A gamma error correction method for a fringe projection system

Abstract

The present invention discloses a gamma error correction method for a fringe projection system, comprising: step S1: building a fringe projection three-dimensional measurement system; step S2: calculating a full-cycle uncorrected truncated phase using a three-step phase shift method; step S3: converting the full-cycle uncorrected truncated phase into a 1 / 6-cycle uncorrected truncated phase; step S4: performing histogram equalization on the 1 / 6-cycle uncorrected truncated phase to obtain a 1 / 6-cycle corrected truncated phase, and converting it into a full-cycle corrected truncated phase; step S5: recovering the corrected absolute phase using a phase unwrapping algorithm, and then mapping the corrected absolute phase to a three-dimensional space based on the fringe projection system calibration result to reconstruct the three-dimensional shape of the object to be measured. The gamma error correction method for a fringe projection system provided by the present invention fully considers the periodicity and symmetry of the gamma error, does not require any pre-calibration process or additional fringe images, and has the advantages of high measurement accuracy, high speed, and strong flexibility.

Description

Technical Field

[0001] The present invention belongs to the field of visual measurement technology, and in particular, relates to a gamma error correction method for a fringe projection system. Background Art

[0002] Fringe projection profilometry, a commonly used optical 3D measurement method, offers advantages such as non-contact, high speed, high accuracy, and dense point clouds. It is widely used in industrial inspection, smart agriculture, biomedicine, consumer entertainment, and other fields. However, the gamma effect of fringe projection systems alters the intensity of fringe images, making it impossible to accurately calculate the fringe phase distribution using the phase shift method, introducing periodic phase errors.

[0003] Traditional gamma error correction methods generally require a pre-calibration process or additional fringe images, which reduces the measurement efficiency of the fringe projection system. The literature [Optics Express, 2019, 27(22): 32047-57] uses a probability density function to calibrate the gamma value, and the literature [Chinese Optics Letters, 2021, 19(10): 101201] uses a probability density function to calibrate the phase error coefficient. This method still requires a pre-calibration process to match the probability density curve. The literature [Optics Letters, 2021, 46(3): 476-479] directly performs histogram equalization on the truncated phase image to correct the gamma error without the need for a pre-calibration process. However, this method does not take into account the periodicity of the gamma error and needs to further improve the measurement accuracy. The literature [IEEE Transactions on Instrumentation and Measurement, 2022, 71: 5005509] utilizes the periodicity of gamma error, fuses three truncated phase images before and after the offset, and then uses histogram equalization to correct the gamma error, effectively improving the measurement accuracy. However, this method does not consider the symmetry of the gamma error, and the fusion of three truncated phase images increases the computational complexity.

[0004] In summary, how to effectively correct the gamma error of the fringe projection system is still of great practical significance. Summary of the Invention

[0005] The present invention provides a gamma error correction method for a fringe projection system to solve the problems existing in the above background technology.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is: a gamma error correction method for a fringe projection system, specifically comprising the following steps:

[0007] Step S1: Building a fringe projection 3D measurement system, including a projector, a camera, and an object to be measured. The projector, the camera, and the object to be measured form a triangulation relationship. Both the projector and the camera have a gamma effect.

[0008] Step S2: Trigger the projector to sequentially project three-step phase-shifted fringes onto the surface of the object to be measured, and synchronously trigger the camera to sequentially capture the three-step phase-shifted fringe images modulated by the object. The three-step phase shift method is used to calculate the full-cycle uncorrected truncated phase φ of the phase-shifted fringe images. GAM ;

[0009] Step S3: First, according to the periodicity of the gamma error, the uncorrected truncated phase φ of the whole cycle is GAM Converted to 1 / 3 cycle uncorrected truncation phase α GAM , and secondly, according to the symmetry of the gamma error, the 1 / 3 cycle uncorrected truncated phase α GAM Converted to 1 / 6 period uncorrected truncated phase β GAM ;

[0010] Step S4: Directly truncate the 1 / 6 cycle without correcting the phase β GAM Perform histogram equalization to obtain the 1 / 6 period corrected truncated phase β PHE , and then converted into 1 / 3 cycle corrected truncated phase α PHE , and then converted into the corrected truncated phase φ of the entire cycle PHE ;

[0011] Step S5: Calculate the corrected truncated phase φ of the entire cycle using the phase unwrapping algorithm PHE The corresponding fringe order, and then recover the corrected absolute phase Φ PHE , and then according to the calibration results of the fringe projection system, the corrected absolute phase Φ PHE Mapped to three-dimensional space, the three-dimensional shape of the object to be measured is reconstructed.

[0012] Preferably, under ideal conditions, that is, when the fringe projection system does not have a gamma effect, in step S2, the three-step phase-shifted fringe image captured by the camera is expressed as:

[0013] I n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ];

[0014] Where: n = 1, 2, 3; (x, y) represents the pixel coordinates of the camera; A and B represent the average intensity and modulation intensity respectively, φ represents the true truncated phase, δ n =2πn / 3 represents the phase shift of the nth fringe image.

[0015] Preferably, in actual situations, that is, when the fringe projection system has a gamma effect, in step S2, the three-step phase-shifted fringe image captured by the camera is expressed as:

[0016]

[0017] Where: a0 represents the DC component, a m It represents the amplitude of the mth harmonic, and its magnitude is inversely proportional to the value of m.

[0018] Preferably, in step S2, the calculation formula using the phase shift method is as follows:

[0019]

[0020] Because the high-order harmonic components are small, if the m≥6 harmonic components are ignored, the above formula can be converted to:

[0021]

[0022] Furthermore, the phase error introduced by the gamma effect, referred to as the gamma error, can be expressed as:

[0023]

[0024] Where: coefficients c1 and c2 are constants. According to the above gamma error calculation formula, it can be deduced that:

[0025] Δφ GAM ≈c1sin(3φ)=c1sin[3(φ+2π / 3)];

[0026] Δφ GAM ≈c1sin(3φ)=-c1sin[3(2π / 3-φ)];

[0027] The above formula shows that the gamma error is not only periodic, with a phase period of 2π / 3, but also symmetrical, with a central symmetry about the phase π / 3.

[0028] Preferably, in step S3, the conversion formula for the 1 / 3 cycle uncorrected truncation phase α is:

[0029] α GAM =mod(φ GAM ,2π / 3);

[0030] Where: function mod represents the remainder operation of two input parameters; at the same time, in order to identify each 1 / 3 period within a single fringe period, the following integer needs to be calculated:

[0031] b=floor[3φ GAM / (2π)];

[0032] In the formula: the function floor represents the operation of rounding down the input parameter.

[0033] Preferably, in step S3, the 1 / 6 cycle uncorrected truncation phase β GAM The conversion formula is:

[0034]

[0035] Similarly, to identify each 1 / 6 period within a single fringe period, the following integers need to be calculated:

[0036] d=floor(3α GAM / π).

[0037] Preferably, in step S4, the 1 / 3 cycle has been corrected and the truncated phase α PHE The conversion formula is:

[0038]

[0039] In step S4, the entire cycle has been corrected and the truncated phase φ PHE The conversion formula is:

[0040] φ PHE =α PHE +2πb / 3.

[0041] Preferably, in step S5, the phase unwrapping algorithm uses a multi-frequency method or a Gray code method to calculate the corrected truncated phase φ PHE The corresponding fringe order k can be used to recover the corrected absolute phase Φ PHE as follows:

[0042] Φ PHE =φ PHE +2πk.

[0043] The beneficial effects of adopting the above technical solution are:

[0044] 1. The present invention provides a gamma error correction method for a fringe projection system, which fully considers the periodicity and symmetry of the gamma error, does not require any pre-calibration process or additional fringe images, and has the advantages of high measurement accuracy, fast speed, and strong flexibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Basic principle of gamma error correction; where: (a) true truncated phase; (b) uncorrected truncated phase; (c) corrected truncated phase; (d) histogram of true truncated phase; (e) histogram of uncorrected truncated phase; (f) histogram of corrected truncated phase;

[0046] Figure 2 Gamma error correction real experiment; where: (a) image of the object to be measured; (b) distorted fringe image; (c) uncorrected truncated phase; (d) corrected truncated phase; (e) uncorrected 3D shape of the object to be measured; (f) corrected 3D shape of the object to be measured; DETAILED DESCRIPTION

[0047] The following is a further detailed description of the specific implementation methods of the present invention through the description of embodiments with reference to the accompanying drawings, with the aim of helping those skilled in the art to have a more complete, accurate and in-depth understanding of the concept and technical solution of the present invention and to facilitate its implementation.

[0048] like Figures 1 to 2 As shown, the present invention is a gamma error correction method for a fringe projection system, which fully considers the periodicity and symmetry of the gamma error, does not require any pre-calibration process and additional fringe images, and has the advantages of high measurement accuracy, fast speed and strong flexibility.

[0049] The specific working method is described below with specific embodiments:

[0050] Example 1:

[0051] Step S1: Build a fringe projection 3D measurement system, including a projector, a camera and an object to be measured. The projector, camera and object to be measured form a triangulation relationship. Both the projector and the camera have a gamma effect. The image of the object to be measured is as follows: Figure 2 As shown in (a);

[0052] Step S2: Trigger the projector to sequentially project three-step phase-shifted stripes onto the surface of the object to be measured, and synchronously trigger the camera to sequentially capture the three-step phase-shifted stripe images modulated by the object, such as Figure 2 As shown in (b), the three-step phase shift method is used to calculate the full-cycle uncorrected truncated phase φ of the phase-shifted fringe image. GAM ,like Figure 2 As shown in (c), the linearity is poor;

[0053] Step S3: First, according to the periodicity of the gamma error, the uncorrected truncated phase φ of the whole cycle is GAM Converted to 1 / 3 cycle uncorrected truncation phase α GAM , and secondly, according to the symmetry of the gamma error, the 1 / 3 cycle uncorrected truncated phase α GAM Converted to 1 / 6 period uncorrected truncated phase β GAM ; Figure 1(a) shows the true truncated phase of the full cycle, 1 / 3 cycle and 1 / 6 cycle; Figure 1 (d) shows the histogram of the true truncated phase of 1 / 6 period. Figure 1(b) shows the uncorrected truncated phases of the full cycle, 1 / 3 cycle, and 1 / 6 cycle; Figure 1 (e) shows the histogram of the uncorrected truncated phase of 1 / 6 period;

[0054] Step S4: Directly truncate the 1 / 6 cycle without correcting the phase β GAM Perform histogram equalization to obtain the 1 / 6 period corrected truncated phase β PHE , and then converted into 1 / 3 cycle corrected truncated phase α PHE , and then converted into the corrected truncated phase φ of the entire cycle PHE ;like Figure 2 As shown in (d), the linearity is good; Figure 1 (c) shows the corrected truncated phases of the full cycle, 1 / 3 cycle, and 1 / 6 cycle; Figure 1 (f) shows the histogram of the 1 / 6 period corrected truncated phase;

[0055] Step S5: Calculate the corrected truncated phase φ of the entire cycle using the phase unwrapping algorithm PHE The corresponding fringe order is then used to recover the corrected absolute phase Φ PHE , and then according to the calibration results of the fringe projection system, the corrected absolute phase Φ PHE Mapped to three-dimensional space, the three-dimensional shape of the object to be measured is reconstructed. Figure 2 (e) and Figure 2 (f) compares the three-dimensional morphology of the object to be measured before and after correction. Figure 2 The gamma error in (f) is significantly lower than Figure 2 The comparison results show the effectiveness of the method proposed in this invention.

[0056] The present invention is described above by way of example in conjunction with the accompanying drawings. Obviously, the specific implementation of the present invention is not limited to the above-mentioned method. As long as various non-substantial improvements are made using the method concept and technical solution of the present invention; or the above-mentioned concept and technical solution of the present invention are directly applied to other occasions without improvement, they are all within the scope of protection of the present invention.

Claims

1. A gamma error correction method for a fringe projection system, characterized by: The specific steps include: Step S1: Building a fringe projection 3D measurement system, including a projector, a camera, and an object to be measured. The projector, the camera, and the object to be measured form a triangulation relationship. Both the projector and the camera have a gamma effect. Step S2: Trigger the projector to sequentially project three-step phase-shifted fringes onto the surface of the object to be measured, and synchronously trigger the camera to sequentially capture the three-step phase-shifted fringe images modulated by the object. The three-step phase shift method is used to calculate the full-cycle uncorrected truncated phase φ of the phase-shifted fringe images. GAM ; Step S3: First, according to the periodicity of the gamma error, the uncorrected truncated phase φ of the whole cycle is GAM Converted to 1 / 3 cycle uncorrected truncation phase α GAM , and secondly, according to the symmetry of the gamma error, the 1 / 3 cycle uncorrected truncated phase α GAM Converted to 1 / 6 period uncorrected truncated phase β GAM ; Step S4: Directly truncate the 1 / 6 cycle without correcting the phase β GAM Perform histogram equalization to obtain the 1 / 6 period corrected truncated phase β PHE , and then converted into 1 / 3 cycle corrected truncated phase α PHE , and then converted into the corrected truncated phase φ of the entire cycle PHE ; Step S5: Calculate the corrected truncated phase φ of the entire cycle using the phase unwrapping algorithm PHE The corresponding fringe order, and then recover the corrected absolute phase Φ PHE , and then according to the calibration results of the fringe projection system, the corrected absolute phase Φ PHE Mapped to three-dimensional space, the three-dimensional shape of the object to be measured is reconstructed.

2. The gamma error correction method for a fringe projection system according to claim 1, wherein: In an ideal situation, that is, when the fringe projection system does not have a gamma effect, in step S2, the three-step phase-shifted fringe image captured by the camera is expressed as: Yo n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ]; Where: n = 1, 2, 3; (x, y) represents the pixel coordinates of the camera; A and B represent the average intensity and modulation intensity respectively, φ represents the true truncated phase, δ n =2πn / 3 represents the phase shift of the nth fringe image.

3. The gamma error correction method for a fringe projection system according to claim 2, wherein: In actual situations, that is, when the fringe projection system has a gamma effect, in step S2, the three-step phase-shifted fringe image captured by the camera is expressed as: Where: a0 represents the DC component, a m It represents the amplitude of the mth harmonic, and its magnitude is inversely proportional to the value of m.

4. The gamma error correction method for a fringe projection system according to claim 3, wherein: In step S2, the calculation formula using the phase shift method is as follows: Because the high-order harmonic components are small, if the m≥6 harmonic components are ignored, the above formula can be converted to: Furthermore, the phase error introduced by the gamma effect, referred to as the gamma error, can be expressed as: Where: coefficients c1 and c2 are constants. According to the above gamma error calculation formula, it can be deduced that: Df GAM ≈c1sin(3φ)=c1sin[3(φ+2π / 3)]; Df GAM ≈c1sin(3φ)=-c1sin[3(2π / 3-φ)]; The above formula shows that the gamma error is not only periodic, with a phase period of 2π / 3, but also symmetrical, with a central symmetry about the phase π / 3.

5. The gamma error correction method for a fringe projection system according to claim 1, wherein: In step S3, the 1 / 3 cycle uncorrected truncation phase α GAM The conversion formula is: a GAM =mod(φ GAM ,2π / 3); Where: function mod represents the remainder operation of two input parameters; at the same time, in order to identify each 1 / 3 period within a single fringe period, the following integer needs to be calculated: b=floor[3φ GAM / (2π)]; In the formula: the function floor represents the operation of rounding down the input parameter.

6. The gamma error correction method for a fringe projection system according to claim 5, characterized in that: In step S3, the 1 / 6 period uncorrected truncation phase β GAM The conversion formula is: Similarly, to identify each 1 / 6 period within a single fringe period, the following integers need to be calculated: d=floor(3a GAM / p).

7. The gamma error correction method for a fringe projection system according to claim 6, wherein: In step S4, the 1 / 3 cycle has been corrected and the truncated phase α PHE The conversion formula is: In step S4, the entire cycle has been corrected and the truncated phase φ PHE The conversion formula is: f PHE =a PHE +2πb / 3.

8. The gamma error correction method for a fringe projection system according to claim 1, wherein: In step S5, the phase unwrapping algorithm uses a multi-frequency method or a Gray code method to calculate the corrected truncated phase φ PHE The corresponding fringe order k can be used to recover the corrected absolute phase Φ PHE as follows: F PHE =φ PHE +2πk.

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