GR2T vs L2E with Nuisance Scale

We compare the objective functions used by GR
²
T [1] and the L
₂
E estimator [2] that have both been proposed for robust parameter estimation. We show their similarity when estimating location parameters. Of particular interest is their ability for dealing with the scale parameter that is often unknown and acts as a nuisance parameter. Both techniques are tested experimentally for regression (e.g. to find patterns such as line and circle in noisy datasets) and for registration between datasets.