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Image registration is a single point of failure in the image-guided computer-assisted surgery. Registration is primarily used to align and fuse the data sets taken from patient's anatomy before and during surgeries. Point-based rigid-body registration is usually performed by identifying corresponding fiducials (either natural landmarks or implanted ones) in the data sets. Since the localization of fiducials is imprecise and is generally perturbed by random noise, the performed registration is imperfect and has some error. Previous work has extensively analyzed the behavior of this error when the fiducial localization error has zero-mean over the entire set of fiducials. However, if noise has a nonzero-mean or a bias, no formulation yet exists to determine the effect of noise on the overall registration accuracy. In this work, we derive novel formulations that relate the bias in the localized fiducials to the accuracy of the performed registration. We analytically and numerically demonstrate that by eliminating the estimated bias from the measured fiducial locations, one can effectively increase the accuracy of the performed registration.