Deformable image registration (DIR) algorithms have inherent uncertainties in their displacement vector fields (DVFs).The purpose of this study is to develop an optimal metric to estimate DIR uncertainties. Six computational phantoms have been developed from the CT images of lung cancer patients using a finite element method (FEM). The FEM generated DVFs were used as a standard for registrations performed on each of these phantoms. A mechanics-based metric, unbalanced energy (UE), was developed to evaluate these registration DVFs. The potential correlation between UE and DIR errors was explored using multivariate analysis, and the results were validated by landmark approach and compared with two other error metrics: DVF inverse consistency (IC) and image intensity difference (ID). Landmark-based validation was performed using the POPI-model. The results show that the Pearson correlation coefficient between UE and DIR error is rUE-error = 0.50. This is higher than rIC-error = 0.29 for IC and DIR error and rID-error = 0.37 for ID and DIR error. The Pearson correlation coefficient between UE and the product of the DIR displacements and errors is rUE-error × DVF = 0.62 for the six patients and rUE-error × DVF = 0.73 for the POPI-model data. It has been demonstrated that UE has a strong correlation with DIR errors, and the UE metric outperforms the IC and ID metrics in estimating DIR uncertainties. The quantified UE metric can be a useful tool for adaptive treatment strategies, including probability-based adaptive treatment planning.
