SCoPE-Reg: Efficient Rigid Ultrasound Slice-to-Volume Registration via State-Space Correlation and Closed-Form Pose Estimation

Ultrasound-guided interventions can require localization of an untracked 2D frame within a 3D anatomical reference. Rigid slice-to-volume registration (SVR) estimates this six-degree-of-freedom pose but remains challenging because of limited anatomical context, acoustic artifacts, and view-dependent appearance. Existing methods often use dense cross-attention, whose cost scales with the product of slice and volume token counts, or direct pose regression without explicit correspondence constraints. We introduce SCoPE-Reg, combining state-space slice--volume interaction, dense 3D coordinate prediction, and parameter-free weighted Kabsch estimation. On SVR tasks from CAMUS and μ-RegPro, SCoPE-Reg yields mean target registration errors of 0.73 mm and 2.27 mm against 1.24 mm and 2.63 mm for the state of the art (SOTA), reduces peak error on CAMUS by 56% below SOTA (12.5!→!5.5 mm), and registers 100% and 80% of frames within 3 mm. On CAMUS at 1282 it retains the lowest error at increasing pose-perturbation magnitude. It holds 6.49 M parameters independent of resolution, sustaining 51 FPS at 5122. SCoPE-Reg establishes a SOTA in rigid ultrasound SVR: by coupling correspondence-based accuracy with bounded worst-case error and resolution-independent cost, it becomes viable at native acquisition resolution during intervention, where prior methods trade accuracy, reliability, or frame rate against one another. Supplementary code provided and will be open-sourced upon acceptance.