% \begin{figure}
%     \centering
%     \begin{minipage}[c]{0.75\textwidth}
%         \centering
%         \includegraphics[width=1\linewidth]{5_results/figures/uncertainty/uncertainty_grid_patients.png}
%     \end{minipage}
%     \hfill
%     \begin{minipage}[c]{0.24\textwidth}
%         \centering
%         \includegraphics[width=\linewidth]{5_results/figures/uncertainty/uncertainty_boxplot_ALL.png}
%     \end{minipage}
%     \caption{Uncertainty calculation of each landmark when dropout rate is $0.1$.}
%     \label{fig:uncertainty_plot}
% \end{figure}


\begin{figure}
    \centering
    \includegraphics[width=1\linewidth]{5_results/figures/image_dropout/dropout_analysis_baseline.png}
    \caption{Mean error as samples are removed in order of their estimated uncertainty. The curves show the reduction in mean rotation (left) and translation (right) errors as the most uncertain samples are progressively filtered out (0\% to 100\%).}
    \label{fig:image_dropout}
\end{figure}

\section{Conclusion}
% In this work, we presented a novel uncertainty-aware framework for 2D/3D landmark-based pelvis registration. By integrating MC dropout into a U-Net landmark detector, we enabled the estimation of per-landmark reliability scores without requiring addtiional ground truth labels. Our experiments demonstrate that automated anatomical landmarks vary significantly in their reliability and that blind trust in all detected points is suboptimal for registration. We showed that filtering a subset of highly uncertain landmarks improves pose estimation accuracy by removing outliers that would otherwise skew the non-linear optimization. Importantly, we established that this filtering must be balanced against the need for geometric redundancy as excessive removal of landmarks destabilizes the pose estimation. Ultimately, this method offers a path toward more robust image-guided surgery, allowing registration pipelines to ``know what they do not know'' and prioritize high confidence anatomical landmark for precise surgical navigation.
% In this work, we presented an uncertainty-aware framework for 2D/3D landmark-based pelvis registration. By integrating MC dropout into a U-Net landmark detector, we enabled the estimation of per-landmark reliability scores per-image without requiring additional ground truth labels. Our experiments demonstrate that each landmarks vary significantly in their reliability and that blind trust in all detected points is suboptimal for registration. 
% % We established that incorporating these reliability scores into the training process via continuous weighting achieves the highest pose estimation accuracy, as it prevents the model from overfitting to ambiguous labels. 
% We established that incorporating these reliability scores using uncertainty-based weighting for training and inference both achieve best pose estimation accuracy. Furthermore, we showed that uncertainty-based filtering at inference serves as an effective safeguard against residual outliers, provided that geometric redundancy is maintained. Ultimately, this method offers a path toward more robust image-guided surgery, allowing registration pipelines to ``know what they do not know'' and prioritize high-confidence anatomical landmarks for precise surgical navigation.
% We present an uncertainty-aware framework for landmark-based 2D/3D pelvis registration that integrates epistemic uncertainty into both continuous weighting and discrete landmark selection. By estimating per-landmark reliability with MC dropout and incorporating these estimates into the PnP formulation, our method reduces sensitivity to erroneous detections and substantially improves rotational and translational accuracy compared to conventional landmark-based registration. The results demonstrate that uncertainty provides a principled mechanism for identifying unreliable keypoints, stabilizing pose estimation, and enabling graceful failure on ambiguous frames. While remaining limited by the subjective nature of anatomical landmark definitions and fixed hyperparameters, this framework establishes a foundation for adaptive, uncertainty-guided registration strategies and suggests future opportunities for fully automated, label-free geometric feature selection in image-guided surgical workflows.

We present an uncertainty-aware framework for landmark-based 2D/3D pelvis registration that integrates epistemic uncertainty into both continuous weighting and discrete landmark selection. By estimating per-landmark reliability with MC dropout and incorporating these estimates into the PnP formulation, our method reduces sensitivity to erroneous detections and improves registration accuracy compared to conventional landmark-based registration. Across synthetic and fluoroscopy image evaluations, continuous weighting provided the most consistent gains, while discrete selection was beneficial primarily in the synthetic setting. Overall, these results demonstrate that uncertainty provides a principled mechanism for identifying unreliable keypoints, stabilizing pose estimation, and enabling graceful failure on ambiguous frames, with continuous weighting offering the most consistent improvements across both simulated and real fluoroscopic data.