ReCo-SVF: Geometric Region Tokens for Dense Atlas Registration under Controlled Source Truncation

A deformation is predicted at every voxel, but the evidence that disambiguates a local match may lie far away—or be absent from a truncated moving volume. ReCo-SVF (Relational Context SVF) addresses this mismatch with a sparse-to-dense design: 32 learned region tokens exchange relative-position messages on a geometric 6-nearest-neighbour graph and condition a voxel-supported stationary velocity field through three-scale cross-attention. A six-carrier intervention family holds the dense prediction path fixed while replacing geometric tokens with no-token, dense, edge-free, random-edge, or coordinate-shuffled carriers. Across five seeds, the geometric carrier exceeds the edge-free 32-token mixer by +0.008 [0.005,0.011] Dice on complete OASIS images and +0.026 [0.019,0.033] at 40% shared-visible-field extent; random and shuffled neighbourhoods do not recover the full geometric carrier's accuracy. A moving-only protocol then removes source context while preserving the complete fixed target and ROI population. Over 10,900 degraded outputs per learned method, the geometric-carrier advantage over edge-free tokens widens by +0.027 [0.019,0.035], raises degradation AUC from $0.907\pm 0.006$ to $0.934\pm 0.004$, and reduces 40%-extent failures from 356 to 228 of 545 subject–offset cases. The complete system reaches 0.774 Dice with 0.038% folding on OASIS, transfers to IXI at 0.748 Dice without fine-tuning, and achieves 0.641 Dice with 0.052% folding on BTCV. These results show that explicit geometry in a fixed-budget context carrier preserves correspondence quality under controlled source truncation while retaining dense, regular deformation.