Fig. 14:

Comparisons of the appearance uncertainty estimates derived from the predictive variance and the predicted model error. Left panel: Calibration plots and uncertainty calibration error (UCE) for TransMorph-Bayes on two inter-patient brain MR test sets (top), two atlas-to-patient brain MR test sets (middle), and two XCAT-to-CT test sets (bottom). The blue lines represent the results obtained using the uncertainty estimate ${\widehat{\Sigma }}_f^2$. The dashed lines represent the perfect calibration, which are the results achieved when the uncertainty estimate is ${\Sigma }_f^2$ or $err(I_m\circ \varphi )$ (i.e., the expected model error). The values are obtained from 10 repeated runs, and the shaded regions represent the standard deviation. Right panel: Visualization of the registration uncertainty on an inter-patient brain MRI test set (i.e., a-f), an atlas-to-patient brain MRI test set (i.e., g-l), and a CT test set (i.e., m-r). (a), (g), & (m): Moving image. (b), (h), & (n): Fixed image. (c), (i), & (o): Deformed moving image. (d), (j), & (p): Per-pixel uncertainty, represented by ${\Sigma }_f^2$, overlays the deformed image. (e), (k), & (q): Per-pixel uncertainty given by ${\Sigma }_f^2$ (i.e., the proposed method). (f), (l), & (r): Per-pixel uncertainty given by ${\widehat{\Sigma }}_f^2$. The yellow arrows highlight sites where ${\Sigma }_f^2$ identifies registration failures but ${\widehat{\Sigma }}_f^2$ does not.