Sparse and Adaptive Fringe-Enhancement Efficiency Analysis in 3D Optical Digital Fringe-Projection Imaging

Obtaining a three-dimensional profile of an object in optical fringe pattern projection techniques with phase-shifting algorithms and methods requires phase unwrapping. This is known to be prone not only to the sampling rate and sharp profile edges but also to perturbations in the fringe pattern image. The efficiency of sparse decomposition and localized adaptive fringe pattern image enhancement in optical digital fringe-projection profilometry is comparatively analyzed and presented in this paper. The sparse decomposition technique utilizes correlation in three-dimensional transform domain to obtain a sparse representation of the signal for matching decomposed blocks with desired qualities while the localized adaptive method uses thresholding to correlate signal coefficients in transform domain to shrink undesired components. Analysis shows that sparse decomposition preserves essential features of phase signal, and tends to produce filtered fringe image of consistently good wrapped phase map for further wrap processing; yet localized adaptive method's enhancement capability seemingly diminishes with increase in variation of noise standard deviation or sigma. Numerical simulations and results are presented to demonstrate the differential efficiency and comparative advantage of two enhancement techniques. This analysis is promising as a measure of robustness in fringe-enhancement techniques and other methods for three-dimensional measurement accuracy in optical fringe projection profilometry and metrology.