caa a22 4500 467915083 CHVBK 20180406152859.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s11263-006-6486-z doi (NATIONALLICENCE)springer-10.1007/s11263-006-6486-z When are Simple LS Estimators Enough? An Empirical Study of LS, TLS, and GTLS [Elektronische Daten] [Arvind Nayak, Emanuele Trucco, Neil Thacker] A variety of least-squares estimators of significantly different complexity and generality are available to solve over-constrained linear systems. The most theoretically general may not necessarily be the best choice in practice; problem conditions may be such that simpler and faster algorithms, if theoretically inferior, would yield acceptable errors. We investigate when this may happen using homography estimation as the reference problem. We study the errors of LS, TLS, equilibrated TLS and GTLS algorithms with different noise types and varying intensity and correlation levels. To allow direct comparisons with algorithms from the applied mathematics and computer vision communities, we consider both inhomogeneous and homogeneous systems. We add noise to image co-ordinates and system matrix entries in separate experiments, to take into account the effect on noise properties (heteroscedasticity) of pre-processing data transformations. We find that the theoretically most general algorithms may not always be worth their higher complexity; comparable results are obtained with moderate levels of noise intensity and correlation. We identify such levels quantitatively for the reference problem, thus suggesting when simpler algorithms can be applied with limited errors in spite of their restrictive assumptions. Springer Science + Business Media, LLC, 2006 least squares nationallicence total least squares nationallicence generalized total least squares nationallicence 2-D homography nationallicence correlated noise nationallicence Nayak Arvind Vision, Image and Signal Processing Group, EECE-EPS, Heriot Watt University, EH14 4AS, Edinburgh, UK aut Trucco Emanuele Vision, Image and Signal Processing Group, EECE-EPS, Heriot Watt University, EH14 4AS, Edinburgh, UK aut Thacker Neil Division of Imaging Science & Biomedical Engineering, Medical School, University of Manchester, M13 9PT, Manchester, UK aut International Journal of Computer Vision Kluwer Academic Publishers 68/2(2006-06-01), 203-216 0920-5691 68:2<203 2006 68 11263 https://doi.org/10.1007/s11263-006-6486-z text/html Onlinezugriff via DOI 1 brief-communication jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11263-006-6486-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nayak Arvind Vision, Image and Signal Processing Group, EECE-EPS, Heriot Watt University, EH14 4AS, Edinburgh, UK aut NATIONALLICENCE 700 1- Trucco Emanuele Vision, Image and Signal Processing Group, EECE-EPS, Heriot Watt University, EH14 4AS, Edinburgh, UK aut NATIONALLICENCE 700 1- Thacker Neil Division of Imaging Science & Biomedical Engineering, Medical School, University of Manchester, M13 9PT, Manchester, UK aut NATIONALLICENCE 773 0- International Journal of Computer Vision Kluwer Academic Publishers 68/2(2006-06-01), 203-216 0920-5691 68:2<203 2006 68 11263 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer