# Gaussian Primitives for Deformable Image Registration

arXiv: https://arxiv.org/abs/2406.03394 · HTML: https://mlsanity.com/paper/2406.03394/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 70 references that are in the map.
- First posted on arXiv 5 Jun 2024.

## Builds on (most cited first, 27 of 27)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [GaussianFormer: Scene as Gaussians for Vision-Based 3D Semantic Occupancy Prediction](https://mlsanity.com/paper/2405.17429/) (2024)
- [SynthMorph: learning contrast-invariant registration without acquired images](https://mlsanity.com/paper/2004.10282/) (2020)
- [Multi-Scale 3D Gaussian Splatting for Anti-Aliased Rendering](https://mlsanity.com/paper/2311.17089/) (2023)
- [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020)
- [DynMF: Neural Motion Factorization for Real-time Dynamic View Synthesis with 3D Gaussian Splatting](https://mlsanity.com/paper/2312.00112/) (2023)
- [Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks](https://mlsanity.com/paper/2003.09514/) (2020)
- [GaussianImage: 1000 FPS Image Representation and Compression by 2D Gaussian Splatting](https://mlsanity.com/paper/2403.08551/) (2024)
- [HyperMorph: Amortized Hyperparameter Learning for Image Registration](https://mlsanity.com/paper/2101.01035/) (2021)
- [DiffuseMorph: Unsupervised Deformable Image Registration Using Diffusion Model](https://mlsanity.com/paper/2112.05149/) (2021)
- [Dual-Stream Pyramid Registration Network](https://mlsanity.com/paper/1909.11966/) (2019)
- [textttGradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency](https://mlsanity.com/paper/2206.05897/) (2022)
- [Fast 3D registration with accurate optimisation and little learning for Learn2Reg 2021](https://mlsanity.com/paper/2112.03053/) (2021)
- [Correlation-aware Coarse-to-fine MLPs for Deformable Medical Image Registration](https://mlsanity.com/paper/2406.00123/) (2024)
- [Learning the Effect of Registration Hyperparameters with HyperMorph](https://mlsanity.com/paper/2203.16680/) (2022)
- [NODEO: A Neural Ordinary Differential Equation Based Optimization Framework for Deformable Image Registration](https://mlsanity.com/paper/2108.03443/) (2021)
- [CNN-based Lung CT Registration with Multiple Anatomical Constraints](https://mlsanity.com/paper/2011.14372/) (2020)
- [ICON: Learning Regular Maps Through Inverse Consistency](https://mlsanity.com/paper/2105.04459/) (2021)
- [Estimation of Large Motion in Lung CT by Integrating Regularized Keypoint Correspondences into Dense Deformable Registration](https://mlsanity.com/paper/1807.00467/) (2018)
- [FSDiffReg: Feature-wise and Score-wise Diffusion-guided Unsupervised Deformable Image Registration for Cardiac Images](https://mlsanity.com/paper/2307.12035/) (2023)
- [Robust deformable image registration using cycle-consistent implicit representations](https://mlsanity.com/paper/2310.01934/) (2023)
- [Inverse Consistency by Construction for Multistep Deep Registration](https://mlsanity.com/paper/2305.00087/) (2023)

## Built on by (most cited first, 2 of 2)

- [Disentangling Progress in Medical Image Registration: Beyond Trend-Driven Architectures towards Domain-Specific Strategies](https://mlsanity.com/paper/2512.01913/) (2025)
- [Implicit representations are dead. Long live explicit primitives!](https://mlsanity.com/paper/2608.10001/) (2026)

## Abstract (arXiv)

Deformable Image Registration (DIR) is essential for aligning medical images that exhibit anatomical variations, facilitating applications such as disease tracking and radiotherapy planning. While classical iterative methods and deep learning approaches have achieved success in DIR, they are often hindered by computational inefficiency or poor generalization. In this paper, we introduce GaussianDIR, a novel, case-specific optimization DIR method inspired by 3D Gaussian splatting. In general, GaussianDIR represents image deformations using a sparse set of mobile and flexible Gaussian primitives, each defined by a center position, covariance, and local rigid transformation. This compact and explicit representation reduces noise and computational overhead while improving interpretability. Furthermore, the movement of individual voxel is derived via blending the local rigid transformation of the neighboring Gaussian primitives. By this, GaussianDIR captures both global smoothness and local rigidity as well as reduces the computational burden. To address varying levels of deformation complexity, GaussianDIR also integrates an adaptive density control mechanism that dynamically adjusts the density of Gaussian primitives. Additionally, we employ multi-scale Gaussian primitives to capture both coarse and fine deformations, reducing optimization to local minima. Experimental results on brain MRI, lung CT, and cardiac MRI datasets demonstrate that GaussianDIR outperforms existing DIR methods in both accuracy and efficiency, highlighting its potential for clinical applications. Finally, as a training-free approach, it challenges the stereotype that iterative methods are inherently slow and transcend the limitations of poor generalization.