Optimal illumination for three-image photometric stereo using sensitivity analysis

The optimal placement of the illumination for three-image photometric stereo acquisition of smooth and rough surface textures with respect to camera noise is derived and verified experimentally. The sensitivities of the scaled surface normal elements are derived and used to provide expressions for the noise variances. An overall figure of merit is developed by considering the image-based rendering (i.e. relighting) of Lambertian surfaces. This metric is optimised numerically with respect to the illumination angles. An orthogonal configuration was found to be optimal. With regard to constant slant, the optimal separation between the tilt angles of successive illumination vectors was found to be 120°. The optimal slant angle was found to be 90° for smooth surface textures and 55° for rough surface textures.