Bootstrapping Errors-in-Variables Models

The bootstrap is a numerical technique, with solid theoretical foundations, to obtain statistical measures about the quality of an estimate by using only the available data. Performance assessment through bootstrap provides the same or better accuracy than the traditional error propagation approach, most often without requiring complex analytical derivations. In many computer vision tasks a regression problem in which the measurement errors are point dependent has to be solved. Such regression problems are called heteroscedastic and appear in the linearization of quadratic forms in ellipse fitting and epipolar geometry, in camera calibration, or in 3D rigid motion estimation. The performance of these complex vision tasks is difficult to evaluate analytically, therefore we propose in this paper the use of bootstrap. The technique is illustrated for 3D rigid motion and fundamental matrix estimation. Experiments with real and synthetic data show the validity of bootstrap as an evaluation tool and the importance of taking the heteroscedasticity into account.