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Parametric spatial transformation models have been successfully applied to image registration tasks. In such models, the transformation of interest is parameterized by a fixed set of basis functions as for example B-splines. Each basis function is located on a fixed regular grid position among the image domain because the transformation of interest is not known in advance. As a consequence, not all basis functions will necessarily contribute to the final transformation which results in a non-compact representation of the transformation.

Neural Information Processing Systems http://nips.cc/

Regularization is essential in deformable image registration (DIR) to ensure that the estimated Deformation Vector Field (DVF) remains smooth, physically plausible, and anatomically consistent. However, fine-tuning regularization parameters in learning-based DIR frameworks is computationally expensive, often requiring multiple training iterations. To address this, we propose cIDI, a novel DIR framework based on Implicit Neural Representations (INRs) that conditions the registration process on regularization hyperparameters. Unlike conventional methods that require retraining for each regularization hyperparameter setting, cIDIR is trained over a prior distribution of these hyperparameters, then optimized over the regularization hyperparameters by using the segmentations masks as an observation. Additionally, cIDIR models a continuous and differentiable DVF, enabling seamless integration of advanced regularization techniques via automatic differentiation. Evaluated on the DIR-LAB dataset, $\operatorname{cIDIR}$ achieves high accuracy and robustness across the dataset.

Recent developments in neural networks have improved de-formable image registration (DIR) by amortizing iterative optimization, enabling fast and accurate DIR results. However, learning-based methods often face challenges with limited training data, large deformations, and tend to underperform compared to iterative approaches when label supervision is unavailable. While iterative methods can achieve higher accuracy in such scenarios, they are considerably slower than learning-based methods. To address these limitations, we propose VoxelOpt, a discrete optimization-based DIR framework that combines the strengths of learning-based and iterative methods to achieve a better balance between registration accuracy and runtime. VoxelOpt uses displacement entropy from local cost volumes to measure displacement signal strength at each voxel, which differs from earlier approaches in three key aspects. First, it introduces voxel-wise adaptive message passing, where voxels with lower entropy receives less influence from their neighbors. Second, it employs a multi-level image pyramid with 27-neighbor cost volumes at each level, avoiding exponential complexity growth. Third, it replaces hand-crafted features or contrastive learning with a pretrained founda-tional segmentation model for feature extraction. In abdominal CT registration, these changes allow VoxelOpt to outperform leading iterative in both efficiency and accuracy, while matching state-of-the-art learning-based methods trained with label supervision.

Deformable medical image registration is an essential task in computer-assisted interventions. This problem is particularly relevant to oncological treatments, where precise image alignment is necessary for tracking tumor growth, assessing treatment response, and ensuring accurate delivery of therapies. Recent AI methods can outperform traditional techniques in accuracy and speed, yet they often produce unreliable deformations that limit their clinical adoption. In this work, we address this challenge and introduce a novel implicit registration framework that can predict accurate and reliable deformations. Our insight is to reformulate image registration as a signal reconstruction problem: we learn a kernel function that can recover the dense displacement field from sparse keypoint correspondences. We integrate our method in a novel hierarchical architecture, and estimate the displacement field in a coarse-to-fine manner. Our formulation also allows for efficient refinement at test time, permitting clinicians to easily adjust registrations when needed. We validate our method on challenging intra-patient thoracic and abdominal zero-shot registration tasks, using public and internal datasets from the local University Hospital. Our method not only shows competitive accuracy to state-of-the-art approaches, but also bridges the generalization gap between implicit and explicit registration techniques. In particular, our method generates deformations that better preserve anatomical relationships and matches the performance of specialized commercial systems, underscoring its potential for clinical adoption.

Deformable registration is a fundamental task in medical image processing, aiming to achieve precise alignment by establishing nonlinear correspondences between images. Traditional methods offer good adaptability and interpretability but are limited by computational efficiency. Although deep learning approaches have significantly improved registration speed and accuracy, they often lack flexibility and generalizability across different datasets and tasks. In recent years, foundation models have emerged as a promising direction, leveraging large and diverse datasets to learn universal features and transformation patterns for image registration, thus demonstrating strong cross-task transferability. However, these models still face challenges in generalization and robustness when encountering novel anatomical structures, varying imaging conditions, or unseen modalities. To address these limitations, this paper incorporates Sharpness-Aware Minimization (SAM) into foundation models to enhance their generalization and robustness in medical image registration. By optimizing the flatness of the loss landscape, SAM improves model stability across diverse data distributions and strengthens its ability to handle complex clinical scenarios. Experimental results show that foundation models integrated with SAM achieve significant improvements in cross-dataset registration performance, offering new insights for the advancement of medical image registration technology. Our code is available at https://github.com/Promise13/fm_sam}{https://github.com/Promise13/fm\_sam.

Longitudinal image registration enables studying temporal changes in brain morphology which is useful in applications where monitoring the growth or atrophy of specific structures is important. However this task is challenging due to; noise/artifacts in the data and quantifying small anatomical changes between sequential scans. We propose a novel longitudinal registration method that models structural changes using temporally parameterized neural displacement fields. Specifically, we implement an implicit neural representation (INR) using a multi-layer perceptron that serves as a continuous coordinate-based approximation of the deformation field at any time point. In effect, for any N scans of a particular subject, our model takes as input a 3D spatial coordinate location x, y, z and a corresponding temporal representation t and learns to describe the continuous morphology of structures for both observed and unobserved points in time. Furthermore, we leverage the analytic derivatives of the INR to derive a new regularization function that enforces monotonic rate of change in the trajectory of the voxels, which is shown to provide more biologically plausible patterns. We demonstrate the effectiveness of our method on 4D brain MR registration.

The main advantage of this approach is its efficiency at inference time with comparable performance of B-spline based approach where an optimization is needed per registration. And it has, according to the authors, much less parameters to optimize. Please confirm if this understanding is correct? 2. What is the reason of making the choice of using multiple steps to gradually transform the moving image to the fixed one? Could the local transformation done in one step instead? For instance, the position network could directly predict K locations to transform in one step instead of prediction one location for K steps.

The paper seems to contribute in a significant way in proposing an alternative RNN-based approach for deformable image registration. Although the experimental setting is not extremely strong, the proposed approach seems to give significant computational advantages. Rebuttal clarified most of the reviewers concerns.