Identifying the lights position in photometric stereo under unknown lighting

Ascertaining the Ideality of Photometric Stereo Datasets under Unknown Lighting

“…In this section, we briefly review the mathematical model implementing Lambert's law that is usually adopted in photometric stereo under the assumption of orthographic projection and light source at an infinite distance from the target (see [15] for more details). We also outline the Hayakawa procedure [14] for estimating the lighting directions from the data.…”

“…When the light positions are not known, the Hayakawa procedure [14] can be used to estimate this information from the data, but this requires the availability of at least six images with different lighting conditions. Here, we briefly summarize this technique (see [15] for more details).…”

“…Following the proof of Theorem 1 from [15], we consider the factorization W T Z = M as a tentative approximation of ÑT L = M. Assuming t = 1, we seek a matrix B such that…”

“…For this reason, the final step is to determine a unitary transformation Q, which resolves the uncertainty in the orientation of the normal vectors, the so-called bas-relief ambiguity [30], and rotates the object to a suitable orientation. This can be accomplished by an algorithm introduced in [15], which assumes the photos are taken by following a particular shooting procedure.…”

“…Though in the research community, the position of the light sources is generally assumed to be known [9][10][11], real-world applications of PS often deal with datasets acquired under unknown light conditions [12,13]. In [14], Hayakawa has shown that the lighting directions can be identified directly from the data when at least six images with different illumination are available (see [14] and Section 2 for a proof), yielding the possibility to apply PS to field measurement scenarios, as in the case of archaeological excavations [15].…”