Factored Levenberg-Marquardt for Diffeomorphic Image Registration: An efficient optimizer for FireANTs

Surface registration plays an important role for anatomical shape analysis in medical imaging. Existing surface registration methods often face a trade-off between efficiency and robustness. Local point matching methods are computationally efficient, but vulnerable to noise and initialisation. Methods designed for global point set alignment tend to incur a high computational cost. To address the challenge, here we present a fast surface registration method, which formulates surface meshes as probability measures and surface registration as a distributional optimisation problem. The discrepancy between two meshes is measured using an efficient sliced Wasserstein distance with log-linear computational complexity. We propose a novel optimisation method, AdamFlow, which generalises the well-known Adam optimisation method from the Euclidean space to the probability space for minimising the sliced Wasserstein distance. We theoretically analyse the asymptotic convergence of AdamFlow and empirically demonstrate its superior performance in both affine and non-rigid surface registration across various anatomical structures.

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 .