Examining the uncertainty of the recovered surface normal in three light photometric stereo

Although the three light photometric stereo technique has been used in many applications, there is little published work concerned with characterizing the uncertainty of these systems due to the involvement of a number of complicating factors. This paper presents a methodology used to analyze the uncertainty of the recovered unit surface normal with respect to irradiance variance. Illumination configurations and the values of the composite albedo are found to directly affect the stability of the photometric stereo technique. An orthogonally distributed illumination arrangement is proven to be the theoretically optimal configuration. Further practical considerations are also identified. The derived general uncertainty expression can be easily employed to optimize the location of the light sources. Hence, the work is of significance for the development of practical industrial applications of photometric stereo, including metrology, reverse engineering and various surface inspection tasks.