Error analysis of photometric stereo with colour lights

Abstract

This paper presents a comprehensive error analysis of photometric stereo with colour lights for surface normal estimation. An analytic formulation is introduced for the error in albedo-scaled normal estimation with respect to all inputs to the photometric stereo – pixel colour, light directions and light-sensor-material interaction. This characterises the error in the estimated normal for all possible directions with respect to the light setup given discrepancies in the inputs. The theoretical formulation is validated by an extensive set of experiments with synthetic data. Example discrepancies in each input to the photometric stereo calculation show a complex distribution of the error of an albedo-scaled normal over the space of possible orientations. This is generalised in the empirical sensitivity analysis which demonstrates that the magnitude of the error propagation from the light directions and the light-sensor-material interaction depends on the surface orientation. However, the image noise is propagated uniformly to all normal directions. There is a linear relationship between the uncertainty in the individual inputs and in the output normals. The theoretical and experimental findings provide several recommendations on designing a capture setup which is the least sensitive to the inaccuracies in the pixel colours, the light directions and the light-sensor-material interaction. An example is provided showing how to assess the inaccuracies in PSCL calculation for a real-world setup.