On optimal light configurations in photometric stereo

This paper develops new theory for the optimal placement of photometric stereo lighting in the presence of camera noise. We show that for three lights, any triplet of orthogonal light directions minimises the uncertainty in scaled normal computation. The assumptions are that the camera noise is additive and normally distributed, and uncertainty is defined as the expectation of squared distance of scale normal to the ground truth. If the camera noise is of zero mean and variance sigma² the optimal (minimum) uncertainty in the scaled normal is 3sigma² For case of n > 3 lights, we show that the minimum uncertainty is 9sigma²n, and identify sets of light configurations which reach this theoretical minimum