Abstract Under unknown directional lighting, the uncalibrated Lambertian photometric stereo algorithm recovers the shape of a smooth surface up to the generalized bas-relief (GBR) ambiguity. We resolve this ambiguity from the halfvector symmetry, which is observed in many isotropic materials. Under this symmetry, a 2D BRDF slice with low-rank structure can be obtained from an image, if the surface normals and light directions are correctly recovered. In general, this structure is destroyed by the GBR ambiguity. As a result, we can resolve the ambiguity by restoring this struc ture. We develop a simple algorithm of auto-calibration from separable homogeneous specular re?ection of real images. Compared with previous methods, this method takes a holistic approach to exploiting re?ectance symmetry and produces superior results.