Statistical comparison of DLT versus ILSSC in the calibration of a photogrammetric stereo-system

This paper compares the DLT and ILSSC approaches in the geometrical calibration of a photogrammetric stereo-system in terms of accuracy and speed. To come up with an unbiased quantitative evaluation of the accuracy of the algorithms, the concept of reliable estimate has been introduced: the statistical distribution of the accuracy is assessed over different calibration experiments performed with the same data but with different noise distribution and different test sets. Results show that in the simulations where the only error on the two-dimensional points was Gaussian, zero mean, and on real data which were corrected for distortions through polynomial or linear interpolation, the accuracy of the two methods was quite similar. DLT showed more accurate than ILSSC on simulated data with residual distortion errors and on real data which were not corrected for distortions. As far as speed is concerned, a fast triangulation algorithm is associated with ILSSC while the simultaneous solution of two pairs of DLT equations is associated to DLT. The first algorithm is much faster, requiring 113 flops per point versus 259 of DLT; the fast triangulation with DLT parameters does not achieve the same accuracy on the reconstructed three-dimensional position. Taken all together the results suggest that ILSSC can be theoretically considered the best approach to three-dimensional reconstruction, provided that distortions are corrected in advance. The statistical evaluation of the accuracy allows a fair judgement of the performances of the algorithms to be obtained, unbiased by particular distributions of measurement errors and test points.