On bias correction for geometric parameter estimation in computer vision

Abstract

Maximum likelihood (ML) estimation is widely used in many computer vision problems involving the estimation of geometric parameters, from conic fitting to bundle adjustment for structure and motion. This paper presents a detailed discussion on the bias of ML estimates derived for these problems. Statistical theory states that although ML estimates attain maximum accuracy in the limit as the sample size goes to infinity, they can have non-negligible bias with small sample sizes. In the case of computer vision problems, the ML optimality holds when regarding variance in observation errors as the sample size. A natural question is how large the bias will be for a given strength of observation errors. To answer this for a general class of problems, we analyze the mechanism of how the bias of ML estimates emerges, and show that the differential geometric properties of geometric constraints used in the problems determines the magnitude of bias. Based on this result, we present a numerical method of computing bias-corrected estimates.