A Statistical Model for Rigid Image Registration Performance: The Influence of Soft-Tissue Deformation as a Confounding Noise Source

Soft-tissue deformation presents a confounding factor to rigid image registration by introducing image content inconsistent with the underlying motion model, presenting non-correspondent structure with potentially high power, and creating local minima that challenge iterative optimization. In this paper, we introduce a model for registration performance that includes deformable soft tissue as a power-law noise distribution within a statistical framework describing the Cramer-Rao lower bound (CRLB) and root-mean-squared error (RMSE) in registration performance. The model incorporates both cross-correlation and gradient-based similarity metrics, and the model was tested in application to 3D-2D (CT-to-radiograph) and 3D-3D (CT-to-CT) image registration. Predictions accurately reflect the trends in registration error as a function of dose (quantum noise), and the choice of similarity metrics for both registration scenarios. Incorporating soft-tissue deformation as a noise source yields important insight on the limits of registration performance with respect to algorithm design and the clinical application or anatomical context. For example, the model quantifies the advantage of gradient-based similarity metrics in 3D-2D registration, identifies the low-dose limits of registration performance, and reveals the conditions for which the registration performance is fundamentally limited by soft-tissue deformation.