Polarimetric Inverse Rendering for Label-Efficient Surface Finish Estimation in Robotic Polishing

In-process surface-finish estimation is a prerequisite for closed-loop robotic polishing, yet force- and acoustic-emission sensing is single-point and needs offline recalibration, while learned vision regressors are tied to a fixed optical setup and a single material. On translucent dental ceramics the problem is compounded: sub-surface scattering broadens the specular lobe, so generic regressors over-estimate roughness. We argue that the lobe width is governed by the lateral slope statistics of the surface—an effective root-mean-square gradient related to the areal parameter S_dq—rather than by the height amplitude S_a that convolutional regressors predict; fitting S_a directly therefore entangles material, illumination and process priors and transfers poorly. With a snapshot polarization camera, we use the degree of linear polarization and the Fresnel polarizance to separate the depolarized sub-surface component from the interface reflection and fit a microfacet lobe to it, yielding a dense slope field. The first calibration stage uses no roughness labels and is, to first order, material-agnostic; a monotone S_dq→S_a map then needs only 5–10 interferometer labels per new material. Across translucent ceramics and metals, the approach reduces the ceramic Sa error from 0.180 μm (direct convolutional-network regression) to 0.082 μm, improves cross-material transfer and label efficiency within a bounded, geometric-optics operating range, and supports a preliminary closed-loop demonstration.