Set-Based Groupwise Registration for Variable-Length, Variable-Contrast Cardiac MRI

Quantitative cardiac magnetic resonance imaging (MRI) enables non-invasive myocardial tissue characterization but relies on robust motion correction within these variable-length, variable-contrast image sequences. Groupwise registration, which simultaneously aligns all images, has shown greater robustness than pairwise registration for motion correction. However, current deep-learning-based groupwise registration methods cannot generalize across MRI sequences: the architecture typically encodes input data as a fixed-length channel stack, which rigidly couples network design to protocol-specific sequence length, input ordering, and contrast dynamics. At inference time, any change in imaging protocols will render the network unusable. In this work, we introduce \emph{\AnyTwoReg}, a new set-based groupwise registration framework that takes a quantitative MRI sequence as an unordered set. This set formulation fundamentally decouples network design from sequence length and input ordering. By utilizing a shared encoder and correlation-guided feature aggregation, \emph{\AnyTwoReg} constructs a permutation-invariant canonical reference for registration, and learns a permutation-equivariant mapping from images to deformation fields. Additionally, we extract contrast-insensitive image features from an existing foundation model to handle extreme contrast variations. Trained exclusively on a single public $T_1$ mapping dataset (STONE, sequence length $L=11$), \AnyTwoReg generalizes to two unseen quantitative MRI datasets (MOLLI, ASL) with variable lengths ($L \in [11, 60]$) and different contrast dynamics. It achieves strong cross-protocol generalization in a zero-shot manner, and consistently improves downstream quantitative mapping quality. Notably, while designed for quantitative MRI sequences, our framework is directly applicable to Cine MRI sequences for inter-cardiac-phase registration.