Abstract
Traditional filtering methods only focused on improving the peak signal-to-noise ratio of the single fringe pattern, which ignore the filtering effect on phase extraction. Fringe phase-shifting field based fuzzy quotient space-oriented partial differential equations filtering method is proposed to reduce the phase error caused by Gaussian noise while filtering. First, the phase error distribution that is caused by Gaussian noise is analyzed. Furthermore, by introducing the fringe phase-shifting field and the theory of fuzzy quotient space, the modified filtering direction can be adaptively obtained, which transforms the traditional single image filtering into multi-image filtering. Finally, the improved fourth-order oriented partial differential equations with fidelity item filtering method is established. Experiments demonstrated that the proposed method achieves a higher signal-to-noise ratio and lower phase error caused by noise, while also retaining more edge details.
Highlights
Due to the advantages of non-contact, high speed, high precision, three-dimensional (3D) shape measurement, fringe projection profilometry (FPP) [1,2,3,4] has been widely used in industrial detection, quality inspection, etc
Through the simulated fringe images experiment, we can see that the FOPDEs method improves the peak signal-to-noise ratio of the fringe images and reduces the standard deviation of phase error that is caused by Gaussian noise
Gaussian filtering (Gaussian filtering), and four-step phase shifting with FOPDEs filtering method (FOPDEs) are used to process the fringe images above in Figure 10, respectively, in order to verify the filtering effect on phase error of the FOPDEs method proposed in this paper again, taking simulations listed here arewith implemented (STD) as the evaluation index
Summary
Due to the advantages of non-contact, high speed, high precision, three-dimensional (3D) shape measurement, fringe projection profilometry (FPP) [1,2,3,4] has been widely used in industrial detection, quality inspection, etc. Villa [21] proposed a fringe pattern denoising method based on Gaussian convolution to improve the performance of low-frequency fringes. If the traditional filtering methods were used, the edge information of fringe pattern will be blurred while filtering [9], which reduces the accuracy of phase extraction. To this end, partial differential equations (PDEs) methods, such as second-order. When considering the limitation above, fringe phase-shifting field based fuzzy quotient space-oriented partial differential equations filtering method (FOPDEs) is proposed for fringe image denoising problem, which provides the fringe image with higher PSNR and reduces the phase error that was caused by Gaussian noise.
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