Photometric stereo without multiple images

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Abstract
Photometric stereo (PMS) recovers orientation vectors from a set of graylevel images. Under orthography, when the lights are unknown, and for a single uniform Lambertian surface, one can recover surface normals up to an unknown overall orthogonal transformation. The same situation obtains if, instead of three graylevel images, one uses a single RGB image taken with at least three point or extended colored lights impinging on the surface at once. Then using a robust technique and the constraints among the resulting three effective lighting vectors one can recover effective lights as well as normals, with no unknown rotation. However, in the case of a non-Lambertian object, PMS reduces to the idea of using a lookup table (LUT) based on a calibration sphere. Here, we show that a LUT can also be used in the many-colored- lights paradigm, eliminating the need for three separate images as in standard PMS. As well, we show how to transform a calibration sphere made of a particular material into a theoretical sphere for a cognate material similar in its specular properties but of a different color. In particular, we postulate that a LUT developed from one human's skin can be used for any other person; problems arising from shadows, hair, eyes, etc. are automatically eliminated using robust statistics. Results are shown using both synthetic and real images.

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