Optimal grid pattern generation for automatic 2D-3D correspondence

In general, to calibrate a camera, a set of 2D-3D correspondences are needed. Because of its invariance under projective automorphisms, cross-ratio has been used to identify 2D points on a grid pattern yielding 2D-3D correspondences. However, the pixel errors in detecting grid corner points make the identification challenging. This even gets harder if the given cross-ratios are not distributed separatively enough. To build such a distribution of cross-ratios, in this work the authors have approximated the error propagation from corner point detection to cross-ratio calculation by unscented transform and optimised the distribution by particle swarm optimisation. Experimental results show that the grid patterns generated by the authors are unique enough to give automatic 2D-3D correspondences.