We present a novel method for estimating specular roughness and tangent vectors, per surface point, from polarized second order spherical gradient illumination patterns. We demonstrate that for isotropic BRDFs, only three second order spherical gradients are sufficient to robustly estimate spatially varying specular roughness. For anisotropic BRDFs, an additional two measurements yield specular roughness and tangent vectors per surface point. We verify our approach with different illumination configurations which project both discrete and continuous fields of gradient illumination. Our technique provides a direct estimate of the per-pixel specular roughness and thus does not require off-line numerical optimization that is typical for the measure-and-fit approach to classical BRDF modeling.

In this work, we estimate spatially varying appearance properties of materials by directly acquiring second order statistics of per surface point specular reflectance. This includes an estimate of per-pixel specular roughness as a measure of variance about a mean (e.g., reflection vector), as well as an estimate of the tangent vectors for anisotropic materials. We take a computational illumination approach towards efficient computation of these statistics by employing polarized second order spherical gradient illumination for our measurements. With this approach, we are able to obtain a more complete spatially varying BRDF information for arbitrary objects from observation under just 7 to 9 lighting conditions for isotropic and anisotropic materials respectively. Furthermore, since the proposed method relies on only up to nine distinct illumination conditions with minimal capture time, it is amenable to capturing per-surface point roughness parameters of human subjects.

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