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UBC CS TR-91-18 Summary

Photometric Stereo: Lambertian Reflectance and Light Sources with Unknown Direction and Strength, August 1991 R. J. Woodham, Y. Iwahori and Rob A. Barman, 11 pages

This paper reconsiders the familiar case of photometric stereo under the assumption of Lambertian surface reflectance and three distant point sources of illumination. Here, it is assumed that the directions to and the relative strengths of the three light sources are not known {\it a priori}. Rather, estimation of these parameters becomes part of the problem formulation. \nEach light source is represented by a 3-D vector that points in the direction of the light source and has magnitude proportional to the strength of the light source. Thus, nine parameters are required to characterize the three light sources. It is shown that, regardless of object shape, triples of measured intensity values are constrained to lie on a quadratic surface having six degrees of freedom. Estimation of the six parameters of the quadratic surface allows the determination of the nine parameters of the light sources up to an unknown rotation. \nThis is sufficient to determine object shape, although attitude with respect to the world-based or the camera-based coordinate system can not be simultaneously recovered without additional information.

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