Purpose: The accuracy of image registration is a critical factor in image-guidance systems, so it is important to quantifiably understand factors that fundamentally limit performance of the registration task. In this work, we extend a recently derived model for the effect of quantum noise on registration error to a more "generalized" model in which tissue deformation is incorporated as an additional source of "noise" described by a power-law distribution, analogous to "anatomical clutter" in signal detection theory. Methods: We apply a statistical framework that incorporates objective image quality factors such as spatial resolution and image noise combined with a statistical representation of anatomical clutter to predict the root-mean-squared error (RMSE) of transformation parameters in a rigid registration. Model predictions are compared to simulation studies in CT-to-CT slice registration using the cross-correlation (CC) similarity metric. Results: RMSE predictions are shown to accurately model the impact of dose and soft-tissue clutter on measured RMSE performance. Further, these predictions reveal dose levels at which the registration becomes soft-tissue clutter limited, where further increase provides no improvement in registration performance. Conclusions: Incorporating tissue deformation into a statistical registration model is an important step in understanding the limits of image registration performance and selecting pertinent registration methods for a particular registration task. The generalized noise model and RMSE analysis provide insight on how to optimize registration tasks with respect to image acquisition protocol (e.g., dose, reconstruction parameters) and registration method (e.g., level of blur).