Stabilizing joint rotation selection in skinning decomposition for high-fidelity facial auto rigging

Skinning decomposition-based facial auto rigging aims to construct an actor-specific Linear Blend Skinning (LBS) facial rig from an actor’s example expressions and a predefined rigging template. However, facial rigs recovered by existing skinning decomposition methods may accurately reproduce the target expressions yet yield visible local distortions when the solved joint transformations are interpolated from the neutral configuration to each target expression. We attribute this issue to two factors. First, target-state fitting formulations often admit multiple near-equivalent joint-rotation solutions that reproduce the target expressions similarly. Second, single-step closed-form rotation updates are path-independent and therefore provide little stable preference among these candidates. To address this issue, we propose a rotation-stabilized skinning decomposition method for generating actor-specific LBS facial rigs that produce more stable intermediate deformations under interpolation. Specifically, we improve rotation solving through explicit rotation-space regularization and the implicit bias induced by path-dependent continuous optimization with identity initialization. Furthermore, without changing the alternating optimization framework between joint transformations and skinning weights, we reformulate the optimization under a unified differentiable objective. This objective incorporates the surface normal consistency constraint and allows it to directly supervise joint transformation updates through a shared differentiable optimization process. Experiments show that the proposed method produces a substantially more contracted rotation-angle distribution and more stable intermediate deformations, with a trade-off in target-expression vertex reconstruction error. In addition, the unified differentiable formulation reduces surface normal error.