Sampling Density Criterion for Circular Structured Light 3D Imaging

3D reconstruction work has chiefly focused on the accuracy of reconstruction results in computer vision, and efficient 3D functional camera system has been of interest in the field of mobile camera as well. The optimal sampling density, referred to as the minimum sampling rate for 3D or high-dimensional signal reconstruction, is proposed in this paper. There have been many research activities to develop an adaptive sampling theorem beyond the Shannon-Nyquist Sampling Theorem in the areas of signal processing, but sampling theorem for 3D imaging or reconstruction is an open challenging topic and crucial part of our contribution in this paper. We hence propose an approach to sampling rate (lower / upper bound) determination to recover 3D objects (surfaces) represented by a set of circular light patterns, and the criterion for a sampling rate is formulated using geometric characteristics of the light patterns overlaid on the surface. The proposed method is in a sense a foundation for a sampling theorem applied to 3D image processing, by establishing a relationship between frequency components and geometric information of a surface.