Searcharxiv⌕ Search

arXiv subjects

Moti Freiman

Publications and source records attributed to Moti Freiman.

At least 37 records · Page 2Linked to original sources

A self-attention model for robust rigid slice-to-volume registration of functional MRI

Functional Magnetic Resonance Imaging (fMRI) is vital in neuroscience, enabling investigations into brain disorders, treatment monitoring, and brain function mapping. However, head motion during fMRI scans, occurring between shots of slice acquisition, can result in distortion, biased analyses, and increased costs due to the need for scan repetitions. Therefore, retrospective slice-level motion correction through slice-to-volume registration (SVR) is crucial. Previous studies have utilized deep learning (DL) based models to address the SVR task; however, they overlooked the uncertainty stemming from the input stack of slices and did not assign weighting or scoring to each slice. In this work, we introduce an end-to-end SVR model for aligning 2D fMRI slices with a 3D reference volume, incorporating a self-attention mechanism to enhance robustness against input data variations and uncertainties. It utilizes independent slice and volume encoders and a self-attention module to assign pixel-wise scores for each slice. We conducted evaluation experiments on 200 images involving synthetic rigid motion generated from 27 subjects belonging to the test set, from the publicly available Healthy Brain Network (HBN) dataset. Our experimental results demonstrate that our model achieves competitive performance in terms of alignment accuracy compared to state-of-the-art deep learning-based methods (Euclidean distance of $0.93$ [mm] vs. $1.86$ [mm]). Furthermore, our approach exhibits significantly faster registration speed compared to conventional iterative methods ($0.096$ sec. vs. $1.17$ sec.). Our end-to-end SVR model facilitates real-time head motion tracking during fMRI acquisition, ensuring reliability and robustness against uncertainties in inputs. source code, which includes the training and evaluations, will be available soon.

cs.CV↗

NPB-REC: A Non-parametric Bayesian Deep-learning Approach for Undersampled MRI Reconstruction with Uncertainty Estimation

The ability to reconstruct high-quality images from undersampled MRI data is vital in improving MRI temporal resolution and reducing acquisition times. Deep learning methods have been proposed for this task, but the lack of verified methods to quantify the uncertainty in the reconstructed images hampered clinical applicability. We introduce "NPB-REC", a non-parametric fully Bayesian framework, for MRI reconstruction from undersampled data with uncertainty estimation. We use Stochastic Gradient Langevin Dynamics during training to characterize the posterior distribution of the network parameters. This enables us to both improve the quality of the reconstructed images and quantify the uncertainty in the reconstructed images. We demonstrate the efficacy of our approach on a multi-coil MRI dataset from the fastMRI challenge and compare it to the baseline End-to-End Variational Network (E2E-VarNet). Our approach outperforms the baseline in terms of reconstruction accuracy by means of PSNR and SSIM ($34.55$, $0.908$ vs. $33.08$, $0.897$, $p<0.01$, acceleration rate $R=8$) and provides uncertainty measures that correlate better with the reconstruction error (Pearson correlation, $R=0.94$ vs. $R=0.91$). Additionally, our approach exhibits better generalization capabilities against anatomical distribution shifts (PSNR and SSIM of $32.38$, $0.849$ vs. $31.63$, $0.836$, $p<0.01$, training on brain data, inference on knee data, acceleration rate $R=8$). NPB-REC has the potential to facilitate the safe utilization of deep learning-based methods for MRI reconstruction from undersampled data. Code and trained models are available at \url{https://github.com/samahkh/NPB-REC}.

cs.CV↗

Lirot.ai: A Novel Platform for Crowd-Sourcing Retinal Image Segmentations

Introduction: For supervised deep learning (DL) tasks, researchers need a large annotated dataset. In medical data science, one of the major limitations to develop DL models is the lack of annotated examples in large quantity. This is most often due to the time and expertise required to annotate. We introduce Lirot. ai, a novel platform for facilitating and crowd-sourcing image segmentations. Methods: Lirot. ai is composed of three components; an iPadOS client application named Lirot. ai-app, a backend server named Lirot. ai-server and a python API name Lirot. ai-API. Lirot. ai-app was developed in Swift 5.6 and Lirot. ai-server is a firebase backend. Lirot. ai-API allows the management of the database. Lirot. ai-app can be installed on as many iPadOS devices as needed so that annotators may be able to perform their segmentation simultaneously and remotely. We incorporate Apple Pencil compatibility, making the segmentation faster, more accurate, and more intuitive for the expert than any other computer-based alternative. Results: We demonstrate the usage of Lirot. ai for the creation of a retinal fundus dataset with reference vasculature segmentations. Discussion and future work: We will use active learning strategies to continue enlarging our retinal fundus dataset by including a more efficient process to select the images to be annotated and distribute them to annotators.

cs.CV↗

MA-RECON: Mask-aware deep-neural-network for robust fast MRI k-space interpolation

High-quality reconstruction of MRI images from under-sampled `k-space' data, which is in the Fourier domain, is crucial for shortening MRI acquisition times and ensuring superior temporal resolution. Over recent years, a wealth of deep neural network (DNN) methods have emerged, aiming to tackle the complex, ill-posed inverse problem linked to this process. However, their instability against variations in the acquisition process and anatomical distribution exposes a deficiency in the generalization of relevant physical models within these DNN architectures. The goal of our work is to enhance the generalization capabilities of DNN methods for k-space interpolation by introducing `MA-RECON', an innovative mask-aware DNN architecture and associated training method. Unlike preceding approaches, our `MA-RECON' architecture encodes not only the observed data but also the under-sampling mask within the model structure. It implements a tailored training approach that leverages data generated with a variety of under-sampling masks to stimulate the model's generalization of the under-sampled MRI reconstruction problem. Therefore, effectively represents the associated inverse problem, akin to the classical compressed sensing approach. The benefits of our MA-RECON approach were affirmed through rigorous testing with the widely accessible fastMRI dataset. Compared to standard DNN methods and DNNs trained with under-sampling mask augmentation, our approach demonstrated superior generalization capabilities. This resulted in a considerable improvement in robustness against variations in both the acquisition process and anatomical distribution, especially in regions with pathology. In conclusion, our mask-aware strategy holds promise for enhancing the generalization capacity and robustness of DNN-based methodologies for MRI reconstruction from undersampled k-space data.

eess.IV↗

LUNet: Deep Learning for the Segmentation of Arterioles and Venules in High Resolution Fundus Images

The retina is the only part of the human body in which blood vessels can be accessed non-invasively using imaging techniques such as digital fundus images (DFI). The spatial distribution of the retinal microvasculature may change with cardiovascular diseases and thus the eyes may be regarded as a window to our hearts. Computerized segmentation of the retinal arterioles and venules (A/V) is essential for automated microvasculature analysis. Using active learning, we created a new DFI dataset containing 240 crowd-sourced manual A/V segmentations performed by fifteen medical students and reviewed by an ophthalmologist, and developed LUNet, a novel deep learning architecture for high resolution A/V segmentation. LUNet architecture includes a double dilated convolutional block that aims to enhance the receptive field of the model and reduce its parameter count. Furthermore, LUNet has a long tail that operates at high resolution to refine the segmentation. The custom loss function emphasizes the continuity of the blood vessels. LUNet is shown to significantly outperform two state-of-the-art segmentation algorithms on the local test set as well as on four external test sets simulating distribution shifts across ethnicity, comorbidities, and annotators. We make the newly created dataset open access (upon publication).

eess.IV↗

PCMC-T1: Free-breathing myocardial T1 mapping with Physically-Constrained Motion Correction

T1 mapping is a quantitative magnetic resonance imaging (qMRI) technique that has emerged as a valuable tool in the diagnosis of diffuse myocardial diseases. However, prevailing approaches have relied heavily on breath-hold sequences to eliminate respiratory motion artifacts. This limitation hinders accessibility and effectiveness for patients who cannot tolerate breath-holding. Image registration can be used to enable free-breathing T1 mapping. Yet, inherent intensity differences between the different time points make the registration task challenging. We introduce PCMC-T1, a physically-constrained deep-learning model for motion correction in free-breathing T1 mapping. We incorporate the signal decay model into the network architecture to encourage physically-plausible deformations along the longitudinal relaxation axis. We compared PCMC-T1 to baseline deep-learning-based image registration approaches using a 5-fold experimental setup on a publicly available dataset of 210 patients. PCMC-T1 demonstrated superior model fitting quality (R2: 0.955) and achieved the highest clinical impact (clinical score: 3.93) compared to baseline methods (0.941, 0.946 and 3.34, 3.62 respectively). Anatomical alignment results were comparable (Dice score: 0.9835 vs. 0.984, 0.988). Our code and trained models are available at https://github.com/eyalhana/PCMC-T1.

eess.IV↗

P2T2: a Physically-primed deep-neural-network approach for robust $T_{2}$ distribution estimation from quantitative $T_{2}$-weighted MRI

Estimating $T_2$ relaxation time distributions from multi-echo $T_2$-weighted MRI ($T_2W$) data can provide valuable biomarkers for assessing inflammation, demyelination, edema, and cartilage composition in various pathologies, including neurodegenerative disorders, osteoarthritis, and tumors. Deep neural network (DNN) based methods have been proposed to address the complex inverse problem of estimating $T_2$ distributions from MRI data, but they are not yet robust enough for clinical data with low Signal-to-Noise ratio (SNR) and are highly sensitive to distribution shifts such as variations in echo-times (TE) used during acquisition. Consequently, their application is hindered in clinical practice and large-scale multi-institutional trials with heterogeneous acquisition protocols. We propose a physically-primed DNN approach, called $P_2T_2$, that incorporates the signal decay forward model in addition to the MRI signal into the DNN architecture to improve the accuracy and robustness of $T_2$ distribution estimation. We evaluated our $P_2T_2$ model in comparison to both DNN-based methods and classical methods for $T_2$ distribution estimation using 1D and 2D numerical simulations along with clinical data. Our model improved the baseline model's accuracy for low SNR levels ($SNR<80$) which are common in the clinical setting. Further, our model achieved a $\sim$35\% improvement in robustness against distribution shifts in the acquisition process compared to previously proposed DNN models. Finally, Our $P_2T_2$ model produces the most detailed Myelin-Water fraction maps compared to baseline approaches when applied to real human MRI data. Our $P_2T_2$ model offers a reliable and precise means of estimating $T_2$ distributions from MRI data and shows promise for use in large-scale multi-institutional trials with heterogeneous acquisition protocols.

eess.SP↗

Patient-level Microsatellite Stability Assessment from Whole Slide Images By Combining Momentum Contrast Learning and Group Patch Embeddings

Assessing microsatellite stability status of a patient's colorectal cancer is crucial in personalizing treatment regime. Recently, convolutional-neural-networks (CNN) combined with transfer-learning approaches were proposed to circumvent traditional laboratory testing for determining microsatellite status from hematoxylin and eosin stained biopsy whole slide images (WSI). However, the high resolution of WSI practically prevent direct classification of the entire WSI. Current approaches bypass the WSI high resolution by first classifying small patches extracted from the WSI, and then aggregating patch-level classification logits to deduce the patient-level status. Such approaches limit the capacity to capture important information which resides at the high resolution WSI data. We introduce an effective approach to leverage WSI high resolution information by momentum contrastive learning of patch embeddings along with training a patient-level classifier on groups of those embeddings. Our approach achieves up to 7.4\% better accuracy compared to the straightforward patch-level classification and patient level aggregation approach with a higher stability (AUC, $0.91 \pm 0.01$ vs. $0.85 \pm 0.04$, p-value$<0.01$). Our code can be found at https://github.com/TechnionComputationalMRILab/colorectal_cancer_ai.

cs.CV↗

qDWI-Morph: Motion-compensated quantitative Diffusion-Weighted MRI analysis for fetal lung maturity assessment

Quantitative analysis of fetal lung Diffusion-Weighted MRI (DWI) data shows potential in providing quantitative imaging biomarkers that indirectly reflect fetal lung maturation. However, fetal motion during the acquisition hampered quantitative analysis of the acquired DWI data and, consequently, reliable clinical utilization. We introduce qDWI-morph, an unsupervised deep-neural-network architecture for motion compensated quantitative DWI (qDWI) analysis. Our approach couples a registration sub-network with a quantitative DWI model fitting sub-network. We simultaneously estimate the qDWI parameters and the motion model by minimizing a bio-physically-informed loss function integrating a registration loss and a model fitting quality loss. We demonstrated the added-value of qDWI-morph over: 1) a baseline qDWI analysis without motion compensation and 2) a baseline deep-learning model incorporating registration loss solely. The qDWI-morph achieved a substantially improved correlation with the gestational age through in-vivo qDWI analysis of fetal lung DWI data (R-squared=0.32 vs. 0.13, 0.28). Our qDWI-morph has the potential to enable motion-compensated quantitative analysis of DWI data and to provide clinically feasible bio-markers for non-invasive fetal lung maturity assessment. Our code is available at: https://github.com/TechnionComputationalMRILab/qDWI-Morph.

cs.CV↗

NPB-REC: Non-parametric Assessment of Uncertainty in Deep-learning-based MRI Reconstruction from Undersampled Data

Uncertainty quantification in deep-learning (DL) based image reconstruction models is critical for reliable clinical decision making based on the reconstructed images. We introduce "NPB-REC", a non-parametric fully Bayesian framework for uncertainty assessment in MRI reconstruction from undersampled "k-space" data. We use Stochastic gradient Langevin dynamics (SGLD) during the training phase to characterize the posterior distribution of the network weights. We demonstrated the added-value of our approach on the multi-coil brain MRI dataset, from the fastmri challenge, in comparison to the baseline E2E-VarNet with and without inference-time dropout. Our experiments show that NPB-REC outperforms the baseline by means of reconstruction accuracy (PSNR and SSIM of $34.55$, $0.908$ vs. $33.08$, $0.897$, $p<0.01$) in high acceleration rates ($R=8$). This is also measured in regions of clinical annotations. More significantly, it provides a more accurate estimate of the uncertainty that correlates with the reconstruction error, compared to the Monte-Carlo inference time Dropout method (Pearson correlation coefficient of $R=0.94$ vs. $R=0.91$). The proposed approach has the potential to facilitate safe utilization of DL based methods for MRI reconstruction from undersampled data. Code and trained models are available in \url{https://github.com/samahkh/NPB-REC}.

eess.IV↗

PVBM: A Python Vasculature Biomarker Toolbox Based On Retinal Blood Vessel Segmentation

Introduction: Blood vessels can be non-invasively visualized from a digital fundus image (DFI). Several studies have shown an association between cardiovascular risk and vascular features obtained from DFI. Recent advances in computer vision and image segmentation enable automatising DFI blood vessel segmentation. There is a need for a resource that can automatically compute digital vasculature biomarkers (VBM) from these segmented DFI. Methods: In this paper, we introduce a Python Vasculature BioMarker toolbox, denoted PVBM. A total of 11 VBMs were implemented. In particular, we introduce new algorithmic methods to estimate tortuosity and branching angles. Using PVBM, and as a proof of usability, we analyze geometric vascular differences between glaucomatous patients and healthy controls. Results: We built a fully automated vasculature biomarker toolbox based on DFI segmentations and provided a proof of usability to characterize the vascular changes in glaucoma. For arterioles and venules, all biomarkers were significant and lower in glaucoma patients compared to healthy controls except for tortuosity, venular singularity length and venular branching angles. Conclusion: We have automated the computation of 11 VBMs from retinal blood vessel segmentation. The PVBM toolbox is made open source under a GNU GPL 3 license and is available on physiozoo.com (following publication).

cs.CV↗

SUPER-IVIM-DC: Intra-voxel incoherent motion based Fetal lung maturity assessment from limited DWI data using supervised learning coupled with data-consistency

Intra-voxel incoherent motion (IVIM) analysis of fetal lungs Diffusion-Weighted MRI (DWI) data shows potential in providing quantitative imaging bio-markers that reflect, indirectly, diffusion and pseudo-diffusion for non-invasive fetal lung maturation assessment. However, long acquisition times, due to the large number of different ``b-value'' images required for IVIM analysis, precluded clinical feasibility. We introduce SUPER-IVIM-DC a deep-neural-networks (DNN) approach which couples supervised loss with a data-consistency term to enable IVIM analysis of DWI data acquired with a limited number of b-values. We demonstrated the added-value of SUPER-IVIM-DC over both classical and recent DNN approaches for IVIM analysis through numerical simulations, healthy volunteer study, and IVIM analysis of fetal lung maturation from fetal DWI data. Our numerical simulations and healthy volunteer study show that SUPER-IVIM-DC estimates of the IVIM model parameters from limited DWI data had lower normalized root mean-squared error compared to previous DNN-based approaches. Further, SUPER-IVIM-DC estimates of the pseudo-diffusion fraction parameter from limited DWI data of fetal lungs correlate better with gestational age compared to both to classical and DNN-based approaches (0.555 vs. 0.463 and 0.310). SUPER-IVIM-DC has the potential to reduce the long acquisition times associated with IVIM analysis of DWI data and to provide clinically feasible bio-markers for non-invasive fetal lung maturity assessment.

cs.CV↗

PD-DWI: Predicting response to neoadjuvant chemotherapy in invasive breast cancer with Physiologically-Decomposed Diffusion-Weighted MRI machine-learning model

Early prediction of pathological complete response (pCR) following neoadjuvant chemotherapy (NAC) for breast cancer plays a critical role in surgical planning and optimizing treatment strategies. Recently, machine and deep-learning based methods were suggested for early pCR prediction from multi-parametric MRI (mp-MRI) data including dynamic contrast-enhanced MRI and diffusion-weighted MRI (DWI) with moderate success. We introduce PD-DWI, a physiologically decomposed DWI machine-learning model to predict pCR from DWI and clinical data. Our model first decomposes the raw DWI data into the various physiological cues that are influencing the DWI signal and then uses the decomposed data, in addition to clinical variables, as the input features of a radiomics-based XGBoost model. We demonstrated the added-value of our PD-DWI model over conventional machine-learning approaches for pCR prediction from mp-MRI data using the publicly available Breast Multi-parametric MRI for prediction of NAC Response (BMMR2) challenge. Our model substantially improves the area under the curve (AUC), compared to the current best result on the leaderboard (0.8849 vs. 0.8397) for the challenge test set. PD-DWI has the potential to improve prediction of pCR following NAC for breast cancer, reduce overall mp-MRI acquisition times and eliminate the need for contrast-agent injection.

eess.IV↗

Image translation of Ultrasound to Pseudo Anatomical Display by CycleGAN

Ultrasound is the second most used modality in medical imaging. It is cost effective, hazardless, portable and implemented routinely in numerous clinical procedures. Nonetheless, image quality is characterized by granulated appearance, poor SNR and speckle noise. Specific for malignant tumors, the margins are blurred and indistinct. Thus, there is a great need for improving ultrasound image quality. We hypothesize that this can be achieved, using neural networks, by translation into a more realistic display which mimics an anatomical cut through the tissue. In order to achieve this goal, the preferable approach would be to use a set of paired images. However, this is practically impossible in our case. Therefore, Cycle Generative Adversarial Network (CycleGAN) was used, in order to learn each domain properties separately and enforce cross domain cycle consistency. The two datasets which were used for training the model were "Breast Ultrasound Images" (BUSI) and a set of optic images of poultry breast tissue samples acquired at our lab. The generated pseudo anatomical images provide improved visual discrimination of the lesions with clearer border definition and pronounced contrast. In order to evaluate the preservation of the anatomical features, the lesions in the ultrasonic images and the generated pseudo anatomical images were both automatically segmented and compared. This comparison yielded median dice score of 0.91 for the benign tumors and 0.70 for the malignant ones. The median lesion center error was 0.58% and 3.27% for the benign and malignancies respectively and the median area error index was 0.40% and 4.34% for the benign and malignancies respectively. In conclusion, these generated pseudo anatomical images, which are presented in a more intuitive way, enhance tissue anatomy and can potentially simplify the diagnosis and improve the clinical outcome.

eess.IV↗

NPBDREG: Uncertainty Assessment in Diffeomorphic Brain MRI Registration using a Non-parametric Bayesian Deep-Learning Based Approach

Quantification of uncertainty in deep-neural-networks (DNN) based image registration algorithms plays a critical role in the deployment of image registration algorithms for clinical applications such as surgical planning, intraoperative guidance, and longitudinal monitoring of disease progression or treatment efficacy as well as in research-oriented processing pipelines. Currently available approaches for uncertainty estimation in DNN-based image registration algorithms may result in sub-optimal clinical decision making due to potentially inaccurate estimation of the uncertainty of the registration stems for the assumed parametric distribution of the registration latent space. We introduce NPBDREG, a fully non-parametric Bayesian framework for uncertainty estimation in DNN-based deformable image registration by combining an Adam optimizer with stochastic gradient Langevin dynamics (SGLD) to characterize the underlying posterior distribution through posterior sampling. Thus, it has the potential to provide uncertainty estimates that are highly correlated with the presence of out of distribution data. We demonstrated the added-value of NPBDREG, compared to the baseline probabilistic VoxelMorph model (PrVXM), on brain MRI image registration using $390$ image pairs from four publicly available databases: MGH10, CMUC12, ISBR18 and LPBA40. The NPBDREG shows a better correlation of the predicted uncertainty with out-of-distribution data ($r>0.95$ vs. $r<0.5$) as well as a 7.3%improvement in the registration accuracy (Dice score, $0.74$ vs. $0.69$, $p \ll 0.01$), and 18% improvement in registration smoothness (percentage of folds in the deformation field, 0.014 vs. 0.017, $p \ll 0.01$). Finally, NPBDREG demonstrated a better generalization capability for data corrupted by a mixed structure noise (Dice score of $0.73$ vs. $0.69$, $p \ll 0.01$) compared to the baseline PrVXM approach.

cs.CV↗

Non Parametric Data Augmentations Improve Deep-Learning based Brain Tumor Segmentation

Automatic brain tumor segmentation from Magnetic Resonance Imaging (MRI) data plays an important role in assessing tumor response to therapy and personalized treatment stratification.Manual segmentation is tedious and subjective.Deep-learning-based algorithms for brain tumor segmentation have the potential to provide objective and fast tumor segmentation.However, the training of such algorithms requires large datasets which are not always available. Data augmentation techniques may reduce the need for large datasets.However current approaches are mostly parametric and may result in suboptimal performance.We introduce two non-parametric methods of data augmentation for brain tumor segmentation: the mixed structure regularization (MSR) and shuffle pixels noise (SPN).We evaluated the added value of the MSR and SPN augmentation on the brain tumor segmentation (BraTS) 2018 challenge dataset with the encoder-decoder nnU-Net architecture as the segmentation algorithm.Both MSR and SPN improve the nnU-Net segmentation accuracy compared to parametric Gaussian noise augmentation.Mean dice score increased from 80% to 82% and p-values=0.0022, 0.0028 when comparing MSR to non-parametric augmentation for the tumor core and whole tumor experiments respectively.The proposed MSR and SPN augmentations have the potential to improve neural-networks performance in other tasks as well.

eess.IV↗

Deep-Learning based Motion Correction for Myocardial T1 Mapping

Myocardial T1 mapping is a cardiac MRI technique, used to assess myocardial fibrosis. In this technique, a series of T1-weighted MRI images are acquired with different saturation or inversion times. These images are fitted to the T1 model to estimate the model parameters and construct the desired T1 maps. In the presence of motion, the different T1-weighted images are not aligned. This, in turn, will cause errors and inaccuracies in the final estimation of the T1 maps. Therefore, motion correction is a necessary process for myocardial T1 mapping. We present a deep-learning (DL) based system for cardiac T1-weighted MRI images motion correction. When applying our DL-based motion correction system we achieve a statistically significant improved performance by means of R2 of the model fitting regression, in compared to the model fitting regression without motion correction (0.52 vs 0.29, p<0.05).

eess.IV↗

Unsupervised Deep-Learning Based Deformable Image Registration: A Bayesian Framework

Unsupervised deep-learning (DL) models were recently proposed for deformable image registration tasks. In such models, a neural-network is trained to predict the best deformation field by minimizing some dissimilarity function between the moving and the target images. After training on a dataset without reference deformation fields available, such a model can be used to rapidly predict the deformation field between newly seen moving and target images. Currently, the training process effectively provides a point-estimate of the network weights rather than characterizing their entire posterior distribution. This may result in a potential over-fitting which may yield sub-optimal results at inference phase, especially for small-size datasets, frequently present in the medical imaging domain. We introduce a fully Bayesian framework for unsupervised DL-based deformable image registration. Our method provides a principled way to characterize the true posterior distribution, thus, avoiding potential over-fitting. We used stochastic gradient Langevin dynamics (SGLD) to conduct the posterior sampling, which is both theoretically well-founded and computationally efficient. We demonstrated the added-value of our Basyesian unsupervised DL-based registration framework on the MNIST and brain MRI (MGH10) datasets in comparison to the VoxelMorph unsupervised DL-based image registration framework. Our experiments show that our approach provided better estimates of the deformation field by means of improved mean-squared-error ($0.0063$ vs. $0.0065$) and Dice coefficient ($0.73$ vs. $0.71$) for the MNIST and the MGH10 datasets respectively. Further, our approach provides an estimate of the uncertainty in the deformation-field by characterizing the true posterior distribution.

cs.CV↗