Flexible Error Diffusion Algorithm for Binary Defocusing Fringe Projection Profilometry

The error diffusion algorithm shows great potential in binary defocusing fringe projection profilometry (FPP) for improving the intensity representation of binary patterns. However, the fixed kernel in the error diffusion algorithm makes the generated binary patterns far from optimal patterns because of ignoring the structural differences of patterns and the intensity error induced by the coupling effect among binary patterns. This article proposes a flexible error diffusion algorithm with an unfixed kernel to generate high-quality binary patterns for binary-defocusing FPP, thereby realizing rapid and accurate 3-D shape reconstruction. Dual-objective functions are adopted in the proposed approach for kernel optimization. First, taking the minimum intensity error as one objective, this work presents an unfixed four-coefficient error diffusion algorithm to generate binary patterns with the best intensity representation. Second, taking the minimum phase error as another objective, a dual-objective error diffusion algorithm is developed to select the binary patterns with the best phase quality in the phase domain. Finally, a local intensity correction (LIC) procedure eliminates phase jump errors in the encoding phase of the selected binary patterns to get the optimal projections for binary-defocusing FPP. Simulated and experimental results verify that the binary patterns generated using the proposed approach can support the accurate binary-defocusing FPP at various degrees of defocusing.