Cancelling bias induced by correlation coefficient interpolation for sub-pixel image registration

Accurate sub-pixel image registration has many applications in precision engineering and manufacturing. Due to its computational efficiency, correlation-based sub-pixel image registration is especially useful for real-time applications. This paper presents a theoretical analysis of the bias induced by correlation coefficient interpolation, when employed to achieve two-dimensional sub-pixel registration resolution. An analytical model of bias in terms of true sub-pixel image shift is first derived according to the given reference image model. It is then used to establish an accurate bias map expressed explicitly in terms of sub-pixel image shift estimated from coefficient interpolation. This bias map is readily employed to eliminate the bias error and to significantly improve measurement accuracy for real-time applications. A bias cancellation scheme was implemented and verified by means of both computer simulation and experimental results. Specifically, sub-nanometre measurement precision was experimentally demonstrated using a microscopic vision system implemented for real-time motion tracking.