A Sampling Theorem for a 2D Surface

The sampling rate for signal reconstruction has been and remains an important and central criterion in numerous applications. We propose, in this paper, a new approach to determining an optimal sampling rate for a 2D-surface reconstruction using the so-called Two-Thirds Power Law. This paper first introduces an algorithm of a 2D surface reconstruction from a 2D image of circular light patterns projected on the surface. Upon defining the Two-Thirds Power Law we show how the extracted spectral information helps define an optimal sampling rate of the surface, reflected in the number of projected circular patterns required for its reconstruction. This result is of interest in a number of applications such as 3D face recognition and development of new efficient 3D cameras. Substantive examples are provided.