Spatial–Temporal Binarization Method via Jointly Optimizing Diffusion Kernel and Quantization Threshold for 3-D Surface Imaging

Binary patterns that utilize a diffusion kernel and a fixed quantization threshold to binarize 8-bit sinusoidal fringes are popular in 3-D imaging of dynamic objects by virtue of the fast-switching capability of digital mirror device projectors. Unfortunately, to remove the encoding noise and obtain approximate sinusoidal fringes, a large defocus is generally required for existing binarization methods. This behavior inevitably results in the adopted 3-D measurement system working under a discounted depth of field, while the low signal-to-noise ratio of captured images has an adverse influence on the phase extraction accuracy of commonly adopted high-frequency fringes for practical 3-D reconstruction. In this article, we present a spatial–temporal binary encoding method of jointly optimizing diffusion kernel and quantization threshold for 3-D surface measurement. Our method involves determining the quantization threshold by simulation, searching optimal diffusion kernels in both phase and intensity-domain via particle swarm optimization (PSO) algorithm, and implementing error diffusion (ED) encoding spatially and temporally using the optimized quantization threshold (OptQ) and diffusion kernel. Finally, one 8-bit sinusoidal fringe is temporally decomposed into multiple (<inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>) 1-bit binary patterns, which are nearly in-focus projected to yield approximate sinusoidal pattern in the manner of integral imaging strategy. Comparative experiments verify that the accuracy of our method outperforms the state-of-the-art methods in terms of phase and 3-D measurement accuracy. Additionally, the binary encoding fringe patterns are also to successfully implement dynamic 3-D imaging of a moving arm.