Geometry-Driven Shadow Harmonisation for Composited Faces: A Multiplicative, Albedo-Preserving Relighting Pipeline

Face swapping and face compositing pipelines routinely produce a face that is geometrically well aligned but photometrically implausible: the donor face carries flat, near-frontal studio illumination while the host body and background carry directional scene light. Most existing remedies re-synthesise the face through colour transfer, neural relighting, or inverse rendering, and therefore risk altering identity, skin tone, and texture. We present a conservative alternative: geometry-driven form-shadow injection. The pipeline never repaints the face. It estimates a per-pixel gain field $g\in[g_{\min},1]$ from a rasterised 3D face proxy and multiplies it channel-uniformly onto linear RGB, so the operator can only darken and cannot shift chromaticity. A dense landmark mesh is rasterised into a depth buffer, from which we derive surface normals, a cavity term, and screen-space cast shadows. Key-light direction is estimated from host-side cues (body, background, hair halo); on-face cues are downweighted because they recover the donor's lighting. Shadow magnitude is not matched to the host: it is set by a three-parameter transfer $(\tau,\sigma,g_{\min})$. The shading field is divided by its 75th percentile over skin, then gated, scaled, clamped, smoothed, and re-clipped inside a feathered, skin-gated face mask. On an analytic face heightfield, the default $(\tau,\sigma,g_{\min})=(0.90,0.45,0.82)$ modifies 56.5% of face pixels with mean gain 0.938 (0.890 on modified pixels) and drives 3.4% of pixels to the floor. Hue invariance is a corollary of the operator. We analyse the transfer in closed form, ablate its parameters, and discuss failure modes of a monotone, darkening-only formulation, including double-shadowing of non-flat donors.