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Abstract
In practical measurement, we often need to measure the shape of objects with patterns or letters. As far as we know, no paper has ever reported the shape measurement for objects with patterns or letters by Fourier fringe projection profilometry (FPP). In this paper, we propose a method based on the variational decomposition ${\rm TV} \!-\! {\rm Hilbert} \!-\! {{\rm L}^2}$ model and multi-scale Retinex (MSR) to measure the shape of objects with patterns and letters by Fourier FPP. In this method, we first use the ${\rm TV} \!-\! {\rm Hilbert}\!-\!{{\rm L}^2}$ model to obtain the fringe part, then perform MSR enhancement on the fringe part, and finally decompose the enhanced fringe part with ${\rm TV} \!-\! {\rm Hilbert} \!-\! {{\rm L}^2}$ again. We evaluate the performance of this method via application to one computer-simulated noisy fringe projection pattern and two experimental fringe projection patterns with different types of patterns or letters, and comparison with the Fourier transform method, the variational image decomposition ${\rm TV} \!-\! {\rm Hilbert} \!-\! {{\rm L}^2}$ model. Furthermore, we apply the proposed method to the dynamic three-dimensional shape measurement of hand posture with pattern. The experimental results show that our method can effectively measure the dynamic shape of objects with patterns or letters from a single-frame fringe projection pattern.
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