Fringe pattern denoising using spatial oriented gaussian filters

Fringe Phase-Shifting Field Based Fuzzy Quotient Space-Oriented Partial Differential Equations Filtering Method for Gaussian Noise-Induced Phase Error

“…The PSNR and the standard deviation of phase error that are caused by Gaussian noise (STD) are used as indicators for filtering evaluation. The proposed FOPDEs method is compared with the commonly used methods, such as Gaussian filtering [16,17,18,21], mean filtering [16,17,18], wavelet transform [17], TV [19,20], and OPDEs [24], as shown in Table 1. Table 1 reflects the results of adding uniform noise to phase-shifting images and adding different noise to different phase-shifting images.…”

“…Additionally, I(x,y) is the gray value of pixel (x,y). Introducing time parameter t , then the image evolution process can be expressed as [8,20,21], ∂tu=F[u(x,y,t)],u(x,y,0)=I(x,y) where u(x,y,t) is the evolutionary image. F:R→R is an operator given for different image processing processes.…”

“…Let E and Es represent the energy function and the smoothing item, respectively. To preserve more details while filtering, based on the fourth-order OPDEs energy function model of literatures [8,20,21] and Equation (14), we introduce the fidelity item Ef to obtain an improved fourth-order OPDEs filtering model, which can be defined as, E(u)=Es(u)+Ef(u)=true∫Ω12|∂2u∂ρ2|2dxdy+λ2‖u0−u‖L22 where ρ represents the fringe direction of the image u(x,y), that is, the diffusion direction. λ is a constant, which reflects the fidelity of the original image and the denoised image.…”

“…However, the edges of binary patterns are often difficult to precisely distinguish, which reduces the measurement accuracy. The filtering method [16,17,18,19,20,21,22,23,24] is to reduce noise by means of filtering algorithms. Image filtering is a process of restoring noise-free image from noise image, in which the difficulty is how to protect details while reducing noise.…”

“…Traditional filtering methods [16,17,18,19,20], such as Gaussian filtering, median filtering, and wavelet transform, were proposed to reduce the noise. Villa [21] proposed a fringe pattern denoising method based on Gaussian convolution to improve the performance of low-frequency fringes. However, unlike general images, the digital fringe image has obvious directional characteristics and it presents sinusoidal distribution.…”