Comparing the Performance of Least-Squares Estimators: when is GTLS Better than LS?

Several computer vision problems lead to linear systems affected by noise. These are commonly solved by least-squares estimators, the most popular being ordinary least squares (LS), total least squares (TLS) and generalized total least squares (GTLS). However, the statistical or structural assumptions of these theoretical estimators are very often violated in practice. Given that their computational cost is very different, what should one choose, and in which conditions? We give empirical guidelines, in the absence of a general theoretical answer, observing the behaviour of errors of LS, TLS and GTLS with a representative computer vision problem (homography estimation) in varying noise conditions (noise distribution, intensity, correlation level, added to image co-ordinates or to system matrix). We find that the much more expensive GTLS brings significant advantages with high intensity, highly correlated noise in the system matrix; in other conditions, the three estimators give comparable errors. Least squares, Total least squares, Generalized total least squares, 2-D Homography, Correlated noise.