Image Sensor Model Using Geometric Algebra: From Calibration to Motion Estimation

Abstract

In computer vision image sensors have universally been defined as the nonparametric association of projection rays in the 3D world to pixels in the images. If the pixels’ physical topology can be often neglected in the case of perspective cameras, this approximation is no longer valid in the case of variant scale sensors, which are now widely used in robotics. Neglecting the nonnull pixel area and then the pixel volumic field of view implies that geometric reconstruction problems are solved by minimizing a cost function that combines the reprojection errors in the 2D images. This paper provides a complete and realistic cone-pixel camera model that equally fits constant or variant scale resolution together with a protocol to calibrate such a sensor. The proposed model involves a new characterization of pixel correspondences with 3D-cone intersections computed using convex hull and twists in Conformal Geometric Algebra. Simulated experiments show that standard methods and especially Bundle Adjustment are sometimes unable to reach the correct motion, because of their ray-pixel approach and the choice of reprojection error as a cost function which does not particularly fit the physical reality. This problem can be solved using a nonprojective cone intersection cost function as introduced below.