Uncertainty estimation and evaluation of deformation image registration based convolutional neural networks.

Objective&#xD;Fast and accurate deformable image registration (DIR) that include DIR uncertainty estimation are essential for safe and reliable clinical deployment. While recent deep learning models have shown promise in predicting DIR with its uncertainty, challenges persist in proper uncertainty evaluation and hyperparameter optimization for these methods. This work aims to develop and evaluate a model that can perform fast DIR and predict its uncertainty in seconds.&#xD;Approach&#xD;In this study, we introduce a novel probabilistic multi-resolution image registration model utilizing convolutional neural networks (CNNs) to estimate a multivariate normal distributed dense displacement field (DDF) in a multimodal image registration problem. To assess the quality of the DDF distribution predicted by the model, we propose a new metric based on the Kullback-Leibler divergence. The performance of our approach was evaluated against three other DIR algorithms (VoxelMorph, Monte Carlo Drop-Out, and Monte Carlo B-splines) capable of predicting uncertainty. The evaluation of the models included not only the quality of the deformation but also the reliability of the estimated uncertainty. Our application investigated registration of a treatment planning computed tomography (CT) to follow-up cone beam CT for daily adaptive radiotherapy.&#xD;Main results&#xD;The hyperparameter tuning of the models showed that there is a trade-off between the reliability of the estimated uncertainty and the accuracy of the deformation. In the optimal trade-off our model excelled in contour propagation and uncertainty estimation (p < 0.01) compared to existing uncertainty estimation models. We obtained an average dice similarity coefficient of 0.89 and a KL-divergence of 0.15.&#xD;Significance&#xD;By addressing challenges in DIR uncertainty estimation and evaluation, our work showed that both the DIR and its uncertainty can be reliably predicted paving the way for safe deployment in clinical environment.&#xD.