Fast and Explicit: Slice-to-Volume Reconstruction via 3D Gaussian Primitives with Analytic Point Spread Function Modeling

Maik Dannecker, Steven Jia, Nil Stolt-Ansó, Nadine Girard, Guillaume Auzias, François Rousseau, Daniel Rueckert
Proceedings of The 9th International Conference on Medical Imaging with Deep Learning, PMLR 315:1473-1491, 2026.

Abstract

Recovering high-fidelity 3D images from sparse or degraded 2D images is a fundamental challenge in medical imaging, with broad applications ranging from 3D ultrasound reconstruction to MRI super-resolution. In the context of fetal MRI, high-resolution 3D reconstruction of the brain from motion-corrupted low-resolution 2D acquisitions is a prerequisite for accurate neurodevelopmental diagnosis. While implicit neural representations (INRs) have recently established state-of-the-art performance in self-supervised slice-to-volume reconstruction (SVR), they suffer from a critical computational bottleneck: accurately modeling the image acquisition physics requires expensive stochastic Monte Carlo sampling to approximate the point spread function (PSF). In this work, we propose a shift from neural network based implicit representations to Gaussian based explicit representations. By parameterizing the HR 3D image volume as a field of anisotropic Gaussian primitives, we leverage the property of Gaussians being closed under convolution and thus derive a closed-form analytical solution for the forward model. This formulation reduces the previously intractable acquisition integral to an exact covariance addition ($\mathbf{\Sigma}_{obs} = \mathbf{\Sigma}_{HR} + \mathbf{\Sigma}_{PSF}$), effectively bypassing the need for compute-intensive stochastic sampling while ensuring exact gradient propagation. We demonstrate that our approach matches the reconstruction quality of self-supervised state-of-the-art SVR frameworks while delivering a 5$\times$–10$\times$ speed-up on neonatal and fetal data. With convergence often reached in under 30 seconds, our framework paves the way towards translation into clinical routine of real-time fetal 3D MRI.

Cite this Paper

BibTeX
@InProceedings{pmlr-v315-dannecker26a, title = {Fast and Explicit: Slice-to-Volume Reconstruction via 3D Gaussian Primitives with Analytic Point Spread Function Modeling}, author = {Dannecker, Maik and Jia, Steven and Stolt-Ans{\'o}, Nil and Girard, Nadine and Auzias, Guillaume and Rousseau, Fran{\c{c}}ois and Rueckert, Daniel}, booktitle = {Proceedings of The 9th International Conference on Medical Imaging with Deep Learning}, pages = {1473--1491}, year = {2026}, editor = {Huo, Yuankai and Gao, Mingchen and Kuo, Chang-Fu and Jin, Yueming and Deng, Ruining}, volume = {315}, series = {Proceedings of Machine Learning Research}, month = {08--10 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v315/main/assets/dannecker26a/dannecker26a.pdf}, url = {https://proceedings.mlr.press/v315/dannecker26a.html}, abstract = {Recovering high-fidelity 3D images from sparse or degraded 2D images is a fundamental challenge in medical imaging, with broad applications ranging from 3D ultrasound reconstruction to MRI super-resolution. In the context of fetal MRI, high-resolution 3D reconstruction of the brain from motion-corrupted low-resolution 2D acquisitions is a prerequisite for accurate neurodevelopmental diagnosis. While implicit neural representations (INRs) have recently established state-of-the-art performance in self-supervised slice-to-volume reconstruction (SVR), they suffer from a critical computational bottleneck: accurately modeling the image acquisition physics requires expensive stochastic Monte Carlo sampling to approximate the point spread function (PSF). In this work, we propose a shift from neural network based implicit representations to Gaussian based explicit representations. By parameterizing the HR 3D image volume as a field of anisotropic Gaussian primitives, we leverage the property of Gaussians being closed under convolution and thus derive a closed-form analytical solution for the forward model. This formulation reduces the previously intractable acquisition integral to an exact covariance addition ($\mathbf{\Sigma}_{obs} = \mathbf{\Sigma}_{HR} + \mathbf{\Sigma}_{PSF}$), effectively bypassing the need for compute-intensive stochastic sampling while ensuring exact gradient propagation. We demonstrate that our approach matches the reconstruction quality of self-supervised state-of-the-art SVR frameworks while delivering a 5$\times$–10$\times$ speed-up on neonatal and fetal data. With convergence often reached in under 30 seconds, our framework paves the way towards translation into clinical routine of real-time fetal 3D MRI.} }
Endnote
%0 Conference Paper %T Fast and Explicit: Slice-to-Volume Reconstruction via 3D Gaussian Primitives with Analytic Point Spread Function Modeling %A Maik Dannecker %A Steven Jia %A Nil Stolt-Ansó %A Nadine Girard %A Guillaume Auzias %A François Rousseau %A Daniel Rueckert %B Proceedings of The 9th International Conference on Medical Imaging with Deep Learning %C Proceedings of Machine Learning Research %D 2026 %E Yuankai Huo %E Mingchen Gao %E Chang-Fu Kuo %E Yueming Jin %E Ruining Deng %F pmlr-v315-dannecker26a %I PMLR %P 1473--1491 %U https://proceedings.mlr.press/v315/dannecker26a.html %V 315 %X Recovering high-fidelity 3D images from sparse or degraded 2D images is a fundamental challenge in medical imaging, with broad applications ranging from 3D ultrasound reconstruction to MRI super-resolution. In the context of fetal MRI, high-resolution 3D reconstruction of the brain from motion-corrupted low-resolution 2D acquisitions is a prerequisite for accurate neurodevelopmental diagnosis. While implicit neural representations (INRs) have recently established state-of-the-art performance in self-supervised slice-to-volume reconstruction (SVR), they suffer from a critical computational bottleneck: accurately modeling the image acquisition physics requires expensive stochastic Monte Carlo sampling to approximate the point spread function (PSF). In this work, we propose a shift from neural network based implicit representations to Gaussian based explicit representations. By parameterizing the HR 3D image volume as a field of anisotropic Gaussian primitives, we leverage the property of Gaussians being closed under convolution and thus derive a closed-form analytical solution for the forward model. This formulation reduces the previously intractable acquisition integral to an exact covariance addition ($\mathbf{\Sigma}_{obs} = \mathbf{\Sigma}_{HR} + \mathbf{\Sigma}_{PSF}$), effectively bypassing the need for compute-intensive stochastic sampling while ensuring exact gradient propagation. We demonstrate that our approach matches the reconstruction quality of self-supervised state-of-the-art SVR frameworks while delivering a 5$\times$–10$\times$ speed-up on neonatal and fetal data. With convergence often reached in under 30 seconds, our framework paves the way towards translation into clinical routine of real-time fetal 3D MRI.
APA
Dannecker, M., Jia, S., Stolt-Ansó, N., Girard, N., Auzias, G., Rousseau, F. & Rueckert, D.. (2026). Fast and Explicit: Slice-to-Volume Reconstruction via 3D Gaussian Primitives with Analytic Point Spread Function Modeling. Proceedings of The 9th International Conference on Medical Imaging with Deep Learning, in Proceedings of Machine Learning Research 315:1473-1491 Available from https://proceedings.mlr.press/v315/dannecker26a.html.

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