The new second-order single oriented partial differential equations for optical interferometry fringes with high density

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

“…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.…”

“…Therefore, how to filter the Gaussian noise effectively is very important in accurately extracting the phase information. 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.…”

“…To this end, partial differential equations (PDEs) methods, such as second-order PDEs, total variation (TV), fourth-order PDEs, oriented PDEs (OPDEs), etc., have been applied for filtering electronic speckle pattern interferometry (ESPI) fringe patterns, which makes the filtering only be carried out along the fringe direction. Tang [20,22,23] proposed a second-order single oriented PDEs method to solve the denoising problems for optical interferometry fringes, and then provided various methods that were based on PDEs. Yang [24] put forward an adaptive model combining the TV and fractional-order differentiation filter for such problems.…”

“…Yang [24] put forward an adaptive model combining the TV and fractional-order differentiation filter for such problems. The second-order PDEs [20,23,24,25] easily lead to the phenomenon of the staircase effect, while the four-order PDEs [26] can effectively reduce the staircase phenomenon and get more attention and application. Recently, through introducing the controlling speed function, Tang [9] established an adaptive oriented PDEs filtering method for discontinuous optical fringe patterns.…”

Variational image decomposition for estimation of fringe orientation and density from electronic speckle pattern interferometry fringe patterns with greatly variable density

“…Fringe orientation and density are important properties of fringes for directing electronic speckle pattern interferometry (ESPI) fringes processing such as image filtering [1][2][3] and skeleton extraction [4]. Obviously, errors in estimation of fringe orientation or density will affect noise reduction and as a consequence the accuracy of the fringe analysis.…”