrated, the pinhole model must be modified for hypercentric lenses, or it is not applicable at all for telecentric lenses. Instead, this contribution shows how the widely used pinhole camera model can be generalized for entocentric (converging chief rays), hypercentric (diverging chief rays) and telecentric (parallel chief rays) lens types by using the unifying methods of Plane-based Geometric Algebra. By mainly taking advantage of the algebra’s inherently incorporated projective geometry to describe the intrinsic camera behavior, the proposed enhanced pinhole model contains a smooth transition between perspective projection and orthographic projection, making it well suited for the optimization process during camera calibration and resulting in a more complete and more general camera model without greatly increasing its complexity.