Temporal Periodic Image Registration with Implicit Neural Representations

We address the problem of cross-domain image registration, where paired images exhibit coupled geometric misalignment and domain-specific appearance shift. We formalize this as a factorization problem: decomposing each image into a domain-invariant scene representation and a global appearance statistic, such that registration reduces to recombining the scene structure of the moving image with the appearance of the fixed image via Adaptive Instance Normalization (AdaIN). This factorization eliminates the need for explicit deformation field estimation. To exploit temporal coherence in sequential acquisitions, we introduce a position-encoded cross-frame attention mechanism that fuses learnable and sinusoidal position embeddings with multi-head attention over a sliding window of neighboring frames, enriching the scene representation with inter-frame context. We instantiate this framework as GPEReg-Net and evaluate on two benchmarks: FIRE-Reg-256 (retinal fundus, semi-rigid) and HPatches-Reg-256 (synthetic textured patches, affine). GPEReg-Net achieves state-of-the-art performance on both benchmarks (FIRE: SSIM = 0.928, PSNR = 33.47 dB; HPatches: SSIM = 0.450, PSNR = 21.01 dB), surpassing all baselines, including deformation-based methods, while running 1.87x faster than SAS-Net. Code: https://github.com/JiahaoQin/GPEReg-Net.

Implicit neural representations (INRs) have been applied to deformable image registration, where a lightweight network maps a spatial coordinate to a deformation vector. Because an INR encodes one specific signal in its parameters, a fresh network must be optimized for every image pair at test time, which is slow. Existing methods reduce this cost by meta-learning an initialization across a population of image pairs, and condition the weights of the INR globally, so the same conditioning applies at every coordinate while the deformation field it initializes varies across the domain. We propose LUMINR, a meta-learning framework that accelerates this per-pair fitting and in which the conditioning is local instead. LUMINR uses an INR that maps a coordinate, together with local intensity and gradient features, to a deformation vector, so the conditioning varies over the domain at the resolution of the field being modelled. Its objective is to find an initialization of the INR parameters from which the network can be fine-tuned to register any unseen pair in only a few optimization iterations. We evaluate LUMINR on 3D deformable registration of brain MRI from the OASIS dataset, where local conditioning and the meta-learned initialization prove complementary: early in fitting they reach a markedly higher accuracy than either does alone. Fine-tuned from that initialization, LUMINR matches the accuracy of the same conditioned INR fit from scratch in roughly a tenth of the gradient steps and a tenth of the wall-clock time, while the deformation fields stay smooth with negligible folding.

Deformable image registration models implicitly encode deformation priors through their parametrization and optimization. In this work, we conduct a validation study on continuous registration methods to examine how these implicit priors affect performance across different registration tasks. Classic B-Spline transformations impose locality, smoothness, and scale through their control-point structure, whereas recent INR-based methods impose different priors through neural parameterization and optimization. We compare INR-Dense (IDIR), which directly models a dense displacement field using a SIREN-based INR; INR-BSCP (SINR), which predicts B-Spline control points with an INR; D-BSCP, which directly optimizes single-scale B-Spline control points; and MR-D-BSCP, which adds a multiresolution coarse-to-fine scheme. Experiments on inter-subject brain MR registration (OASIS) and intra-subject exhale-to-inhale lung CT registration (DIR-LAB 4DCT) reveal different behavior across deformation regimes. On OASIS, where deformations are moderate but locally complex, D-BSCP matches or slightly outperforms INR-BSCP, suggesting that the B-Spline parameterization accounts for much of INR-BSCP's effectiveness. On DIR-LAB 4DCT, where respiratory motion is larger and more coherent, single-scale B-Spline methods (D-BSCP and INR-BSCP) are less suitable, while INR-Dense and MR-D-BSCP are more effective. Across both tasks, MR-D-BSCP achieves the best performance among the tested continuous parameterizations. These findings highlight that registration accuracy depends strongly on matching the induced deformation prior to the target motion pattern, and support prior-deformation matching as a practical design principle for medical image registration. Our code will be available at https://github.com/HengjieLiu/RightPriorDIR.