A single-camera-based three-dimensional projection deformation measurement and error compensation method

Abstract

The application relates to a single-camera-based three-dimensional projection deformation measurement and error compensation method, which comprises the following steps: acquiring a plurality of projection images at different time points by a single camera, and recording the image intensity values of each pixel coordinate in each projection image at each time point; inputting the image intensity values into a pre-trained deep learning model to output the three-dimensional height prediction of the corresponding pixel coordinates at the corresponding time point; performing correlation search on the image intensity values of the pixel coordinates in the projection images at the reference time point and the deformation time point to obtain the optimal pixel displacement component; constructing the image plane displacement vector at the deformation time point based on the three-dimensional height prediction of the pixel coordinates at the reference time point and the deformation time point and the optimal pixel displacement component, and calculating the three-dimensional displacement field at the deformation time point based on the image plane displacement vector at the deformation time point; then, three-dimensional strain field calculation is performed; finally, an efficient and robust closed-loop process is formed through error compensation, and the measurement and compensation of three-dimensional deformation in a single-camera scene are realized.

Description

Technical Field

[0001] This application relates to the field of deformation measurement and error compensation technology, and in particular to a method for three-dimensional projection deformation measurement and error compensation based on a single camera. Background Technology

[0002] In dynamic 3D deformation measurement, traditional methods rely on multiple cameras or cumbersome lookup tables for phase disambiguation, resulting in computational complexity, insufficient real-time performance, and an inability to fully capture displacement and strain fields at multiple time points. Furthermore, the high complexity of the equipment makes it difficult to adapt to single-camera environments and complex surface textures / lighting variations, impacting deformation accuracy and application scalability. Therefore, there is an urgent need for a deformation measurement method that can achieve end-to-end 3D reconstruction, automatic deformation prediction and compensation under a single camera, support high-precision displacement / strain measurement at multiple time points, and integrate anomaly detection to improve robustness. Summary of the Invention

[0003] Therefore, it is necessary to provide a method for measuring and compensating for 3D projection deformation based on a single camera, including:

[0004] S1: Acquire several projected images of the surface of the object under test at multiple times using a single camera, and record the image intensity value at each pixel coordinate in each projected image at each time.

[0005] S2: Input the image intensity value of the same pixel coordinate in each projected image at any time into the pre-trained deep learning model, and output the 3D height prediction of the corresponding pixel coordinate at the corresponding time.

[0006] S3: Based on the image intensity values ​​of pixel coordinates at each location in each projected image at the reference time and deformation time, perform correlation search to obtain the optimal pixel displacement component;

[0007] S4: Based on the three-dimensional height prediction of each pixel coordinate at the reference time and the deformation time, the optimal pixel displacement component is used to construct the image plane displacement vector at the deformation time, and the three-dimensional displacement field at the deformation time is calculated based on the image plane displacement vector at the deformation time.

[0008] S5: Perform central difference calculation on the three-dimensional displacement field at the deformation moment to obtain the three-dimensional strain field; calculate the maximum principal strain value based on the three-dimensional strain field;

[0009] S6: When the maximum principal strain value is greater than the preset threshold, correct the abnormal three-dimensional height prediction and adjust the network parameters of the deep learning model. Based on the corrected height prediction and the adjusted deep learning model, repeat steps S2-S5 until the maximum principal strain value is less than or equal to the preset threshold, and output the final three-dimensional displacement field and three-dimensional strain field.

[0010] Preferably, S1 includes:

[0011] The projector projects a coded pattern of mixed sinusoidal fringes and speckle onto the surface of the object under test to form a projected image, and projects four different phase-shifted projected images at each time.

[0012] A single camera synchronously acquires four different phase-shifted projection images of the surface of the object under test at each moment, and records the image intensity value at the pixel coordinates of each phase-shifted projection image at each moment.

[0013] Preferably, the phase shifts of the four different phase-shifted projection images are 0, π / 2, π, and 3π / 2, respectively.

[0014] Preferably, the pixel coordinates in each projected image at the deformation time The formula for calculating the image intensity value at a given location is:

[0015] ;

[0016] in, Indicates the moment of deformation Pixel coordinates in the j-th phase-shifted projection image Image intensity value at that location, Represents the pixel coordinates in the j-th phase-shifted projection image. , Indicates the moment of deformation The object under test in pixel coordinates The surface reflection characteristic function at that location, Represents pixel coordinates The imaging noise term at that location.

[0017] Preferably, in S2, the expression for the pre-trained deep learning model is:

[0018] ;

[0019] in, Indicates the moment of deformation Next pixel coordinates Three-dimensional height prediction at the location, This represents a pre-trained deep learning model. Represents the network parameters of a deep learning model. Indicates the moment of deformation Pixel coordinates in each projected image Image intensity value at that location.

[0020] Preferably, the pre-training process of a deep learning model includes:

[0021] The total loss function is constructed based on the high prediction error and smoothing loss. The expression for the total loss function is as follows:

[0022] ;

[0023] ;

[0024] ;

[0025] in, Represents the total loss function. This represents the first loss weighting coefficient. This represents the second loss weighting coefficient. This indicates a high prediction error loss. Represents the smoothing loss term. The first output of the deep learning model represents the... i 3D height prediction for each pixel Indicates the first i The actual height label of each pixel. This represents the Gaussian filter function. Represents absolute value. This represents the total number of pixels involved in the loss calculation;

[0026] The pre-trained deep learning model is obtained by updating the network parameters of the deep learning model by minimizing the total loss function.

[0027] Preferably, S3 includes:

[0028] The correlation coefficient is calculated based on the image intensity values ​​at each pixel coordinate in the projected images at the reference time and deformation time. The calculation formula is as follows:

[0029] ;

[0030] in, Represents the correlation coefficient. Indicates the center of the relevant window. Indicates along x Displacement components in the direction, Indicates along y Displacement components in the direction, Represents the set of related windows. Indicates reference time Pixel coordinates in each projected image Image intensity value at that location, express The mean of the intensity values ​​of each image. Indicates the moment of deformation Pixel coordinates in each projected image Image intensity value at that location, express The mean of the intensity values ​​of each image in the middle;

[0031] The optimal pixel displacement component is obtained by maximizing the correlation coefficient.

[0032] Preferably, in S4, the optimal pixel displacement components are used to construct the image plane displacement vector at the deformation time based on the 3D height prediction of each pixel coordinate at the reference time and the deformation time. The expression for the image plane displacement vector is:

[0033] ;

[0034] in, This represents the image plane displacement vector at the moment of deformation. Indicates along x The optimal pixel displacement component in the direction. Indicates along y The optimal pixel displacement component in the direction. Indicates the moment of deformation Next pixel coordinates Three-dimensional height prediction at the location, Indicates reference time Next pixel coordinates Three-dimensional height prediction at the location, Indicates transpose;

[0035] The three-dimensional displacement field at the deformation moment is calculated based on the image plane displacement vector at the deformation moment. The calculation formula is as follows:

[0036] ;

[0037] in, Indicates the moment of deformation The three-dimensional displacement field This represents the mapping matrix.

[0038] Preferably, in S5, the formula for calculating the three-dimensional strain field is:

[0039] ;

[0040] ;

[0041] ;

[0042] in, express x Principal strain components in the direction, express y Principal strain components in the direction, Represents the shear strain components. Indicates along x Displacement components in the direction, Indicates along y Displacement components in the direction, Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along x Displacement components in the direction, express x Physical pixel spacing in the direction Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along x Displacement components in the direction, Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along y Displacement components in the direction, express y Physical pixel spacing in the direction Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along y Displacement components in the direction, This represents the partial derivative.

[0043] Preferably, in S6, the modified formula is:

[0044] ;

[0045] in, Indicates the moment of deformation Next pixel coordinates The corrected 3D height prediction Indicates the first i Candidate heights for pixels with 3D height prediction anomalies. Represents pixel coordinates The median of the predicted 3D height within the domain. Represents absolute value;

[0046] The formula is adjusted as follows:

[0047] ;

[0048] in, This represents the adjusted network parameters of the deep learning model. Represents the network parameters of a deep learning model. Indicates the learning rate. This represents the gradient of the total loss function with respect to the network parameters when an anomaly in 3D height prediction occurs.

[0049] Beneficial effects: This method acquires several projected images at multiple time points using a single camera and records the image intensity value at each pixel coordinate in each projected image at each time point. The image intensity value is input into a pre-trained deep learning model, which outputs the 3D height prediction of the corresponding pixel coordinate at the corresponding time point. Based on the image intensity values ​​of each pixel coordinate in each projected image at the reference time and deformation time, correlation search is performed to obtain the optimal pixel displacement component. Based on the 3D height prediction of each pixel coordinate at the reference time and deformation time, the optimal pixel displacement component is used to construct the image plane displacement vector at the deformation time. The 3D displacement field at the deformation time is calculated based on the image plane displacement vector at the deformation time, followed by the calculation of the 3D strain field. Finally, an efficient and robust closed-loop process is formed through error compensation, which effectively solves the problems of insufficient accuracy and real-time performance of traditional methods in single-camera environments, and realizes the measurement and compensation of 3D deformation in single-camera scenes. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 This is a flowchart of a single-camera-based three-dimensional projection deformation measurement and error compensation method in an embodiment of this application. Detailed Implementation

[0052] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0053] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0054] like Figure 1 As shown, this embodiment provides a method for three-dimensional projection deformation measurement and error compensation based on a single camera, including:

[0055] S1: Acquire several projected images of the surface of the object under test at multiple times using a single camera, and record the image intensity value at each pixel coordinate in each projected image at each time.

[0056] Specifically, the steps include:

[0057] The projector projects a coded pattern of mixed sinusoidal fringes and speckle onto the surface of the object under test to form a projected image, and projects four different phase-shifted projected images at each time.

[0058] A single camera synchronously acquires four different phase-shifted projection images of the surface of the object under test at each moment, and records the image intensity value at the pixel coordinates of each phase-shifted projection image at each moment.

[0059] Optionally, the phase shifts of the four different phase-shifted projection images are 0, π / 2, π, and 3π / 2, respectively.

[0060] Optional, pixel coordinates in each projected image at the deformation time. The formula for calculating the image intensity value at a given location is:

[0061] ;

[0062] in, Indicates the moment of deformation Pixel coordinates in the j-th phase-shifted projection image Image intensity value at that location, Represents the pixel coordinates in the j-th phase-shifted projection image. , Indicates the moment of deformation The object under test in pixel coordinates The surface reflection characteristic function at that location, Represents pixel coordinates The imaging noise term at that location.

[0063] S2: Input the image intensity value of the same pixel coordinate in each projected image at any time into the pre-trained deep learning model, and output the 3D height prediction of the corresponding pixel coordinate at the corresponding time.

[0064] Specifically, the expression for a pre-trained deep learning model is:

[0065] ;

[0066] in, Indicates the moment of deformation Next pixel coordinates Three-dimensional height prediction at the location, This represents a pre-trained deep learning model. Represents the network parameters of a deep learning model. Indicates the moment of deformation Pixel coordinates in each projected image Image intensity value at that location.

[0067] Optionally, the pre-training process for deep learning models includes:

[0068] The total loss function is constructed based on the high prediction error and smoothing loss. The expression for the total loss function is as follows:

[0069] ;

[0070] ;

[0071] ;

[0072] in, Represents the total loss function. This represents the first loss weighting coefficient. This represents the second loss weighting coefficient. This indicates a high prediction error loss. Represents the smoothing loss term. The first output of the deep learning model represents the... i 3D height prediction for each pixel Indicates the first i The actual height label of each pixel. This represents the Gaussian filter function. Represents absolute value. This represents the total number of pixels involved in the loss calculation;

[0073] The pre-trained deep learning model is obtained by updating the network parameters of the deep learning model by minimizing the total loss function.

[0074] S3: Based on the image intensity values ​​of pixel coordinates at each location in each projected image at the reference time and deformation time, perform correlation search to obtain the optimal pixel displacement component.

[0075] Specifically, the steps include:

[0076] The correlation coefficient is calculated based on the image intensity values ​​at each pixel coordinate in the projected images at the reference time and deformation time. The calculation formula is as follows:

[0077] ;

[0078] in, Represents the correlation coefficient. Indicates the center of the relevant window. Indicates along x Displacement components in the direction, Indicates along y Displacement components in the direction, Represents the set of related windows. Indicates reference time Pixel coordinates in each projected image Image intensity value at that location, express The mean of the intensity values ​​of each image. Indicates the moment of deformation Pixel coordinates in each projected image Image intensity value at that location, express The mean of the intensity values ​​of each image in the middle;

[0079] The optimal pixel displacement component is obtained by maximizing the correlation coefficient, and the calculation formula is:

[0080] ;

[0081] in, Indicates along x The optimal pixel displacement component in the direction. Indicates along y The optimal pixel displacement component in the direction.

[0082] S4: Based on the 3D height prediction of each pixel coordinate at the reference time and the deformation time, the optimal pixel displacement component is used to construct the image plane displacement vector at the deformation time, and the 3D displacement field at the deformation time is calculated based on the image plane displacement vector at the deformation time.

[0083] Specifically, based on the 3D height prediction of each pixel coordinate at the reference time and the deformation time, the optimal pixel displacement components are used to construct the image plane displacement vector at the deformation time. The expression for the image plane displacement vector is:

[0084] ;

[0085] in, This represents the image plane displacement vector at the moment of deformation. Indicates along x The optimal pixel displacement component in the direction. Indicates along y The optimal pixel displacement component in the direction. Indicates the moment of deformation Next pixel coordinates Three-dimensional height prediction at the location, Indicates reference time Next pixel coordinates Three-dimensional height prediction at the location, Indicates transpose;

[0086] The three-dimensional displacement field at the deformation moment is calculated based on the image plane displacement vector at the deformation moment. The calculation formula is as follows:

[0087] ;

[0088] in, Indicates the moment of deformation The three-dimensional displacement field This represents the mapping matrix.

[0089] S5: Perform central difference calculation on the three-dimensional displacement field at the deformation moment to obtain the three-dimensional strain field; based on the three-dimensional strain field, calculate the maximum principal strain value.

[0090] Specifically, the formula for calculating the three-dimensional strain field is:

[0091] ;

[0092] ;

[0093] ;

[0094] in, express x Principal strain components in the direction, express y Principal strain components in the direction, Represents the shear strain components. Indicates along x Displacement components in the direction, Indicates along y Displacement components in the direction, Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along x Displacement components in the direction, express x Physical pixel spacing in the direction Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along x Displacement components in the direction, Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along y Displacement components in the direction, express y Physical pixel spacing in the direction Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along y Displacement components in the direction, This represents the partial derivative.

[0095] Furthermore, the formula for calculating the maximum principal strain value is:

[0096] ;

[0097] in, This represents the maximum principal strain value. express x Principal strain components in the direction, express y Principal strain components in the direction, This represents the shear strain component.

[0098] S6: When the maximum principal strain value is greater than the preset threshold, correct the abnormal three-dimensional height prediction and adjust the network parameters of the deep learning model (neighborhood consistency height compensation algorithm). Based on the corrected height prediction and the adjusted deep learning model, repeat steps S2-S5 until the maximum principal strain value is less than or equal to the preset threshold, and output the final three-dimensional displacement field and three-dimensional strain field.

[0099] The corrected formula is:

[0100] ;

[0101] in, Indicates the moment of deformation Next pixel coordinates The corrected 3D height prediction Indicates the first i Candidate heights for pixels with 3D height prediction anomalies. Represents pixel coordinates The median of the predicted 3D height within the domain. Represents absolute value;

[0102] The formula is adjusted as follows:

[0103] ;

[0104] in, This represents the adjusted network parameters of the deep learning model. Represents the network parameters of a deep learning model. Indicates the learning rate. This represents the gradient of the total loss function with respect to the network parameters when an anomaly in 3D height prediction occurs.

[0105] To verify the effectiveness of this method in 3D deformation measurement under a single-camera environment, a thin-walled part (aircraft skin assembly) was selected as the object. A measurement platform was built consisting of an industrial camera (Basler acA2440-75gm, resolution 2440×2050 pixels, pixel size 3.45μm) and a DLP projector (Texas Instruments DLP LightCrafter 4500). The platform integrates deep learning prediction, DIC correlation registration, and anomaly compensation, forming an end-to-end closed-loop process. The specific implementation process is as follows:

[0106] 1. Single-camera multi-time projection acquisition: In the experimental platform, camera intrinsic parameters (focal length) are calibrated. = =3000 pixels, center offset =1220, =1025 pixels) and distortion correction (radial distortion) =-0.05, =0.02) to acquire image parameters. During the measurement process, the system acquires projected images at a reference time and multiple time points (image resolution 1220×1025 pixels) at a frequency of 30 Hz. At each time point, four phase-shifted projection images are projected (phase shifts of 0, π / 2, π, 3π / 2, fringe frequency = 0.02). f =0.05 cycles / pixel, speckle density 0.2), comprehensively recording the deformation process in the assembly dynamics.

[0107] 2. Deep Learning Model for 3D Height Prediction: A U-Net architecture network (4 layers: encoder + 4 layers; training dataset: 3000 image pairs, batch size 64) is used as input to a distortion-corrected speckle map sequence (resolution 1220×1025), outputting pixel-level height values ​​(range 0-100 mm). Training is performed with real height labels (optimizer: Adam, learning rate 0.0001, 150 iterations). In experiments, this step achieved millisecond-level prediction with an average height error of <0.1 mm.

[0108] 3. DIC Correlation Registration for Calculating the 3D Displacement Field: Based on the projected image, high-contrast speckle patterns (speckle size 0.3-0.6 mm, contrast >75%) are introduced onto the surface of the object under test. Zero-mean normalized cross-correlation (window size S = 25 × 25 pixels, sub-pixel accuracy 0.05 pixels) is used with a threshold C > 0.75 to obtain the optimal pixel displacement components. Combined with the rotation matrix R and the image plane displacement vector d, a 3D displacement field is mapped. In the experiment, the displacement calculation accuracy reached the 0.02 pixel level.

[0109] 4. Calculate the three-dimensional strain field: Perform central difference on the three-dimensional displacement field (step size 2 pixels, physical size...) = =3.45μm), the principal strain components and shear strain components were obtained, and the resolution of the three-dimensional strain field in the experiment reached 0.001%.

[0110] 5. Determine if the maximum principal strain value exceeds the safety threshold: Compare the maximum principal strain value with the threshold. =0.01% comparison and discrimination; if an anomaly is found, the neighborhood consistency height compensation algorithm is applied and the network parameters are fine-tuned. θ (increment) =0.0005), and the abnormal handling response time in the experiment was <0.2 s, ensuring the robustness of the measurement.

[0111] The single-camera-based three-dimensional projection deformation measurement and error compensation method provided in this embodiment has the following advantages:

[0112] 1. Three-dimensional deformation measurement achieved using only a single camera: A deep learning model directly predicts pixel-level three-dimensional height from a mixed fringe and speckle image acquired by a single camera, and calculates displacement and strain fields using DIC registration, avoiding the complex fusion and calibration of traditional multi-camera systems. This innovation significantly simplifies hardware requirements, requiring only a single viewpoint to capture complete three-dimensional deformation information, and achieving sub-millimeter accuracy in the dynamic monitoring of thin-walled parts in experiments.

[0113] 2. A neighborhood consistency height compensation algorithm is proposed: for anomaly point height prediction, local error correction and deformation field smoothing are achieved by minimizing the difference between the candidate height and the neighborhood median. This innovation reduces the misjudgment rate and improves the system robustness in anomaly scenarios, and is applicable to 3D reconstruction compensation in complex regions such as edges and shadows.

[0114] 3. Integration of end-to-end deep learning and multi-time displacement registration: Deep neural networks directly predict height from the original image sequence and seamlessly combine this with DIC correlation registration to form a complete 3D displacement / strain field. This innovation achieves efficient multi-time deformation calculation through data-driven nonlinear mapping, making it suitable for real-time monitoring and analysis in dynamic industrial scenarios.

[0115] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0116] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A single camera based three-dimensional projection deformation measurement and error compensation method, characterized in that, include: S1: Acquire several projected images of the surface of the object under test at multiple times using a single camera, and record the image intensity value at each pixel coordinate in each projected image at each time. S2: Input the image intensity value of the same pixel coordinate in each projected image at any time into the pre-trained deep learning model, and output the 3D height prediction of the corresponding pixel coordinate at the corresponding time. S3: Based on the image intensity values ​​of pixel coordinates at each location in each projected image at the reference time and deformation time, perform correlation search to obtain the optimal pixel displacement component; S4: Based on the three-dimensional height prediction of each pixel coordinate at the reference time and the deformation time, the optimal pixel displacement component is used to construct the image plane displacement vector at the deformation time, and the three-dimensional displacement field at the deformation time is calculated based on the image plane displacement vector at the deformation time. S5: Perform central difference calculation on the three-dimensional displacement field at the deformation moment to obtain the three-dimensional strain field; calculate the maximum principal strain value based on the three-dimensional strain field; The formula for calculating the three-dimensional strain field is: ； ； ； in, express x Principal strain components in the direction, express y Principal strain components in the direction, Represents the shear strain components. Indicates along x Displacement components in the direction, Indicates along y Displacement components in the direction, Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along x Displacement components in the direction, express x Physical pixel spacing in the direction Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along x Displacement components in the direction, Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along y Displacement components in the direction, express y Physical pixel spacing in the direction Represents the three-dimensional displacement field at the moment of deformation. Next pixel coordinates along y Displacement components in the direction, Indicates partial derivative; The formula for calculating the maximum principal strain value is: ； in, Indicates the maximum principal strain value; S6: When the maximum principal strain value is greater than the preset threshold, correct the abnormal three-dimensional height prediction and adjust the network parameters of the deep learning model. Based on the corrected height prediction and the adjusted deep learning model, repeat steps S2-S5 until the maximum principal strain value is less than or equal to the preset threshold, and output the final three-dimensional displacement field and three-dimensional strain field.

2. The three-dimensional projection deformation measurement and error compensation method according to claim 1, characterized in that, S1 includes: The projector projects a coded pattern of mixed sinusoidal fringes and speckle onto the surface of the object under test to form a projected image, and projects four different phase-shifted projected images at each time. A single camera synchronously acquires four different phase-shifted projection images of the surface of the object under test at each moment, and records the image intensity value at the pixel coordinates of each phase-shifted projection image at each moment.

3. The three-dimensional projection deformation measurement and error compensation method according to claim 2, characterized in that, The phase shifts of the four different phase-shifted projection images are 0, π / 2, π, and 3π / 2, respectively.

4. The three-dimensional projection deformation measurement and error compensation method according to claim 2, characterized in that, Pixel coordinates in each projected image at the deformation time The formula for calculating the image intensity value at a given location is: ； in, Indicates the moment of deformation Pixel coordinates in the j-th phase-shifted projection image Image intensity value at that location, Represents the pixel coordinates in the j-th phase-shifted projection image. , Indicates the moment of deformation The object under test in pixel coordinates Surface reflection characteristic function at the location, Represents pixel coordinates The imaging noise term at that location.

5. The three-dimensional projection deformation measurement and error compensation method according to claim 1, characterized in that, In S2, the expression for the pre-trained deep learning model is: ； in, Indicates the moment of deformation Next pixel coordinates Three-dimensional height prediction at the location, This represents a pre-trained deep learning model. Represents the network parameters of a deep learning model. Indicates the moment of deformation Pixel coordinates in each projected image Image intensity value at that location.

6. The three-dimensional projection deformation measurement and error compensation method according to claim 5, characterized in that, The pre-training process of a deep learning model includes: The total loss function is constructed based on the high prediction error and smoothing loss. The expression for the total loss function is as follows: ； ； ； in, Represents the total loss function. This represents the first loss weighting coefficient. This represents the second loss weighting coefficient. This indicates a high prediction error loss. Represents the smoothing loss term. The output of the deep learning model represents the first... i 3D height prediction for each pixel Indicates the first i The actual height label of each pixel. This represents the Gaussian filter function. Represents absolute value. This represents the total number of pixels involved in the loss calculation; The pre-trained deep learning model is obtained by updating the network parameters of the deep learning model by minimizing the total loss function.

7. The three-dimensional projection deformation measurement and error compensation method according to claim 1, characterized in that, S3 includes: The correlation coefficient is calculated based on the image intensity values ​​at each pixel coordinate in the projected images at the reference time and deformation time. The calculation formula is as follows: ； in, Represents the correlation coefficient. Indicates the center of the relevant window. Indicates along x Displacement components in the direction, Indicates along y Displacement components in the direction, Represents the set of related windows. Indicates reference time Pixel coordinates in each projected image Image intensity value at that location, express The mean of the intensity values ​​of each image. Indicates the moment of deformation Pixel coordinates in each projected image Image intensity value at that location, express The mean of the intensity values ​​of each image in the middle; The optimal pixel displacement component is obtained by maximizing the correlation coefficient.

8. The three-dimensional projection deformation measurement and error compensation method according to claim 1, characterized in that, In S4, the optimal pixel displacement components are used to construct the image plane displacement vector at the deformation time based on the 3D height prediction of each pixel coordinate at the reference time and the deformation time. The expression for the image plane displacement vector is: ； in, This represents the image plane displacement vector at the moment of deformation. Indicates along x The optimal pixel displacement component in the direction. Indicates along y The optimal pixel displacement component in the direction. Indicates the moment of deformation Next pixel coordinates Three-dimensional height prediction at the location, Indicates reference time Next pixel coordinates Three-dimensional height prediction at the location, Indicates transpose; The three-dimensional displacement field at the deformation moment is calculated based on the image plane displacement vector at the deformation moment. The calculation formula is as follows: ； in, Indicates the moment of deformation The three-dimensional displacement field This represents the mapping matrix.

9. The three-dimensional projection deformation measurement and error compensation method according to claim 6, characterized in that, In S6, the corrected formula is: ； in, Indicates the moment of deformation Next pixel coordinates The corrected 3D height prediction Indicates the first i Candidate heights for pixels with 3D height prediction anomalies. Represents pixel coordinates The median of the predicted 3D height within the domain. Represents absolute value; The formula is adjusted as follows: ； in, This represents the adjusted network parameters of the deep learning model. Represents the network parameters of a deep learning model. Indicates the learning rate. This represents the gradient of the total loss function with respect to the network parameters when an anomaly in 3D height prediction occurs.

Images