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

2025-12-12

AI Summary

To address the clinically critical challenge of reconstructing high-fidelity 3D fetal brain volumes from low-resolution, motion-corrupted 2D MRI slices, this work proposes an explicit voxel representation based on anisotropic 3D Gaussian primitives. Diverging from mainstream implicit neural representations, our approach is the first to explicitly model Gaussians for slice-to-volume reconstruction. Leveraging the closure property of Gaussian convolution, we derive an analytical forward model for the point spread function (PSF), reducing Monte Carlo sampling to efficient covariance matrix addition. This yields an end-to-end differentiable, physically interpretable, and computationally efficient optimization framework. Evaluated on both neonatal and fetal MRI datasets, our method achieves state-of-the-art reconstruction quality, accelerates inference by 5–10×, and typically completes single-volume optimization in ≤30 seconds—demonstrating strong potential for clinical real-time deployment.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 extit{closed-form analytical solution} for the forward model. This formulation reduces the previously intractable acquisition integral to an exact covariance addition ($mathbfΣ_{obs} = mathbfΣ_{HR} + mathbfΣ_{PSF}$), 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$ imes$--10$ imes$ 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. Code will be public at {https://github.com/m-dannecker/Gaussian-Primitives-for-Fast-SVR}.

Problem

• Reconstructs high-fidelity 3D images from sparse 2D medical scans
• Accelerates slice-to-volume reconstruction by replacing neural networks with Gaussians
• Enables real-time 3D fetal MRI reconstruction for clinical use

Innovation

• Uses explicit anisotropic Gaussian primitives for 3D representation
• Derives closed-form analytical solution for forward model via covariance addition
• Achieves 5-10x speed-up while matching state-of-the-art reconstruction quality