# On the Degrees of Freedom of Gridded Control Points in Learning-Based Medical Image Registration

arXiv: https://arxiv.org/abs/2603.16940 · HTML: https://mlsanity.com/paper/2603.16940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 41 references that are in the map.
- First posted on arXiv 15 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [SynthMorph: learning contrast-invariant registration without acquired images](https://mlsanity.com/paper/2004.10282/) (2020)
- [Learn2Reg: comprehensive multi-task medical image registration challenge, dataset and evaluation in the era of deep learning](https://mlsanity.com/paper/2112.04489/) (2021)
- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [Differentiable Registration of Images and LiDAR Point Clouds with VoxelPoint-to-Pixel Matching](https://mlsanity.com/paper/2312.04060/) (2023)
- [Real-time multimodal image registration with partial intraoperative point-set data](https://mlsanity.com/paper/2109.05023/) (2021)
- [Combiner and HyperCombiner Networks: Rules to Combine Multimodality MR Images for Prostate Cancer Localisation](https://mlsanity.com/paper/2307.08279/) (2023)
- [Cross-Modality Image Registration using a Training-Time Privileged Third Modality](https://mlsanity.com/paper/2207.12901/) (2022)
- [BrainMorph: A Foundational Keypoint Model for Robust and Flexible Brain MRI Registration](https://mlsanity.com/paper/2405.14019/) (2024)
- [Unsupervised End-to-end Learning for Deformable Medical Image Registration](https://mlsanity.com/paper/1711.08608/) (2017)

## Abstract (arXiv)

Many registration problems are ill-posed in homogeneous or noisy regions, and dense voxel-wise decoders can be unnecessarily high-dimensional. A sparse control-point parameterisation provides a compact, smooth deformation representation while reducing memory and improving stability. This work investigates the required control points for learning-based registration network development. We present GridReg, a learning-based registration framework that replaces dense voxel-wise decoding with displacement predictions at a sparse grid of control points. This design substantially cuts the parameter count and memory while retaining registration accuracy. Multiscale 3D encoder feature maps are flattened into a 1D token sequence with positional encoding to retain spatial context. The model then predicts a sparse gridded deformation field using a cross-attention module. We further introduce grid-adaptive training, enabling an adaptive model to operate at multiple grid sizes at inference without retraining. This work quantitatively demonstrates the benefits of using sparse grids. Using three data sets for registering prostate gland, pelvic organs and neurological structures, the results suggested a significant improvement with the usage of grid-controled displacement field. Alternatively, the superior registration performance was obtained using the proposed approach, with a similar or less computational cost, compared with existing algorithms that predict DDFs or displacements sampled on scattered key points.