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

Yu, Changzhi; Ji, Fang; Xue, Juan; Wang, Yajun

doi:10.3390/s19235202

Cited by 5 publications

(6 citation statements)

References 35 publications

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“…It is worth noting that Gaussian filtering improves the quality of fringes without changing the sine of the fringes [5,6]. This is the theoretical premise that step 3 can improve the accuracy of the wrapped phase by regenerating the phase shift fringe images from the wrapped phase.…”

Section: Principles Of the Iterative Phase-correction Methodsmentioning

confidence: 99%

“…For instance, in [5], Gaussian filtering was used to filter the captured phase-shiftfringe images, thereby inhibiting phase errors caused by noise. Other researchers [6] have used a fuzzy-quotient spaceoriented partial-differential-equations filtering method to suppress Gaussian noise in captured images and improve phase accuracy. In [7], median filtering was used to preprocess captured images and filter out invalid data using a masking algorithm to improve the accuracy and precision of the phase solution.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An iterative phase-correction method for low-quality phase-shift images and its application

Chen¹,

Jin²,

Zhang³

et al. 2021

Meas. Sci. Technol.

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To solve the issue of phase recovery from low-quality fringe images (where the low quality is caused by noise, non-linear intensity and surface reflectivity changes), an iterative phase-correction method is proposed. The high-phase-precision solution is achieved by regenerating the phase-shift-fringe images from the wrapped phase and performing iterative filtering. In general, compared with conventional methods, the proposed iterative phase-correction method has three main advantages: (a) it suppresses the influence of noise without interference from surface reflectivity; (b) it effectively improves the wrapped phase accuracy, thereby improving 3D measurement accuracy, and (c) it effectively recovers the absolute phase (determined by a multi-frequency heterodyne method) information of surfaces with very low or very high reflectivities, without the additional projection of phase-shift-fringe images. The effectiveness of the proposed iterative phase-correction method is verified by simulation and experiment. The proposed method, applied to binocularly structured light, can improve measurement accuracy and greatly improve the effectiveness of measurement of objects with drastic changes in reflectivity. Based on the calibration accuracy (without gamma calibration of the projector) described in this paper, the root-mean-square deviation of the measurement results for binocularly structured light can reach 0.0094 mm.

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Section: Principles Of the Iterative Phase-correction Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An iterative phase-correction method for low-quality phase-shift images and its application

Chen¹,

Jin²,

Zhang³

et al. 2021

Meas. Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…In this section, we introduce the theory of fuzzy quotient space [35][36][37][38][39], and propose the dynamic granularity matrix space model. Considering the consistence of granularity division and image segmentation theory, a dynamic granularity matrix space model is proposed, and the problem of image segmentation can be reconstructed based on the DGMS model.…”

Section: B Dynamic Granularity Matrix Space Modelmentioning

confidence: 99%

“…According to Theorem 8, through the inclusion relation of quotient sets, the cluster of quotient sets will generate an ordered chain, that is, a hierarchical structure [35][36][37][38]. According to Theorem 8-9, a fu zzy equivalence relation corresponds to a hierarchical structure, also corresponds to a distance function.…”

Section: Ab  Must Have Solution On (X F T)mentioning

confidence: 99%

Dynamic Granularity Matrix Space Model Based High Robust Multi-Ellipse Center Extraction Method for Camera Calibration

Xue

2020

IEEE Access

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Ellipse center extract ion is the important basis of camera calib ration with circle arrays calibrat ion board, wh ich direct ly affects the measurement accuracy of mach ine vision system. A iming at the problem of high noise sensitivity of the most ellipse center extract ion methods, a high robust multi-ellipse center extraction method is proposed. The idea is to transform the problem of mult i-ellipse center extraction into the problems of ellipse sub-pixel edge segmentation and edge based ellipse center clustering. Firstly, the flowchart of the proposed method is introduced. Then, the theory of fuzzy quotient space is introduced to establish the dynamic granularity matrix space model, which describes image segmentation problem as the jump ing and transformat ion of the image by hierarchical structure. Finally, an adaptive multi-ellipse sub-pixel edge segmentation method and an optimal ellipse center ext raction method are proposed based on the dynamic granularity matrix space model. Experimental results sh ow that the proposed method has higher accuracy, robustness and lower camera calibration error. INDEX TERMS multi-ellipse center, dynamic granularity matrix space, sub-pixel edge segmentation, hierarchical structure, camera calibration.

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“…Yu et al [ 25 ] proposed a fringe phase-shifting, field-based, fuzzy quotient, space-oriented, partial differential equations filtering method, to reduce the phase error caused by Gaussian noise while filtering. Experiments demonstrated that the method achieves a higher signal-to-noise ratio and lower phase error caused by noise, while also retaining more edge details.…”

mentioning

confidence: 99%

Data, Signal and Image Processing and Applications in Sensors

Reis

2021

Sensors

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

Cited by 5 publications

References 35 publications

An iterative phase-correction method for low-quality phase-shift images and its application

An iterative phase-correction method for low-quality phase-shift images and its application

Dynamic Granularity Matrix Space Model Based High Robust Multi-Ellipse Center Extraction Method for Camera Calibration

Data, Signal and Image Processing and Applications in Sensors

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