The Right Prior for the Right Deformation: Rethinking Continuous Deformable Image Registration

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 (DIR) is a core problem in medical image analysis; but, unlike labeling decision problems such as classification and segmentation, registration is a problem class that involves stringent physical constraints. Although deep learning methods have made faster registration possible, the resulting models are often difficult to interpret compared to hand-crafted methods with explicit objectives and interpretable physical meaning. In this work, we show that an analytical method can still yield competitive and superior results to deep learning in a common deformable registration task. We study pTVreg as a parametric total variation based registration in that context. Observing its different implementations to perform at various degrees, we introduce here an accessible implementation of this method, together with a Bayesian optimization framework that automatically sets self-parameters for any DIR task from a set of sample examples. Experiments on Lung250M-4B show that our proposed implementation achieves state-of-the-art results in this benchmark, substantially superior to existing deep learning solutions and other pTVreg variants as baselines. The source code will be made publicly available at https://github.com/oazeybekoglu/ptvreg-python .

Objective. Deformable image registration remains challenging because corresponding anatomy may exhibit different intensity relationships. Hand-crafted modality-robust descriptors such as Modality-Independent Neighborhood Descriptor with Self-Similarity Context (MIND-SSC) and features from pretrained vision encoders provide distinct representations for correspondence estimation, but how they should be combined remains unclear. We investigate whether tighter integration improves registration over a sequential, scale-separated design. Approach. We introduce FlexiMIND, a training-free and label-free two-stage framework in which frozen FlexiCT-2D encoder features establish contextual correspondence and MIND-SSC refines the deformation within ConvexAdam. Five alternative feature-coupling strategies were evaluated under a protocol across CT-CT (DIR-Lab 4DCT 4DCT, 10 cases), MR-MR (ACDC, 50 patients), and MR-CT (Learn2Reg Abdomen MR-CT, 8 pairs) registration. Performance was assessed using target registration error (TRE), Dice similarity coefficient (Dice), SDlogJ, and local folding. Main results. FlexiMIND achieved a TRE of 1.27 mm on DIR-Lab 4DCT, a DSC of 0.807 on ACDC, and an organ-averaged DSC of 0.825 on Abdomen MR-CT. Across 15 coupling-strategy dataset comparisons, only four outperformed the reference method, with a maximum absolute improvement of 0.0043 in Dice, whereas degradation reached 20.6 % in TRE and 37.9 % in Dice. Changes in registration accuracy were closely associated with changes in deformation-field regularity, and strategies that better preserved regularity generally remained closest to the reference performance. Landmark-level analysis showed that the pretrained encoder stage primarily reduced large correspondence errors rather than uniformly improving local precision. Code is available upon acceptance at https://github.com/mosaf/FlexiMIND.