Automatic facial rigging across heterogeneous mesh topologies remains challenging because high-quality expression supervision is often tied to canonical templates, while deformation transfer to arbitrary meshes can introduce geometric artifacts and correspondence errors. We present TopoRig, a topology-agnostic facial rigging framework that predicts FACS-conditioned deformations directly on input mesh vertices while preserving the original topology. Starting from the ICT FaceKit expression model, we construct complementary supervision from accurate but template-biased common-topology rigs, topology-diverse but noisier transferred rigs, and targeted image-based cues for controls poorly captured by geometric transfer. TopoRig combines local surface geometry, landmark-relative semantic features, global shape context, and FACS controls to predict per-vertex displacements. We train on 3,496 generated identities using 45 non-gaze expression controls from the 53-control ICT FaceKit vocabulary. On held-out identities and unseen mesh topologies, TopoRig more faithfully reproduces the reference expression space than prior neural facial-rigging methods, while qualitative results show consistent localized deformations across diverse character geometries. Ablations demonstrate that semantic landmark features and complementary supervision improve cross-identity and cross-topology generalization. Overall, TopoRig amortizes heterogeneous and imperfect expression supervision into a single topology-preserving deformation model.

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