Crack segmentation method and system based on strain prior constraint

Abstract

The application provides a crack segmentation method and system based on strain prior constraint, comprising: collecting a CT image of a to-be-tested sample; labeling a crack in the CT image of the to-be-tested sample to generate a corresponding label image; calculating three-dimensional strain field information according to the CT image of the to-be-tested sample to obtain a strain atlas corresponding to each CT image of the to-be-tested sample; constructing a neural network model, taking the CT image and the label image of the to-be-tested sample as input, and taking the strain atlas as prior constraint knowledge to guide the training of the neural network model; and inputting a to-be-segmented CT image and a strain atlas of the to-be-segmented CT image into the trained neural network model to obtain a pixel-level segmentation result. By introducing strain as prior constraint information, a good crack segmentation result is obtained through a convolutional neural network, and the objectivity and accuracy of the segmentation result are improved.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and more specifically, to a crack segmentation method and system based on strain prior constraints. Background Technology

[0002] X-ray computed tomography (CT) utilizes the attenuation signal of X-rays passing through different materials and employs reconstruction algorithms to obtain the internal density distribution of the object under test. It is a relatively advanced non-destructive testing method and is widely used in in-situ experiments to detect the evolution of the microstructure of materials under different experimental conditions.

[0003] To better study the mechanical properties of composite fiber materials, CT technology is needed to observe their internal structure and evolution. CT images contain rich microstructural information, such as cracks and pores. Among these, the location, morphological characteristics, and propagation trend of cracks are crucial analytical bases for subsequent mechanical analysis. Therefore, accurately segmenting the crack shape from CT images is key to quantitative analysis.

[0004] Currently, there are numerous methods for image segmentation. Traditional segmentation methods include threshold-based segmentation, region-based segmentation, and edge detection-based segmentation. Later, a series of image segmentation algorithms combining specific theories were developed, incorporating wavelet transform, active contour models, and so on. However, the above methods all require manually designed features, which are not objective enough. Therefore, segmentation based on convolutional neural networks has developed rapidly, allowing computers to learn the features of the objects to be segmented and achieve pixel-level segmentation. The most classic example is the fully convolutional network U-Net and its series of variants.

[0005] Chinese invention patent document CN112991370A discloses a method for identifying and segmenting cracks in core CT scans, belonging to the field of image processing technology. The dataset is divided into a test set and a training set at a 1:6 ratio. Adaptive median filtering and Hessian matrix linear filtering are applied to all images to enhance image quality. The training set images are then segmented into several smaller images of uniform size. Hu invariant moment features, gray-level co-occurrence matrix features, and gray-level mean features are extracted from the segmented sub-images, and an SVM prediction model is trained using the obtained feature matrix. The test set images are segmented into image blocks of the same size, and the same features are extracted. The obtained SVM model is used to predict the image blocks, completing the coarse localization of cracks. Finally, the active contour segmentation method is used to segment the image blocks containing cracks, obtaining the final crack segmentation result.

[0006] Regarding the aforementioned technologies, the inventors believe that the crack contrast in CT images of composite fiber materials is low, making it difficult to distinguish micro-cracks. Furthermore, the cracks are similar to some pores and internal fiber morphology features, which makes it difficult for computers to distinguish cracks and other internal structures, thus hindering accurate crack segmentation. Summary of the Invention

[0007] In view of the deficiencies in the prior art, the purpose of this invention is to provide a crack segmentation method and system based on strain prior constraints.

[0008] A crack segmentation method based on strain prior constraints provided by the present invention includes the following steps:

[0009] CT image acquisition steps: Acquire CT images of the sample to be tested;

[0010] Label image generation steps: Mark the cracks in the CT image of the sample to be tested to generate the corresponding label image;

[0011] Strain spectrum acquisition steps: Calculate the three-dimensional strain field information based on the CT image of the sample to be tested, and obtain the strain spectrum corresponding to the CT image of each sample to be tested;

[0012] Network model training steps: Construct a neural network model, using the CT image and label image of the sample to be tested as input, and the strain spectrum as prior constraint knowledge to guide the training of the neural network model;

[0013] Segmentation result acquisition steps: Input the CT image to be segmented and the strain spectrum of the CT image to be segmented into the trained neural network model to obtain pixel-level segmentation results.

[0014] Preferably, in the strain spectrum acquisition step, a three-dimensional strain volume between adjacent tensile states is obtained through digital volume correlation analysis, including but not limited to; the three-dimensional strain volume is sliced ​​to obtain a strain spectrum corresponding to the CT image of each sample to be tested.

[0015] Preferably, in the label image generation step, a CT image of the sample to be tested is acquired, the CT image of the sample to be tested is pre-processed in size, the cracks in the pre-processed image are labeled, and a corresponding label image is generated.

[0016] Preferably, in the strain spectrum acquisition step, the volume images of the same object before and after deformation obtained by the volume imaging device are processed by digital volume correlation analysis. The volume image before deformation is used as a reference volume image, and the volume image after deformation is used as the target volume image. The three-dimensional displacement of the voxel point is tracked, and a preset area is taken as the sub-region with the voxel point as the center.

[0017] In the target image, search for sub-regions pixel by pixel, find the target sub-region with the highest similarity to the reference sub-region, and obtain the integer pixel displacement, which is the initial shape function;

[0018] A subpixel iterative algorithm is used to optimize the relevant functions and iteratively update the shape functions;

[0019] Each sub-region is calculated sequentially to obtain the three-dimensional displacement field, and the three-dimensional strain field information is obtained from the three-dimensional displacement vector field using the finite difference method.

[0020] Preferably, in the strain spectrum acquisition step, the similarity between the sub-regions before and after deformation is determined by a zero-mean normalized cross-correlation function C. ZNCC Quantitative evaluation:

[0021]

[0022] Where, f(x) i ,y i ,z i ) represents the gray level of the i-th point in the reference sub-region; g(x) i +u0,y i +v0,z i +w0) is the gray level of the i-th point in the target sub-region; i = 1, 2, 3, ..., n; n represents the number of voxels; f m The average gray value of the reference sub-region; g m is the average gray value of the target sub-region; u0 represents the x-axis displacement from the reference sub-region to the center voxel of the target sub-region; v0 represents the y-axis displacement from the reference sub-region to the center voxel of the target sub-region; w0 represents the z-axis displacement from the reference sub-region to the center voxel of the target sub-region; x i Represents the x-coordinate of the i-th point in the reference sub-region; y i This represents the y-coordinate of the i-th point in the reference sub-region; z i This represents the z-coordinate of the i-th point in the reference sub-region;

[0023] When the gray levels of the pre-deformation sub-region and the target sub-region are linearly correlated, C ZNCC =1; when unrelated, C ZNCC =0.

[0024] Preferably, in the network model training step, a convolutional neural network U-Net is constructed, with CT images and corresponding strain maps as dual-channel inputs, and backpropagation using the loss functions CE Loss and Dice Loss from semantic segmentation, and the labeled images are used as real labels to train the model.

[0025] A crack segmentation system based on strain prior constraints provided by the present invention includes the following modules:

[0026] CT image acquisition module: Acquires CT images of the sample to be tested;

[0027] Label image generation module: Annotates cracks in the CT images of the sample to be tested and generates corresponding label images;

[0028] Strain spectrum acquisition module: Calculates three-dimensional strain field information based on the CT images of the sample to be tested, and obtains the strain spectrum corresponding to the CT image of each sample to be tested;

[0029] Network model training module: Constructs a neural network model, taking the CT image and label image of the sample to be tested as input, and the strain spectrum as prior constraint knowledge, to guide the training of the neural network model;

[0030] Segmentation result acquisition module: Input the CT image to be segmented and the strain spectrum of the CT image to be segmented into the trained neural network model to obtain pixel-level segmentation results.

[0031] Preferably, in the strain spectrum acquisition module, three-dimensional strains between adjacent tensile states are obtained through methods including but not limited to digital volume correlation analysis; the three-dimensional strains are sliced ​​to obtain strain spectra corresponding to the CT images of each sample to be tested.

[0032] Preferably, in the label image generation module, a CT image of the sample to be tested is acquired, the CT image of the sample to be tested is pre-processed in size, the cracks in the pre-processed image are labeled, and a corresponding label image is generated.

[0033] Preferably, in the strain spectrum acquisition module, the volume images of the same object before and after deformation obtained by the volume imaging device are processed by digital volume correlation analysis. The volume image before deformation is used as a reference volume image, and the volume image after deformation is used as the target volume image.

[0034] Track the three-dimensional displacement of the voxel point, and take a preset area as the sub-region centered on the voxel point;

[0035] In the target image, search for sub-regions pixel by pixel, find the target sub-region with the highest similarity to the reference sub-region, and obtain the integer pixel displacement, which is the initial shape function;

[0036] A subpixel iterative algorithm is used to optimize the relevant functions and iteratively update the shape functions;

[0037] Each sub-region is calculated sequentially to obtain the three-dimensional displacement field, and the three-dimensional strain field information is obtained from the three-dimensional displacement vector field using the finite difference method.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. This invention introduces strain as a priori constraint information and obtains good crack segmentation results through a convolutional neural network, thereby improving the objectivity and accuracy of the segmentation results;

[0040] 2. This invention has a high accuracy rate for solving difficult-to-divide micro-cracks;

[0041] 3. This invention greatly reduces the error rate in identifying other non-cracked structures. Attached Figure Description

[0042] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0043] Figure 1 This is a flowchart of the algorithm involved in the present invention;

[0044] Figure 2 A schematic diagram illustrating the basic principles of digital volume correlation methods;

[0045] Figure 3 This is a diagram showing the segmentation results. Detailed Implementation

[0046] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0047] This invention provides a crack segmentation method based on strain prior constraints, referring to... Figure 1 As shown, the specific steps include the following:

[0048] Step S1: Acquire CT images of the sample to be tested and annotate the cracks in the images to generate corresponding label images. To analyze the mechanical properties of the composite fiber material, relevant samples are prepared and scanned using CT technology. CT images of the sample to be tested are acquired and preprocessed, with the size uniformized to 512 pixels x 512 pixels for subsequent use. Cracks in the images are manually annotated to generate corresponding binary label images.

[0049] Step S2: Calculate the three-dimensional strain field information to obtain the strain spectrum corresponding to each CT image. The three-dimensional strain between adjacent tensile states is obtained using methods including but not limited to digital volume correlation analysis (DVC). The three-dimensional strain is then sliced ​​to obtain the strain spectrum corresponding to each CT image. For example, the three-dimensional strain field information is calculated using the digital volume correlation method (DVC) to obtain the strain spectrum corresponding to each CT image. Step S2 includes the following steps:

[0050] Step S2.1: The DVC method processes two volume images of the same object before and after deformation, obtained by a volume imaging device. The image before deformation serves as the reference, while the volume image obtained after deformation is called the target volume image. A schematic diagram of the basic principle of DVC is shown below. Figure 2 As shown. Due to the limited grayscale range of digital images, it is impossible to track the three-dimensional displacement vector of a single voxel before and after deformation. Therefore, in order to track the three-dimensional displacement of a voxel, it is necessary to take a cubic region centered on the voxel as a sub-region, and determine the integer pixel displacement of the center point of the sub-region by tracking the precise position of the selected sub-region in the target volume image.

[0051] Digital volume correlation analysis is used to process volumetric images of the same object before and after deformation, obtained through a volumetric imaging device. The pre-deformation image is used as the reference image, and the post-deformation image is used as the target image. The 3D displacement of voxel points is tracked, and a preset region is selected centered on each voxel point as a sub-region. The sub-region is searched pixel-by-pixel in the target image to find the target sub-region with the highest similarity to the reference sub-region, thus obtaining the integer pixel displacement, i.e., the initial shape function. A sub-pixel iterative algorithm is used to optimize the correlation function to achieve iterative updates of the shape function. Each sub-region is calculated sequentially to obtain the 3D displacement field. The 3D strain field information is obtained from the 3D displacement vector field using the finite difference method.

[0052] Any subregion can be identified by finding the target subregion with the highest similarity in the deformed volumetric image to determine its overall elemental displacement. The similarity between the subregions before and after deformation can be determined using the zero-mean normalized cross-correlation function (ZNCC). ZNCC To conduct a quantitative evaluation:

[0053]

[0054] In the formula f(x) i ,y i ,z i ) and g(x i +u0,y i +v0,z i +w0) are the gray levels of the i-th (i = 1, 2, 3, ..., n) point in the sub-region before and after deformation, respectively; f m g m Let f(x) be the average grayscale value of the reference sub-region and the target sub-region, and let u0, v0, and w0 be the displacement of the center pixel of the reference sub-region. i ,y i ,z i ) represents the gray level of the i-th point in the reference sub-region; g(x) i +u0,y i +v0,z i+w0) is the gray level of the i-th point in the target sub-region; i = 1, 2, 3, ..., n; n represents the number of voxels; f m The average gray value of the reference sub-region; g m is the average gray value of the target sub-region; u0 represents the x-axis displacement from the reference sub-region to the center voxel of the target sub-region; v0 represents the y-axis displacement from the reference sub-region to the center voxel of the target sub-region; w0 represents the z-axis displacement from the reference sub-region to the center voxel of the target sub-region; x i Represents the x-coordinate of the i-th point in the reference sub-region; y i This represents the y-coordinate of the i-th point in the reference sub-region; z i This represents the z-coordinate of the i-th point in the reference sub-region.

[0055] The ZNCC function has strong anti-interference capabilities. When the gray levels of the reference sub-region and the target sub-region are linearly correlated, C... ZNCC =1; when the two are unrelated, C ZNCC =0.

[0056] Compared to the reference sub-region, the target sub-region typically undergoes a series of deformations, including translation, rotation, uniform deformation, and non-uniform deformation. Therefore, a shape function is needed to describe the displacement and deformation from the reference sub-region to the target sub-region. The initially obtained integer pixel displacement can be considered as the initial shape function. A sub-pixel iterative algorithm is required to update the shape function, thereby obtaining a sub-pixel accurate three-dimensional displacement field. The finite difference method is used to obtain the three-dimensional strain field from the three-dimensional displacement field.

[0057] To reduce computation, some background information is removed, and the image volume is cropped to 1061 pixels x 1101 pixels x 1100 pixels. This process is repeated for multiple pixels in the reference image to obtain a three-dimensional displacement vector field. Then, the three-dimensional strain field is obtained from the three-dimensional displacement vector field using the translational displacement field difference method.

[0058] Step S2.2: After obtaining the three-dimensional strain field of the volume image, it needs to be sliced. In this example, the acquired CT images are all xz tomographic images. Therefore, to find the stress spectrum corresponding to the position in the CT image, the three-dimensional strain field needs to be sliced ​​along the y-direction to match the CT image with the strain spectrum.

[0059] Step S3: Construct a neural network model, using CT images and label images as input, and strain maps as prior constraints to guide model training. CT images and strain maps represent image grayscale information and mechanical strain information, respectively. Relying solely on image grayscale information cannot accurately segment microcracks and may lead to incorrect segmentation of other structures within the material. Since areas with high strain have a higher probability of crack initiation, introducing strain information in the form of strain maps as prior constraints can guide network training. A classic convolutional neural network, U-Net, is constructed, using CT images and corresponding strain maps as dual-channel input. Backpropagation is performed using two commonly used loss functions in semantic segmentation: cross-entropy loss (CELoss) and Dice loss (Dice Loss). Label images are used as ground truth labels to train the model.

[0060] Step S4: Input the CT image to be segmented and its strain map into the trained network model to obtain pixel-level segmentation results. Input the image to be segmented and its strain map into the trained U-Net network model to obtain the following... Figure 3 The pixel-level segmentation results are shown. Figure 3 The segmentation results are shown in the image, from left to right: CT image, labeled image, strain map, and segmentation result.

[0061] This invention relates to X-ray computed tomography (CT), convolutional neural networks (CNNs), and digital volume correlation (DVC). Crack initiation often corresponds to high strain values, therefore, there is a close correlation between strain maps and crack location distribution. Thus, by introducing strain maps as a priori constraints for training a convolutional neural network, pixel-level segmentation of cracks in CT images can be achieved accurately and rapidly.

[0062] This invention can introduce strain field information as prior constraint information and combine it with the pixel-level segmentation capability of neural networks to remove erroneous identification information while maintaining the crack shape. It can accurately and quickly segment cracks in CT images of composite fiber materials and is more sensitive to micro-cracks.

[0063] The present invention also provides a crack segmentation system based on strain prior constraints. The crack segmentation system based on strain prior constraints can be implemented by executing the process steps of the crack segmentation method based on strain prior constraints. That is, those skilled in the art can understand the crack segmentation method based on strain prior constraints as a preferred embodiment of the crack segmentation system based on strain prior constraints.

[0064] The system includes the following modules:

[0065] CT image acquisition module: Acquires CT images of the sample to be tested.

[0066] Label Image Generation Module: This module annotates cracks in the CT images of the test sample to generate corresponding label images. It acquires CT images of the test sample, performs size preprocessing on the CT images, annotates cracks in the preprocessed images, and generates corresponding label images.

[0067] Strain spectrum acquisition module: Calculates three-dimensional strain field information based on CT images of the test samples to obtain the strain spectrum corresponding to each CT image of the test sample. Through methods including but not limited to digital volume correlation analysis, obtains the three-dimensional strain volume between adjacent tensile states; slices the three-dimensional strain volume to obtain the strain spectrum corresponding to the CT image of each test sample.

[0068] Digital volume correlation analysis is used to process volume images of the same object before and after deformation, obtained through a volume imaging device. The pre-deformation volume image is used as the reference volume image, and the post-deformation volume image is used as the target volume image. The three-dimensional displacement of voxel points is tracked, and a preset region is selected as a sub-region centered on the voxel point in the reference volume image. The sub-region is searched pixel by pixel in the target volume image to find the target sub-region with the highest similarity to the reference sub-region, thereby obtaining the integer pixel displacement, i.e., the initial shape function. A sub-pixel iterative algorithm is used to optimize the correlation function to achieve iterative update of the shape function. Each sub-region is calculated sequentially to obtain the three-dimensional displacement field. The three-dimensional strain field information is obtained from the three-dimensional displacement vector field using the finite difference method.

[0069] Network model training module: Constructs a neural network model, using CT images and label images of the test sample as input and strain maps as prior constraint knowledge to guide the training of the neural network model.

[0070] Segmentation result acquisition module: Input the CT image to be segmented and the strain spectrum of the CT image to be segmented into the trained neural network model to obtain pixel-level segmentation results.

[0071] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0072] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for crack segmentation based on strain prior constraints, characterized in that, The method comprises the following steps: a CT image acquisition step: acquiring a CT image of a sample to be measured; a label image generation step: labeling cracks in the CT image of the sample to be measured to generate a corresponding label image; a strain map acquisition step: calculating three-dimensional strain field information from the CT image of the sample to be measured to obtain a strain map corresponding to each CT image of the sample to be measured; a network model training step: constructing a neural network model, taking the CT image and the label image of the sample to be measured as input, and taking the strain map as prior constraint knowledge to guide the training of the neural network model; a segmentation result acquisition step: inputting the CT image to be segmented and the strain map of the CT image to be segmented into the trained neural network model to obtain a pixel-level segmentation result; In the strain map acquisition step, a three-dimensional strain body between adjacent stretching states is obtained through digital volume correlation analysis, and the three-dimensional strain body is sliced to obtain a strain map corresponding to each CT image of the sample to be measured; In the strain map acquisition step, a volume image of the same object before and after deformation obtained by a volume imaging device is processed through digital volume correlation analysis, the volume image before deformation is taken as a reference, the volume image after deformation is taken as a target; Tracking the three-dimensional displacement of a voxel point, taking a preset region centered on the voxel point as a subregion; In the target volume image, a target subregion with the highest similarity to the reference subregion is searched pixel by pixel in the subregion to obtain an integer pixel displacement as an initial shape function; A subpixel iterative algorithm is used to optimize the correlation function and update the shape function iteratively; Each subregion is calculated in turn to obtain a three-dimensional displacement field, and a three-dimensional strain field information is obtained from the three-dimensional displacement vector field by using a difference method; In the strain map acquisition step, the similarity of the sub-areas before and after deformation is determined by a zero-mean normalized cross-correlation function C ZNCC Quantitative evaluation: C ZNCC = wherein, is the gray value of the point i in the reference subregion; is the gray value of the point i in the target subregion; i = 1, 2, 3, ···, n ; n denotes the number of voxel points; is the average gray value of the reference subregion; is the average gray value of the target subregion; denotes the x ward displacement of the reference subregion to the central voxel of the target subregion; denotes the y ward displacement of the reference subregion to the central voxel of the target subregion; is the z ward displacement of the reference subregion to the central voxel of the target subregion; denotes the i ard coordinate of the point x in the reference subregion; denotes the i ard coordinate of the point y in the reference subregion; denotes the i ard coordinate of the point z in the reference subregion; C = 1 when the gray scale of the pre-deformation sub-area and the gray scale of the target sub-area are linearly correlated ZNCC = 1; C ZNCC = 0 when they are not correlated. In the label image generation step, the CT image of the sample to be measured is acquired, the CT image of the sample to be measured is preprocessed in size, and the cracks in the preprocessed image are labeled to generate a corresponding label image; In the network model training step, a convolutional neural network U-Net is constructed, the CT image and the corresponding strain map are taken as dual-channel input, loss functions CE Loss and Dice Loss in semantic segmentation are used for back propagation, and the label image is taken as a real label to train the model.

2. A crack segmentation system based on strain prior constraints, characterized in that, The method comprises the following modules: a CT image acquisition module: acquiring a CT image of a sample to be measured; a label image generation module: labeling cracks in the CT image of the sample to be measured to generate a corresponding label image; a strain map acquisition module: calculating three-dimensional strain field information from the CT image of the sample to be measured to obtain a strain map corresponding to each CT image of the sample to be measured; a network model training module: constructing a neural network model, taking the CT image and the label image of the sample to be measured as input, and taking the strain map as prior constraint knowledge to guide the training of the neural network model; a segmentation result acquisition module: inputting the CT image to be segmented and the strain map of the CT image to be segmented into the trained neural network model to obtain a pixel-level segmentation result; In the strain map acquisition module, a three-dimensional strain body between adjacent tensile states is obtained through digital volume correlation analysis; the three-dimensional strain body is sliced to obtain a strain map corresponding to a CT image of each sample to be measured; In the strain map acquisition module, a volume image of an object before and after deformation is obtained through a volume imaging device through digital volume correlation analysis processing, the volume image before deformation is taken as a reference, the volume image after deformation is taken as a target; a three-dimensional displacement of a voxel point is tracked, and a preset region centered on the voxel point is taken as a subregion; A target subregion with the highest similarity to the reference subregion is found by searching the subregion in the target volume image pixel by pixel, and an integer pixel displacement is obtained as an initial shape function; A subpixel iterative algorithm is used to optimize the correlation function and update the shape function iteratively; Each subregion is calculated in turn to obtain a three-dimensional displacement field, and a three-dimensional strain field information is obtained from the three-dimensional displacement vector field by using a difference method; In the strain map acquisition module, the similarity degree of the sub-regions before and after deformation is obtained by a zero-mean normalized cross-correlation function C ZNCC Quantitative evaluation: C ZNCC = wherein, is the gray scale of the i-th point in the reference sub-region; i is the gray scale of the i-th point in the target sub-region; is the gray scale of the i-th point in the reference sub-region; i is the gray scale of the i-th point in the target sub-region; i = 1, 2, 3, ···, n ; n denotes the number of voxel points; is the average gray scale value of the reference sub-region; is the average gray scale value of the target sub-region; denotes the lateral displacement of the reference sub-region to the central voxel of the target sub-region; x denotes the lateral displacement of the reference sub-region to the central voxel of the target sub-region; is the lateral displacement of the reference sub-region to the central voxel of the target sub-region; y is the lateral displacement of the reference sub-region to the central voxel of the target sub-region; is the lateral displacement of the reference sub-region to the central voxel of the target sub-region; z is the lateral displacement of the reference sub-region to the central voxel of the target sub-region; denotes the x-coordinate of the i-th point in the reference sub-region; i denotes the x-coordinate of the i-th point in the reference sub-region; x denotes the x-coordinate of the i-th point in the reference sub-region; denotes the x-coordinate of the i-th point in the reference sub-region; i denotes the x-coordinate of the i-th point in the reference sub-region; y denotes the x-coordinate of the i-th point in the reference sub-region; denotes the y-coordinate of the i-th point in the reference sub-region; i denotes the y-coordinate of the i-th point in the reference sub-region; z denotes the y-coordinate of the i-th point in the reference sub-region; C = 1 when the gray scale of the pre- deformation sub-region and the gray scale of the target sub-region are linearly correlated ZNCC = 1; C ZNCC = 0 when they are not correlated. In the label image generation module, a CT image of the sample to be measured is collected, the CT image of the sample to be measured is preprocessed in size, and the cracks in the image after size preprocessing are labeled to generate a corresponding label image; In the network model training module, a convolutional neural network U-Net is constructed, the CT image and the corresponding strain map are taken as double-channel input, the loss function CE Loss and Dice Loss in semantic segmentation are used for back propagation, and the label image is taken as a real label to train the model.

Images