In this paper, we investigate the estimation of the maximum target registration error (TRE) magnitude of the target location while using point-based rigid registration in the image guided system. Under the uniform restriction of fiducial localization error (FLE) magnitude, we explicitly formulate the estimation as an optimization problem. Through analyzing the approximated problem which assumes the rigidity of the fiducial set holds with the perturbation of FLE, we present a strict lower bound for the maximum TRE magnitude. The simulations show that the lower bound is close to the actual maximum TRE magnitude for the target locations lying far away from the fiducial points. Unlike the expected TRE magnitude in which all fiducial points contribute, the lower bound is only related to the fiducial points serving as the vertices of the convex hull of the fiducial set. Our analysis provides a new perspective of investigating the problem of TRE estimation and is helpful for the surgeons to learn about the worst situation during using the image guided system.