Deep learning-based missing stripe information restoration method

Abstract

The invention relates to the technical field of three-dimensional measurement, and provides a missing stripe information repairing method based on deep learning. The method is realized through the following steps: firstly, constructing an initial measurement system to acquire saturated and normal stripe images; then, constructing a data set by using the collected stripe images, and training a U-Net network model; and then a U-Net network model is adopted to predict the saturated fringe image, and a restored normal fringe image is obtained for phase calculation. And then adjusting the angle of the camera to construct a new measurement system, and collecting a saturated fringe image. And repairing the acquired saturated fringe image by using the network model trained by the initial measurement system. And combining the repaired fringe image with the original saturated fringe image and then carrying out phase calculation. The method has the beneficial effects that the phase calculation of the saturated image can be realized without additional external conditions, and the method can be used for the phase calculation of the saturated image under a plurality of measurement systems.

Description

Technical Field

[0001] The present invention belongs to the technical field of fringe projection three-dimensional measurement, and specifically relates to a method for repairing missing fringe information based on deep learning. Background Art

[0002] With the development of three-dimensional measurement technology, optical three-dimensional measurement technology has been widely applied in fields such as automobile manufacturing, reverse engineering, and industrial inspection. Among them, fringe projection three-dimensional measurement technology plays an important role in structured light three-dimensional measurement due to its advantages such as high precision, full-field measurement, low cost, and high speed. However, fringe projection profilometry faces great challenges when performing three-dimensional measurement of high-reflectivity objects. There is specular reflection on the surface of high-reflectivity objects, and this reflection will concentrate and reflect light, thereby significantly enhancing the light intensity in certain areas, exceeding the dynamic range of the photosensitive elements in the camera. The captured fringe images will show intensity saturation in these areas, resulting in missing fringe information, thus affecting the accuracy of three-dimensional measurement.

[0003] To solve the above problems, scholars have proposed many high-dynamic-range methods to improve the three-dimensional measurement accuracy of fringe projection profilometry for high-reflectivity objects. Zhang et al. fused multiple sets of fringe images collected at different exposure times to synthesize a set of fringe images without saturated areas and with high signal-to-noise ratio, and then used this set of images to perform three-dimensional measurement on high-reflectivity objects. Jiang et al. proposed a method of replacing saturated fringe images with an additional set of inverted fringe images for phase demodulation. Nayar et al. combined a polarization filter with color information to separate specular reflection from diffuse reflection, effectively weakening the captured light intensity. In addition, Feng et al. combined the polarization filter method with the multiple exposure method, installed polarization filters in front of the projector and the camera to eliminate the component from specular reflection, which would reduce the intensity of the entire captured image, and then combined with the multiple exposure method to obtain a set of images without saturated areas and with high signal-to-noise ratio. These studies all require additional conditions to meet their needs, resulting in an increase in measurement complexity or measurement cost. Summary of the Invention

[0004] In order to overcome the limitations of existing high-dynamic-range three-dimensional measurement methods, the present invention provides a method for repairing missing fringe information based on deep learning, which solves the problems of excessive projected fringes, low measurement efficiency, and complex measurement process in the prior art, realizes the phase calculation of saturated areas, and is applicable to different measurement systems.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for repairing missing fringe information based on deep learning, comprising the following steps:

[0007] S1. Construct an initial measurement system and collect saturated and normal fringe images;

[0008] S2. Construct a dataset from the collected fringe images and train a U-Net network model;

[0009] S3. Use the trained U-Net network model to predict the saturated fringe image, obtain the restored normal fringe image, and perform phase calculation using the restored image;

[0010] S4. Adjust the camera angle to construct a new measurement system, collect saturated fringe images for restoration;

[0011] S5. Combine the restored normal fringe image with the collected original saturated fringe image for phase calculation.

[0012] Furthermore, in S1, to construct the initial measurement system to collect saturated and normal fringe images, the following method is adopted:

[0013] S11. Establish a measurement system including an industrial camera, a projector, and a processor;

[0014] S12. By adjusting the camera exposure time and spraying the developer, collect saturated fringe images and normal fringe images under the same scene. In both cases, collect 3-frequency 4-step phase-shifted fringe images. The digital expression of the 4-step phase-shifted fringe image is shown in formula (1), and its fringe frequencies are f h = 64, f m = 56, f l = 49;

[0015]

[0016] In the formula, represents the intensity of the i-th fringe pattern with frequency f t , and t = h, m, l; i = 1, 2, 3, 4. (x, y) represents the pixel coordinates in the captured image, a(x, y) is the background intensity, b(x, y) is the modulation intensity, is the wrapped phase of the fringe image with frequency f t ;

[0017] S13. Repeat the process of S12 to collect saturated fringe images and normal fringe images under multiple different measurement scenes;

[0018] S14. Calculate the mask mask for the collected images using formula (3) to filter out the areas in the images that do not contain the measured object;

[0019]

[0020] In the formula, and respectively represent the wrapped phase of the high-frequency fringe image in the normal image for the sine part and the cosine part, and Tr is the mask threshold.

[0021] Furthermore, in S2, a dataset is constructed from the collected fringe images to train the U-Net network model, using the following method:

[0022] S21. Use the collected normal fringe images as the label values of the network, and the saturated fringe images containing saturated regions as the input values of the network to construct a dataset. The dataset is divided into a training set, a validation set, and a test set according to the ratio of 8:1:1.

[0023] S22. Use MATLAB to build a convolutional neural network with the structure of U-net;

[0024] S23. In the training process, use the mini-batch gradient descent algorithm, batch size = 1, set the initial learning rate to γ = 1×10-3, and use the default initialization method to initialize the convolutional kernel parameters;

[0025] S24. Use formula (4) to calculate the loss between the network output and the label values to learn the network parameters, and use the mean square error to evaluate the generalization performance of the network under the validation set;

[0026]

[0027] In the formula, H is the image height, W is the image width, and I gt (x,y) represents the label value of a certain pixel point, and I out (x,y) represents the predicted value of the same pixel point; use the Adaptive Moment Estimation (Adam) algorithm to dynamically optimize the learning rate;

[0028] S25. During the training process, adopt a dynamic learning rate strategy, and the learning rate drops to 0.5 times the previous value every 20 epochs; during the training process, perform a validation on the validation set every 35 steps to monitor the generalization performance of the model; the training will stop after 200 epochs, and select the network weights corresponding to the minimum mean square error calculated on the validation set during the training process as the final trained network model.

[0029] Furthermore, in S3, use the U-Net network model to predict the saturated fringe image to obtain the restored normal fringe image for phase calculation, using the following method:

[0030] S31. Input the saturated fringe images of the test set into the final network model to obtain the restored fringe image I out (x,y).

[0031] S32. After all the 3-frequency 4-step phase-shifted saturated fringe images in the same measurement scenario are repaired, the wrapped phases at three frequencies are calculated using Equation (5). and

[0032]

[0033] S33. Calculate the wrapped phases of three different superimposed frequencies using Equation (6).

[0034]

[0035] where is the wrapped phase of the fringe image with frequency f hm , and f hm = f h - f m ; is the wrapped phase of the fringe image with frequency f ml , and similarly f ml = f m - f l ; is the wrapped phase of the fringe image with frequency f hml , f hml = f hm - f ml = 1;

[0036] S34. Obtain the unwrapped phase Φ h (x, y) of the highest frequency from the wrapped phases of the superimposed frequencies using Equation (7) and Equation (8).

[0037]

[0038] where Φ hml (x, y) is the unwrapped phase of the fringe image with frequency f hml , Φ hm (x, y) is the unwrapped phase of the fringe image with frequency f hm , Φ h (x, y) is the unwrapped phase of the fringe image with frequency f h , k hm (x, y) and k h (x, y) are the unwrapping orders, and round is the rounding function.

[0039] Furthermore, in S4, the camera angle is adjusted to construct a new measurement system, and the saturated fringe images are collected and repaired using the following method:

[0040] S41. Adjust the angle of the camera in the initial measurement system to obtain different measurement systems.

[0041] S42. Collect saturated and normal fringe images according to S12 and S13 in different measurement systems;

[0042] S43. Input the saturated fringes into the network model for prediction to obtain the restored normal fringe images under different measurement systems;

[0043] Further, in S5, the predicted normal fringe images are combined with the original saturated fringe images for phase calculation, using the following method:

[0044] S51. The unwrapped phases of the original saturated fringe images and the restored normal images under different measurement systems can be calculated respectively using formulas (5), (6), (7) and (8) and

[0045] S52. Obtain the saturation region mask Mask that cannot calculate the result due to missing fringe information using formula (9):

[0046]

[0047] In the formula, is the unwrapped phase of the original saturated fringe image;

[0048] S53. Multiply the unwrapped phase obtained from the restored image by the mask Mask, and combine it with the unwrapped phase of the saturated fringe image, as shown in formula (10):

[0049]

[0050] In the formula, Φ h (x, y) is the unwrapped phase of the measured scene under different measurement systems.

[0051] The beneficial effects of the present invention are:

[0052] 1. The present invention can realize the repair of missing fringe information under the same measurement system only after training one network model;

[0053] 2. The present invention can realize three-dimensional measurement without additional hardware or additional fringe images.

[0054] 3. The present invention can realize three-dimensional measurement of different measurement systems by combining the fringe information before and after repair. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is the structure diagram of the convolutional neural network.

[0056] Figure 2 is the structure diagram of the encoder and decoder.

[0057] Figure 3 This is the implementation flowchart of the proposed method.

[0058] Figure 4 This is the comparison chart of the saturated image, the restored image, and the normal image.

[0059] Figure 5 This is the sine characteristic analysis chart.

[0060] Figure 6 This is the phase loss chart.

[0061] Figure 7 This is the reconstruction result chart.

[0062] Figure 8 This is the comparison chart of the restoration under different saturation degrees in different measurement systems.

[0063] Figure 9 This is the comparison chart of the restoration under different acquisition angles in different measurement systems. Specific implementation manners

[0064] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0065] The present invention first proposes a method for restoring missing fringe information based on deep learning. This method uses a U-net convolutional neural network to restore the fringe information missing due to image saturation, performs phase demodulation through the fringe information in the restored saturated region, and combines with the time-domain phase unwrapping method to obtain accurate absolute phase. The phase error caused by the missing fringe information in the restored captured image is significantly reduced. Using this method, even if there are saturated regions in the image, accurate three-dimensional information can still be obtained. In addition, the model used has good generalization ability and can perform high-precision phase demodulation on saturated images collected by different measurement systems. By combining the restored image and the saturated image for phase calculation, accurate measurement results can be obtained.

[0066] Example 1: The implementation steps of the method of the present invention are as follows:

[0067] S1. Construct an initial measurement system and collect saturated and normal fringe images;

[0068] First, establish a measurement system including an industrial camera, a projector, and a processor;

[0069] After the measurement system is constructed, by adjusting the camera exposure time and spraying a developer, collect the saturated fringe image and the normal fringe image in the same scene. In both cases, collect 3-frequency 4-step phase-shifted fringe images. The digital expression of the 4-step phase-shifted fringe image is shown in the following formula, and its fringe frequencies are f h = 64, f m= 56, f l = 49;

[0070]

[0071] wherein, represents the intensity of the i-th fringe pattern with frequency f t and t = h, m, l; i = 1, 2, 3, 4. (x, y) represents the pixel coordinates in the captured image, a(x, y) is the background intensity, b(x, y) is the modulation intensity, is the wrapped phase of the fringe image with frequency f t ;

[0072] Subsequently, saturated fringe images and normal fringe images under multiple different measurement scenarios are collected. The collected images are filtered by a mask mask calculated according to the following formula to remove the areas in the images that do not contain the measured object.

[0073]

[0074] wherein, and respectively represent the sine part and cosine part of the wrapped phase of the high-frequency fringe image in the normal image , and Tr is the mask threshold.

[0075] S2. Construct a data set from the collected fringe images and train the U-Net network model

[0076] Use the collected normal fringe images as the label values of the network and the saturated fringe images containing saturated regions as the input values of the network to construct a data set. The data set is divided into a training set, a validation set, and a test set according to a ratio of 8:1:1.

[0077] Use MATLAB to build a convolutional neural network with the structure of Unet to predict the fringe information in the fringe image. The network structure is as Figure 1 shown. The Unet structure includes an input layer, an encoder, an intermediate layer, a decoder, an output layer, and a regression layer. The structure in the encoder is as Figure 2 (a) shown, including a convolutional layer, an activation function, and a max pooling layer. The encoder extracts features from the input fringe image, learns different feature patterns through multiple convolutional layers, reduces the size of the feature map through downsampling, extracts key features, improves the spatial invariance of the features, and reduces the computational complexity. The intermediate layer includes a convolutional layer and an activation function, and its role is to further extract and aggregate higher-level features. These features usually appear as more abstract and higher-level patterns, thus providing important information for the subsequent decoder to restore the image details. The structure in the decoder is as Figure 2(b) As shown, it includes a transposed convolutional layer, a connection layer, a convolutional layer, and an activation function. The decoder upsamples the feature map to gradually restore the spatial resolution of the original image, and stitches together the output before downsampling in the encoder and the decoder input through skip connections. In this way, when the decoder extracts features again, it not only uses the high-level features extracted from the encoder but also obtains the low-level features extracted by the encoder, thus better restoring the details of the image. The regression layer calculates the error between the network output and the true value through a loss function to guide the network to optimize the parameters.

[0078] In the training process, the mini-batch gradient descent algorithm is adopted, with batch size = 1, the initial learning rate set to γ = 1×10-3, the convolutional kernel parameters are initialized using the default initialization method, and the mean square error shown in the following formula is used to calculate the loss between the network output and the label value to learn the network parameters, and the mean square error is used to evaluate the generalization performance of the network under the validation set;

[0079]

[0080] In the formula, H is the image height, W is the image width, and I gt (x,y) represents the label value of a certain pixel point, and I out (x,y) represents the predicted value of the same pixel point. The adaptive moment estimation (Adam) algorithm is used to dynamically optimize the learning rate.

[0081] During the training process, a dynamic learning rate strategy is adopted, and the learning rate is decreased to 0.5 times the previous value every 20 epochs; during the training process, validation is performed on the validation set every 35 steps to monitor the generalization performance of the model. The training will stop after 200 epochs, and the network weights corresponding to the minimum mean square error calculated on the validation set during the training process are selected as the final trained network model.

[0082] S3. Use the trained U-Net network model to predict the saturated fringe image to obtain the restored normal fringe image, and perform phase calculation using the restored image

[0083] Input the saturated fringe images in the test set into the final network model to obtain the restored fringe image I out (x,y). After all the 3-frequency 4-step phase-shifted saturated fringe images in the same measurement scene are restored, the wrapped phases at three frequencies are calculated using the following formula and

[0084]

[0085] The wrapped phases of three different superimposed frequencies are calculated using the following formula.

[0086]

[0087] In the formula, is the wrapped phase of the fringe image with frequency f hm and f hm = f h - f m ; is the wrapped phase of the fringe image with frequency f ml and similarly f ml = f m - f l ; is the wrapped phase of the fringe image with frequency f hml and f hml = f hm - f ml = 1;

[0088] The following formula is used to obtain the unwrapped phase Φ h (x, y) of the highest frequency from the wrapped phase of the superimposed frequencies;

[0089]

[0090] In the formula, Φ hml (x, y) is the unwrapped phase of the fringe image with frequency f hml , Φ hm (x, y) is the unwrapped phase of the fringe image with frequency f hm , Φ h (x, y) is the unwrapped phase of the fringe image with frequency f h , k hm (x, y) and k h (x, y) are the unwrapping orders, and round is the rounding function.

[0091] S4. Adjust the camera angle to construct a new measurement system, and collect and repair the saturated fringe images

[0092] Adjust the angle of the camera in the initial measurement system to obtain different measurement systems, and collect saturated and normal fringe images under this measurement system. The collected images are optimized using formula (3) to filter out the areas that do not contain the object to be measured. The saturated fringe images are input into the network model for prediction to obtain the repaired normal fringe images under different measurement systems.

[0093] S5. Combine the repaired normal fringe images with the collected original saturated fringe images for phase calculation

[0094] The unwrapped phases of the original saturated fringe images and the repaired normal images under different measurement systems can be calculated respectively using formulas (5), (6), (7), and (8) and

[0095] The saturated region mask Mask where the result cannot be calculated due to missing fringe information is obtained using the following formula:

[0096]

[0097] In the formula, is the unwrapped phase of the original saturated fringe image;

[0098] Multiply the unwrapped phase obtained from the repaired image by the mask Mask, and combine it with the unwrapped phase of the saturated fringe image, as shown in the following formula:

[0099]

[0100] In the formula, Φh(x,y) is the unwrapped phase of the measured scene under different measurement systems. Figure 3 Fig. is the implementation flowchart of the proposed method.

[0101] Example 2: To demonstrate the performance of the method described in the present invention, the saturated images of four measured objects in the test set before and after repair were analyzed from multiple angles. First, the grayscale images before and after repair were analyzed, and the results are as Figure 4 shown. Figure 4 (a, b, c) respectively show the saturated image, the repaired image, and the normal image. It is observed that the grayscale image repaired by the proposed method is visually indistinguishable from the normal image. To analyze the sine characteristics of the fringe image before and after repair, we selected the input image, output image, and normal image of one object for comparison, and the results are as Figure 5 shown. It can be seen from the results that Figure 5 the "peak platform effect" in the saturated image in (a) disappears after repair, and the sine characteristics that the fringe image of the measured object should have are restored. The repaired image is as Figure 5 (b) shown. Figure 5 (d) The comparison in verifies the effectiveness of the proposed method. The fringe information of the repaired saturated fringe image is very close to the information contained in the normal fringe image. The phase loss rate and root mean square error (RMSE) of the phase information obtained from the images before and after repair by the proposed method were calculated respectively, and the results are shown in Figure 6 and Figure 7 . Figure 6The black area is the phase loss area. After being repaired by the proposed method, the phase loss rate can be significantly reduced. Among them, the loss rates of the first three measured objects can be reduced to less than 0.5%, and although the loss rate of the fourth measured object is not reduced to less than 0.5%, the reduction amplitude is 64.49%. After being repaired, the RMSEs of the four measured objects are reduced from 3.9755 to 0.2214, from 5.9163 to 0.1364, from 7.6636 to 0.2848, and from 5.9386 to 0.6808, with respective reductions of 94.43%, 97.70%, 96.27% and 88.59%. The proposed method significantly improves the quality of the repaired fringe image, enabling it to obtain the complete phase information of the measured object without additional external conditions. Figure 8 shows the repair effects of the proposed method on three different saturation levels under different measurement systems. Under different measurement systems, saturated fringe images are collected at three different exposure times, and the results shown in Figure 8 (c) are obtained after repair and combination. The phase loss rate is lower than 0.3% under three different saturation levels, and the phase error rate in the saturated area is lower than 1%. Figure 9 shows the repair effects of the proposed method on three different angles under different measurement systems. After the saturated fringe images at the three angles are repaired and combined, the overall phase loss rate of the measured object is reduced to less than 0.2%, and the RMSE is reduced by more than 90%. The proposed method can also effectively repair the fringe images collected under different measurement systems and calculate the same phase information as that in the normal fringe images.

[0102] The specific examples described in this article are only illustrative of the present invention. Those skilled in the technical field to which the present invention pertains can make various modifications, supplements, or use similar ways to substitute for the described specific examples, but will not deviate from or exceed the scope defined by the claims of the present invention.

Claims

1. A method for repairing missing stripe information based on deep learning, characterized in that, It includes the following steps: S1. Construct an initial measurement system to collect saturated and normal fringe images; S2. Construct a data set from the collected fringe images and train a U-Net network model; S3. Use the trained U-Net network model to predict the saturated fringe images to obtain repaired normal fringe images, and perform phase calculation using the repaired images; S4. Adjust the camera angle to construct a new measurement system and collect saturated fringe images for repair; S5. Combine the repaired normal fringe images with the collected original saturated fringe images for phase calculation.

2. The method for repairing missing stripe information based on deep learning according to claim 1, wherein In S1, when constructing the initial measurement system to collect saturated and normal fringe images, the following method is adopted: S11. Establish a measurement system including an industrial camera, a projector and a processor; S12. By adjusting the camera exposure time and spraying the developer, saturated fringe images and normal fringe images of the same scene are collected. Under both conditions, 3-frequency 4-step phase-shifted fringe images are collected. The digital expression of the 4-step phase-shifted fringe images is shown in formula (1), and their fringe frequencies are f h denotes the high frequency, f m denotes the medium frequency, f l denotes the low frequency; In the formula, represents the intensity of the i-th fringe pattern with frequency f t , where t = h, m, l; i = 1, 2, 3, 4; (x, y) represents the pixel coordinates in the captured image, a(x, y) is the background intensity, and b(x, y) is the modulation intensity, is the wrapped phase of the fringe image with frequency f t ; S13. Repeat the process of S12 to collect saturated and normal fringe images under multiple different measurement scenarios; S14. Calculate the mask using formula (3) for the collected images to filter out the areas in the images that do not contain the measured object; In the formula, and respectively represent the sine part and the cosine part of the wrapped phase of the high-frequency fringe image in the normal image, and Tr is the mask threshold. ​ 3. A method for repairing missing stripe information based on deep learning according to claim 1, characterized in that, In S2, when constructing a data set from the collected fringe images and training a U-Net network model, the following method is adopted: S21. Use the collected normal fringe images as the label values of the network, and the saturated fringe images containing saturated areas as the input values of the network to construct a data set; divide the data set into a training set, a validation set and a test set according to the ratio of 8:1:1; S22. Use MATLAB to build a convolutional neural network with a U-net structure; S23. In the training process, adopt the mini-batch gradient descent algorithm, set the batch size, set the initial learning rate γ, and initialize the convolutional kernel parameters using the default initialization method; S24. Use formula (4) to calculate the loss between the network output and the label values to learn the network parameters, and use the mean square error to evaluate the generalization performance of the network under the validation set; where H is the image height, W is the image width, and I gt (x, y) represents the label value of a certain pixel point, and I out (x, y) represents the predicted value of the same pixel point; the learning rate is dynamically optimized using the Adaptive Moment Estimation (Adam) algorithm; S25. In the training process, adopt a dynamic learning rate strategy, and the learning rate is decreased to 0.5 times the previous value every 20 epochs; During the training process, perform a validation on the validation set every 35 steps to monitor the generalization performance of the model; the training will stop after 200 epochs, and select the network weights corresponding to the minimum mean square error calculated on the validation set during the training process as the finally trained network model.

4. A method for repairing missing stripe information based on deep learning according to claim 1, characterized in that In S3, use the trained U-Net network model to predict the saturated fringe images to obtain repaired normal fringe images, and perform phase calculation using the repaired images. The specific steps are as follows: S31. Input the saturated fringe image of the test set into the final network model to obtain the restored normal fringe image I out (x, y); S32. After all the 3-frequency 4-step phase-shifted saturation fringe images in the same measurement scenario are restored, the wrapped phases at three frequencies are calculated using Equation (5). and S33. Calculate the wrapped phases of three different superposition frequencies using formula (6); wherein, is the wrapped phase of the fringe image with frequency f hm , and f hm = f h - f m ; is the wrapped phase of the fringe image with frequency f ml , and similarly f ml = f m - f l ; is the wrapped phase of the fringe image with frequency f hml , and f hml = f hm - f ml = 1; S34. Obtain the unwrapped phase Φ h (x,y) of the highest frequency from the wrapped phase of the superimposed frequency by using formula (7) and formula (8). h (x,y); where, Φ hml (x, y) is the unwrapped phase of the fringe image with frequency f hml Φ hm (x, y) is the unwrapped phase of the fringe image with frequency f hm Φ h (x, y) is the unwrapped phase of the fringe image with frequency f h Φ(x, y) is the unwrapped phase of the fringe image, k hm (x, y) and k h (x, y) is the unwrapping order, and round is the rounding function.

5. A method for repairing missing stripe information based on deep learning according to claim 1, characterized in that, In S4, when adjusting the camera angle to construct a new measurement system and collecting saturated fringe images for repair, the following method is adopted: S41. Adjust the angle of the camera in the initial measurement system to obtain different measurement systems; S42. Collect saturated and normal fringe images in different measurement systems according to S12 and S13; S43. Input the saturated fringe into the network model for prediction to obtain the repaired normal fringe images under different measurement systems.

6. The method for repairing missing stripe information based on deep learning according to claim 1, wherein In S5, the normal fringe image to be repaired is combined with the acquired original saturated fringe image for phase calculation. The specific steps are as follows: S51. The unwrapped phases of the original saturated fringe image and the repaired normal image under different measurement systems can be calculated respectively using formulas (5), (6), (7) and (8). and S52. Calculate the saturation region mask Mask of the original saturated fringe image using formula (9): In the formula, is the unwrapped phase of the original saturated fringe image; S53. Multiply the unwrapped phase obtained from the repaired image by the mask Mask, and combine it with the unwrapped phase of the saturated fringe image as shown in Equation (10): where Φ h (x, y) is the unwrapped phase of the measured scene under different measurement systems.

Images