A time-varying nonlinear gamma parameter correction method and three-dimensional measurement system

Abstract

The present invention discloses a flexible projector nonlinear correction method and a three-dimensional measurement system, which relate to the field of optical three-dimensional measurement. First, a simulation program is used to generate a data set, and then a support vector regression machine model is trained with the generated data set. The support vector regression machine estimates the gamma value of the system according to the probability density function of the folded phase, and then an iterative algorithm is run to correct the nonlinear error to obtain an accurate folded phase. Finally, a time phase unfolding algorithm and a triangulation principle are used to generate point cloud data. The proposed nonlinear correction method does not require an increase in the number of projected images, nor does it require a complex photometric calibration process, and the nonlinear error of the system can be corrected in the fringe analysis stage. The method proposed by the present invention can solve the time-varying nonlinear problem and realize high-speed and high-precision three-dimensional measurement.

Description

Technical Field

[0001] The present invention is aimed at the field of structured light three-dimensional measurement, and is mainly a method for nonlinear correction of a projector. Background Art

[0002] Three-dimensional measurement is a widely used three-dimensional data acquisition method, which is widely used in intelligent manufacturing, reverse engineering, medical detection and other fields. Structured light projection technology, especially phase shift profilometry, is widely used in three-dimensional measurement due to its high precision and high speed. This technology projects sinusoidal fringes onto the surface of an object, collects deformed fringes modulated by the depth of the object, and obtains depth information by demodulating the phase of the deformed fringes. It is worth noting that the sinusoidality of the fringe signal directly affects the measurement accuracy, while the nonlinear response of the light source will cause the fringes to be non-sinusoidal, so that the measurement results contain periodic nonlinear errors. Studies have shown that increasing the number of projected images can reduce the phase error caused by nonlinear distortion. However, projecting too many images is not only not conducive to high-speed measurement, but also makes the measurement results affected by illumination fluctuations. Therefore, achieving high-speed and high-precision three-dimensional measurement with only a small number of projected images has always been the focus of phase shift profilometry research. Summary of the invention

[0003] The purpose of the present invention is to propose a time-varying nonlinear gamma parameter correction method and a three-measurement system to solve the above problems.

[0004] To achieve this object, the present invention proposes the following solution.

[0005] The time-varying nonlinear gamma parameter correction method includes the following steps:

[0006] Step A: Use a simulation program to generate probability density curves of the folding phase at different gamma values.

[0007] Step B: The probability density curve and gamma value generated in step A are combined into a training set to train a support vector regression machine. The trained support vector regression machine can estimate the gamma value of the system based on the probability density curve of the folded phase.

[0008] Step C: Project the ideal phase shift pattern generated by the computer onto the surface of the object to be measured, and take a photo to obtain the fringe pattern.

[0009] Step D: Use a phase shift algorithm to solve the folded solution phase, and calculate the probability density curve of the folded phase.

[0010] Step E: Input the probability density curve in step D into the support vector regression machine trained in step B to obtain the gamma value of the system.

[0011] Step F: Establish a loss function according to the gamma value in E, and use the Gauss-Newton method to optimize and solve the minimum point of the loss function, that is, the folding phase that eliminates the nonlinear error.

[0012] Furthermore, all the distortion-free shifted fringes in the present invention are as shown in Formula 1:

[0013] I n (x,y)=a(x,y)+b(x,y)cos(2πfx+δ n ),n=0,1,2 Formula 1;

[0014] Among them I n is the gray level of the fringe pattern, a is the DC component, b is the modulation intensity, f is the fringe spatial frequency, δ n is the phase shift.

[0015] Furthermore, the phase-shifted fringe pattern after gamma distortion is shown in Formula 2:

[0016]

[0017] in is the light intensity output by the projector, and γ is the gamma value of the projector.

[0018] Furthermore, the intensity distribution of the sinusoidal fringes collected by the camera is shown in Formula 3:

[0019]

[0020] in is the light intensity collected by the camera, R is the reflectivity of the object surface, B is the background light intensity, and φ represents the phase after height modulation.

[0021] Furthermore, the solution formulas for the folded phase and the solution formulas for the probability density curve in step A and step D are shown in Formula 4 and Formula 5, respectively:

[0022]

[0023]

[0024] Where F represents the probability density curve and M represents the number of sampling points.

[0025] Furthermore, the loss function in step F is shown in Formula 6:

[0026]

[0027] in Represents the estimated light intensity:

[0028]

[0029] Furthermore, the Gauss-Newton optimization algorithm in step F is shown in Formula 8:

[0030] [R (k+1) ,B (k+1) ,φ (k+1) ] T =[R (k) ,B (k) ,φ (k) ] T -[(J (k) ) T J (k) ] -1 (J (k) ) T r(R (k) ,B (k) ,φ (k) )Formula 8;

[0031] Where J represents the Jacobian matrix:

[0032]

[0033] The initial value of φ in Formula 8 is φ (0) Determined by formula 4, R (0) and B (0) Determined by formula 10 and formula 11:

[0034]

[0035]

[0036] When |φ (k+1) -φ (k) When |<ε0, the Gauss-Newton method iteration stops, and ε0 is the threshold for stopping the iteration.

[0037] The present invention also provides a time-varying nonlinear gamma parameter correction three-dimensional measurement system, which includes a fringe projection module, an image acquisition module, a phase calculation module, a probability density calculation module, a gamma value estimation module, an error correction module, a phase expansion module and a point cloud generation module.

[0038] The projection module is responsible for projecting the ideal sinusoidal fringes generated by the computer onto the surface of the object.

[0039] The image acquisition module acquires the fringe pattern under the control of the synchronization signal.

[0040] The phase calculation module calculates the folding phase according to formula 4.

[0041] The probability density calculation module calculates the probability density of the folded phase according to formula five.

[0042] The gamma value estimation module calculates the gamma value of the system according to the calculated probability density.

[0043] The error correction module runs the iterative algorithm shown in Formula 8 to correct the nonlinear error.

[0044] The phase unwrapping module uses a temporal phase unwrapping algorithm to calculate the unwrapped phase.

[0045] The point cloud generation module converts the phase into a point cloud according to the geometric parameters pre-calibrated by the system.

[0046] The present invention proposes a time-varying nonlinear gamma parameter correction three-dimensional measurement system. First, a data set is generated by simulation, and then a support vector regression machine model is trained with the generated data set. The support vector regression machine estimates the gamma value of the system according to the probability density function of the folded phase, and then an iterative algorithm is run to correct the nonlinear error to obtain an accurate folded phase. Finally, a time phase unfolding algorithm and a triangulation principle are used to generate point cloud data.

[0047] The advantages are: the time-varying nonlinear gamma parameter correction method and three-dimensional measurement system proposed in the present invention do not need to project a large number of images or perform complex photometric calibration on the system in advance, and the nonlinear error correction is simply regarded as a post-processing process, which is suitable for occasions where the nonlinear response of the system changes with time. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings further illustrate the present invention, but the contents of the accompanying drawings do not constitute any limitation to the present invention;

[0049] Figure 1 It is a schematic diagram of the flow chart of the time-varying nonlinear gamma parameter correction method of the present invention;

[0050] Figure 2 It is a structural block diagram of the time-varying nonlinear gamma parameter correction three-dimensional measurement system of the present invention;

[0051] Figure 3 This is a result diagram of an embodiment of the present invention; DETAILED DESCRIPTION

[0052] In order to more clearly demonstrate the technical solutions and device advantages involved in the present invention, the technical details and specific implementation methods of the present invention are described in detail below:

[0053] First, the probability density curves for different gamma values ​​are generated through the simulation program. The sampling range of gamma value is 1 to 5, and the sampling interval is 0.01.

[0054] Use the generated probability density curve and the corresponding gamma value to form a data set to train a support vector regression machine. Training a support vector regression machine requires kernel function selection and hyperparameter optimization. The kernel function selected in this example is the Gaussian kernel function. The three hyperparameters are: kernel size σ = 0.023, regularization coefficient C = 574.81, and insensitivity coefficient ε = 0.0015. After training, the support vector regression machine can estimate the gamma value of the system based on the probability density curve.

[0055] Computer-generated sinusoidal fringes are projected onto the surface of the object and captured by a camera under the control of a synchronization signal.

[0056] The three-step phase shift algorithm shown in formula 4 is used to solve the folded phase.

[0057] Formula 5 is used to solve the probability density function of the folded phase.

[0058] The probability density function is input into the trained support vector regression model, and the model outputs the gamma value of the system.

[0059] The loss function is established according to Formula 6, and then the Gauss-Newton method shown in Formula 8 is used for optimization and solution to obtain the folded phase without nonlinear noise.

[0060] The present invention also provides a three-dimensional measurement system for this method, including a fringe projection module, an image acquisition module, a phase calculation module, a probability density calculation module, a gamma value estimation module, an error correction module, a phase unwrapping module and a point cloud generation module.

[0061] The projection module is responsible for projecting the ideal sinusoidal fringes generated by the computer onto the surface of the object.

[0062] The image acquisition module acquires the fringe pattern under the control of the synchronization signal.

[0063] The phase calculation module calculates the folding phase according to formula 4.

[0064] The probability density calculation module calculates the probability density of the folded phase according to formula five.

[0065] The gamma value estimation module calculates the gamma value of the system according to the calculated probability density.

[0066] The error correction module runs the iterative algorithm shown in Formula 8 to correct the nonlinear error.

[0067] The phase unwrapping module uses a time phase unwrapping algorithm to calculate the unwrapped phase.

[0068] The point cloud generation module converts the phase into a point cloud according to the geometric parameters pre-calibrated by the system.

[0069] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

[0070] The present invention proposes a time-varying nonlinear gamma parameter correction method and a three-dimensional measurement system. Firstly, a data set is generated by simulation, and then a support vector regression machine model is trained with the generated data set. The support vector regression machine estimates the gamma value of the system according to the probability density function of the folded phase, and then an iterative algorithm is run to correct the nonlinear error to obtain an accurate folded phase. Finally, a time phase unfolding algorithm and a triangulation principle are used to generate point cloud data.

[0071] The advantages are: the time-varying nonlinear gamma parameter correction method proposed in the present invention is a flexible projector nonlinear correction method and a three-dimensional measurement system, which does not require projecting a large number of images or performing complex photometric calibration on the system in advance. The nonlinear error correction is simply regarded as a post-processing process, and is suitable for occasions where the nonlinear response of the system changes with time.

Claims

1. A time-varying nonlinear gamma parameter correction method, characterized in that: It includes the following steps: Step A: Use a simulation program to generate probability density curves of folding phases at different gamma values; Step B: The probability density curve and gamma value generated in step A are combined into a training set to train a support vector regression machine. The trained support vector regression machine can estimate the gamma value of the system according to the probability density curve of the folded phase. Step C: Projecting the ideal phase shift pattern generated by the computer onto the surface of the object to be measured, and taking a photo to obtain the fringe pattern; Step D: using a phase shift algorithm to solve the folded solution phase, and calculating a probability density curve of the folded phase; Step E: Input the probability density curve in step D into the support vector regression machine trained in step B to obtain the gamma value of the system; Step F: Establish a loss function according to the gamma value in E, and use the Gauss-Newton method to optimize and solve the minimum point of the loss function, that is, the folding phase that eliminates the nonlinear error.

2. The time-varying nonlinear gamma parameter correction method according to claim 1, characterized in that: All the distortion-free shifted stripes in the present invention are as shown in Formula 1, and the spatial frequency of the stripes should be 16 to 128. I n (x,y)=a(x,y)+b(x,y)cos(2πfx+δ n ),n=0,1,2 or: Among them I n is the grayscale of the fringe pattern, a is the DC component, b is the modulation intensity, f is the fringe spatial frequency, δ n is the phase shift; The grayscale distribution of the phase-shifted stripes after gamma distortion is shown in Formula 2: in is the light intensity output by the projector, γ is the gamma value of the projector; The intensity distribution of the sinusoidal stripes collected by the camera is shown in Formula 3: in is the light intensity collected by the camera, R is the reflectivity of the object surface, and B is the background light intensity.

3. The time-varying nonlinear gamma parameter correction method according to claim 2, characterized in that: The solution formulas for the folding phase and the solution formulas for the probability density curve in step A and step D are shown in formula 4 and formula 5 respectively: Where F represents the probability density curve and M represents the number of sampling points.

4. According to the time-varying nonlinear gamma parameter correction method of claim 3, the gamma value that can be estimated by the support vector regression machine in step E is in the range of 1 to 5.

5. The time-varying nonlinear gamma parameter correction method according to claim 4, characterized in that: The loss function in step F is shown in formula 6: in Represents the estimated light intensity:

6. The time-varying nonlinear gamma parameter correction method according to claim 5, characterized in that: The Gauss-Newton optimization algorithm in step F is shown in Formula 8: [R (k+1) ,B (k+1) ,φ (k+1) T =[R (k) ,B (k) ,φ (k) T -[(J (k) ) T J (k) -1 (J (k) ) T r(R (k) ,B (k) ,φ (k) ) Formula VIII;​​​ Where J represents the Jacobian matrix: The initial value of φ in Formula 8 is φ (0) Determined by formula 4, R (0) and B (0) Determined by formula 10 and formula 11: When |φ (k+1) - φ (k) | < ε0, the Gauss - Newton method iteration stops, where ε0 is the threshold for iteration to stop.

7. A three-dimensional measurement system for time-varying nonlinear gamma parameter correction, which implements the time-varying nonlinear gamma parameter correction method of claim 6, characterized in that: It includes a fringe projection module, an image acquisition module, a phase calculation module, a probability density calculation module, a gamma value estimation module, an error correction module, a phase unwrapping module and a point cloud generation module; The projection module is responsible for projecting the ideal sinusoidal fringes generated by the computer onto the surface of the object; The image acquisition module acquires the fringe pattern under the control of the synchronization signal; The phase calculation module calculates the folding phase according to formula 4; The probability density calculation module calculates the probability density of the folded phase according to formula 5; The gamma value estimation module calculates the gamma value of the system according to the calculated probability density; The error correction module runs the iterative algorithm shown in Formula 8 to correct the nonlinear error; The phase unwrapping module uses a time phase unwrapping algorithm to calculate the unwrapped phase; The point cloud generation module converts the phase into a point cloud according to the geometric parameters pre-calibrated by the system.

8. The time-varying nonlinear gamma parameter correction three-dimensional measurement system according to claim 7, characterized in that: The wavelength range of the projector is in the visible light band, that is, 400nm to 760nm.

9. The three-dimensional measurement system for time-varying nonlinear gamma parameter correction according to claim 7, wherein the maximum time-varying interval that the system can handle is 50 ms.

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