On the Degrees of Freedom of Gridded Control Points in Learning-Based Medical Image Registration
Authors: Wen Yan, Qianye Yang, Yipei Wang, Shonit Punwani, Mark Emberton, Vasilis Stavrinides, Yipeng Hu, Dean Barratt
Organizations: UCL Hawkes Institute; Department of Medical Physics and Biomedical Engineering, University College London, Gower St, London WC1E 6BT, London, U.K. · Centre for Medical Imaging, Division of Medicine, University College London, Gower St, London WC1E 6BT, London, U.K. · Division of Surgery and Interventional Science, University College London, 10 Pond St, London NW3 2PS, U.K. · Cancer Institute, Urology Department, UCL Hospital, University College London, 16-18 Westmoreland St, London W1G 8PH, U.K · Radiology Department, Imperial College Healthcare, The Bays, S Wharf Rd, London W2 1NY, U.K.
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.
Figures & tables
Figure 1: Demonstration of an illustrative example of false-positive correspondence (orange stars), possibly caused by similar intensity patterns (e.g., unsupervised loss similarity) or label errors (e.g., segmentation noise). A sparse low-resolution grid helps filter out such a noise, as stronger “true” correspondences (four corners of the shaded ROIs) dominate. In contrast, a finer high-resolution grid may amplify the noise, distorting additional control points within the ROIs and leading to inaccurate registration.
Figure 2: Illustration of GridReg. The encoder extracts multi-scale 3D feature maps; at each scale, a skip-projection flattens features into 1D tokens that are fused with grid-cell queries via (local) attention. The resulting features are mapped to a sparse control-point displacement field via Bayesian integration, and a dense displacement field (DDF) is obtained by interpolation (e.g., trilinear, B-spline, or transposed convolution).
Figure 3: Examples of anatomical landmarks annotated for the same patient at two different time points. The first and second rows show 5 landmarks at the first and second time points, respectively.
Figure 4: Examples of 7 landmarks labeled by experts in brain dataset.
Dataset
Metric
Original
ANTs SyN
VoxelMorph
TransMorph
KeyMorph
GridReg(Ours)
Prostate
Dice ↑
0.70 ± 0.10
0.81±0.05
0.86 ± 0.02
0.84 ± 0.03
0.86 ± 0.05
0.88 ± 0.02 ‡
DCDldmk↓ (mm)
9.60 ± 4.09
9.09 ± 8.09
8.76 ± 8.59
7.73 ± 6.98
3.98 ± 2.14
4.54 ± 2.77 †
DCDmsk↓ (mm)
8.76 ± 4.04
3.38 ± 0.78
2.70 ± 0.54
3.05 ± 0.84
2.56 ± 0.66
1.87 ± 1.16 ‡
GPU(Mb)
/
/
208
377
274
146
Pelvis
Dice ↑
0.53±0.17
0.69 ±0.09
0.73 ± 0.16
0.73 ± 0.09
0.79 ± 0.07
0.78 ± 0.09 †
DCDmsk↓ (mm)
10.65 ±5.85
6.03 ±2.78
5.99 ±5.68
4.47 ±2.95
4.14 ± 2.47
4.52 ± 2.88 †
Table 1: Performance and memory across methods. Values are mean ± SD over identical holdout test cases. Proposed methods appear in the last columns (GridReg). For each dataset, we compared GridReg to each baseline using paired, one-sided t-tests and controlled multiplicity within the family using BH-FDR ( 5% ); we report q-values. Bold indicates the best mean. ‡ denotes GridReg is significantly better than all baselines ( q<0.05 ); † denotes it is significantly better than three of baselines ( q<0.05 ). Slash / indicates that a result is not available.
Figure 5: Visualisation of prostate registration. The first column and the second column show four examples of the fixed and moving images, respectively. The next four columns show the registration results from (A)GridReg, (B) VoxelMorph, (C) KeyMorph, (D)TransMorph and (E) ANTs SyN, respectively.
Figure 6: Visualisation of brain registration. The first column and the second column show four examples of the fixed and moving images, respectively. The next four columns show the registration results from (A)GridReg, (B) VoxelMorph, (C) KeyMorph, (D)TransMorph and (E) ANTs SyN, respectively.
Setting
Grid
Base-NC
Upsample
Projector
Bayesian
Dice
DCDlmdk (mm)
Cost(Mb)
Config 1
5
32
trilinear
✓
✓
0.86 ± 0.05 ∗
5.29 ± 2.85
146
Config 2
10
32
trilinear
✓
✓
0.89 ± 0.03
4.89 ± 3.19
148
Config 3
10
8
trilinear
✓
✓
0.87 ± 0.04
5.88 ± 3.27
144
Config 4
10
16
trilinear
✓
✓
0.88 ± 0.02
4.54 ± 2.77
146
Config 5
10
16
trilinear
×
✓
0.86 ± 0.03 ∗
6.06 ± 3.23 ∗
145
Config 6
10
16
deconv
✓
✓
0.89 ± 0.04
4.18 ± 2.88
171
Table 3: Ablation study of proposed method with varying configuration of grid number, base channel of encoder, upsampling method and usage of projection module. The ablation studies are performed on holdout test set in Dataset 1. The symbol * represents that the best results have a statistical difference between Config 4 and other methods (all p−values< 0.050).
Figure 7: This figure shows four examples of uncertainty maps generated by the Bayesian Grid transformer. A lighter area in the Uncertainty map represents lower uncertainty, while a darker area represents higher uncertainty.
Dataset
Metric
GridReg Bayesian
GridReg
KeyMorph
VoxelMorph
TransMorph
Prostate
logdet(J)
0.0352±0.0193†
0.0446±0.0228∗
13.3064±32.1452
1.9258±1.0610
0.0975±0.0532
det(J)<0 (%)
0
0
3.8
0.4
0.03
Brain
logdet(J)
0.0022±0.0015†
0.0038±0.0014∗
55.2012±133.4529
1.0793±0.3254
15.9102±6.5335
det(J)<0 (%)
0
0
11.0
0.2
4.5
Table 4: Jacobian statistics across methods. logdet(J) is reported as mean ± standard deviation; folding rate is the percentage of voxels with det(J)<0 . For each dataset, we report paired, one-sided t-tests with BH-FDR(5%) with confidence α=0.05 . † and ∗ denote GridReg Bayesian and GridReg is significantly better than other methods, respectively.
Figure 8: (1)Effect of Bending Energy Weight on Segmentation Accuracy (DSC) and Contour Distance (CD); (2)-(3)Comparisons on Dataset1 showing Dice and centroid distance between separately trained and auto-adapted models with the same grid size range from 5 to 15.
Medical image registration aligns scans across time, patients, or imaging modalities to track anatomy and support diagnosis, treatment, and image-guided procedures.
We present MMD-Reg, a novel correspondence-free approach to point-cloud registration that is differentiable and has linear computational complexity in the number of points. We model registration as a nonlinear least-squares problem based on the Maximum Mean Discrepancy, approximated using random Fourier features. The resulting objective can be solved efficiently with standard methods such as Levenberg-Marquardt, and the solution is differentiable via the implicit function theorem. This allows MMD-Reg to be used as a differentiable optimization layer within end-to-end trainable models, supporting registration under challenging conditions such as poor initial alignment and partial overlap. We demonstrate this Neural MMD-Reg formulation by integrating the layer with a set transformer, training the resulting model in supervised and unsupervised settings, and comparing its performance against recent learning-based methods. We also evaluate standalone MMD-Reg, comparing its accuracy and scalability against widely used non-learning-based registration methods.
Rixon Crane, Fahira Afzal Maken, Nicholas Lawrance +4
Data61, CSIRO, Brisbane, Australia · Data61, CSIRO, Sydney, Australia · Work done while at Data61, CSIRO, Brisbane, Australia +3
Deformable registration is crucial in medical imaging. Several existing applications include lesion tracking, probabilistic atlas generation, and treatment response evaluation. However, current methods often lack robustness and generalizability across two key factors: spatial resolution and differences in anatomical coverage. We jointly optimize a registration field and a learnable dimensionality reduction module so that compressed VFM embeddings remain registration-relevant, and fuse these global semantic cues with MIND local descriptors. GLIDE-Reg achieves average dice similarity coefficients (DSC) across 6 anatomical structures of 0.859, 0.862, and 0.901 in two public cohorts (Lung250M and NLST) and one institution cohort (UCLA5DCT), and outperforms the state-of-the-art DEEDS (0.834, 0.858, 0.900) with relative improvements of 3.0%, 0.5%, and 0.1%. For target registration errors, GLIDE-Reg achieves 1.58 mm on Lung250M landmarks (compared to 1.25 mm on corrField and 1.91 mm on DEEDS) and 1.11 mm on NLST nodule centers (compared to 1.11 mm on DEEDS). The substantiated performance on the nodule centers also demonstrates its robustness across challenging downstream tasks, such as nodule tracking, which is an essential prior step for early-stage lung cancer diagnosis.
Yunzheng Zhu, Aichi Chien, Kimaya kulkarni +5
Medical & Imaging Informatics, Department of Radiological Sciences, David Geffen School of Medicine at UCLA, USA · Magnetic Resonance Research Labs, Department of Radiological Sciences, David Geffen School of Medicine at UCLA, USA · Department of Radiation Oncology, David Geffen School of Medicine at UCLA, Los Angeles, USA
Learning-based medical image registration has matched the accuracy of conventional methods while offering superior computational efficiency. However, existing approaches suffer from poor generalization across diverse clinical scenarios, requiring the laborious development of multiple isolated networks for specific registration tasks, e.g., inter-/intra-subject registration or anatomical region-specific alignment, leading to cumbersome development pipelines. To overcome this limitation, we propose UniReg, the first conditional unified model for multi-scenario medical image registration, which combines the precision advantages of task-specific learning methods with the generalization of traditional optimization methods. Our key innovation is a unified registration framework that adaptively estimates deformation fields conditioned on: (1) anatomical structure priors, (2) registration type constraints (inter/intra-subject), and (3) instance-specific features, enabling effective alignment across heterogeneous CT and MR registration scenarios within a single model. Through comprehensive experiments on multiple CT/MR registration datasets, UniReg achieves superior average registration accuracy compared with current state-of-the-art learning-based methods while exhibiting strong cross-scenario generalization. Moreover, by replacing multiple isolated task-specific models with a compact unified model, UniReg substantially reduces the overall training burden in terms of total training cost and model redundancy.
Zi Li, Jianpeng Zhang, Tai Ma +7
Department of Electrical and Computer Engineering, The University of Hong Kong, Hong Kong SAR, China · DAMO Academy, Alibaba Group · The First Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou, China +1