Embedded phase shifting: Robust phase shifting with embedded signals

We introduce Embedded PS, a new robust and accurate phase shifting algorithm for 3D scanning. The method projects only high frequency sinusoidal patterns in order to reduce errors due to global illumination effects, such as subsurface scattering and interreflections. The frequency set for the projected patterns is specially designed so that our algorithm can extract a set of embedded low frequency sinusoidals with simple math. All the signals, patterns high and embedded low frequencies, are used with temporal phase unwrapping to compute absolute phase values in closed-form, without quantization or approximation via LUT, resulting in fast computation. The absolute phases provide correspondences from projector to camera pixels which enable to recover 3D points using optical triangulation. The algorithm estimates multiple absolute phase values per pixel which are combined to reduce measurement noise while preserving fine details. We prove that embedded periodic signals can be recovered from any periodic signal, not just sinusoidal signals, which may result in further improvements for other 3D imaging methods. Several experiments are presented showing that our algorithm produces more robust and accurate 3D scanning results than state-of-the-art methods for challenging surface materials, with an equal or smaller number of projected patterns and at lower computational cost.