LOGOS: Residual-Gated Witness Refinement for Non-Rigid Shape Correspondence

A correspondence sends every vertex of one mesh to a vertex of another. Truncated spectral bases blur small parts and still swap left with right. An update that moves each vertex on its own can tear one region into islands. A network trained on one connectivity is accurate there and degrades when the mesh changes. is a training-free editor of a hard correspondence. A residual gate reassigns only high-residual vertices, cleanup freezes the largest piece of each cluster, and a polish moves points inside that cluster. From the same SHOT nearest-neighbor start it lowers mean geodesic error on all six splits, from $0.316$/$0.417$/$0.403$/$0.401$/$0.231$/$0.352$ to $0.010$/$0.035$/$0.025$/$0.020$/$0.020$/$0.056$ on SCAPE, SCAPE_r, FAUST_r, TOSCA_r, TOPKIDS, and SMAL_r, and it is the lowest stored mean on TOSCA_r ($0.020$). Pushed labels on SCAPE_r are contiguous on $0.872$ of clusters. A FAUST-trained network is $0.013$ at home and $0.194$ on TOSCA_r. On TOPKIDS, 2D-GEM is $0.006$ and is $0.020$.