Structure-Aware Riemannian Flow Matching for Registration and Fusion of Hyperspectral and Multispectral Images

Precise alignment is a prerequisite for hyperspectral and multispectral image fusion, yet existing methods struggle with complex non-rigid deformations. Existing techniques either suffer from inter-task error accumulation by treating registration and fusion as disjoint processes or neglect the geometric nature of distortions by relying on isotropic Euclidean metrics. We propose Structure-Aware Riemannian Flow Matching (SA-RFM), a geometry-informed framework for joint registration and fusion of hyperspectral and multispectral images. SA-RFM reformulates registration as dynamic optimal transport on a structure-induced Riemannian manifold, where anisotropic costs are derived from MSI structural cues. To circumvent the complexity of explicit OT solvers, we incorporate this geometry into a conditional flow matching framework via a local cost approximation. This formulation is realized through two synergistic mechanisms: a Riemannian Flow Matching objective that enforces structure-aware error measurement, and an optimal transport direction regularization that aligns the velocity field with the induced metric, thereby resolving the fundamental mismatch between anisotropic costs and conventional Euclidean supervision. Extensive experiments on multiple datasets demonstrate the superiority of our method.