Three-dimensional strain calculation method and system for deformed objects

Abstract

The present application provides a method and system for calculating three-dimensional strain of deformed objects, comprising the following steps: for a set of input three-dimensional images of the object after strain deformation, using a zero-normalized cross-correlation function to calculate the pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation; using an alternating minimization algorithm to decompose the problem into two sub-problems and define an augmented Lagrangian function; solving the first sub-problem to obtain a solution to the first sub-problem; solving the second sub-problem to obtain a solution to the second sub-problem; updating the dual variables in the Lagrangian function based on the solutions to the two sub-problems; iteratively calculating the Lagrangian function after the updated variables using alternating minimization, stopping the iteration when a preset iterative stopping condition is met, and obtaining the three-dimensional strain random field of the object's strain deformation as the global displacement field of the last iteration. The high-efficiency three-dimensional strain calculation method for deformed objects provided by the present application has the advantages of higher computational efficiency, strong noise resistance, and fast convergence speed.

Description

Technical Field

[0001] The present application relates to the field of digital image technology, and in particular to a three-dimensional strain calculation method and system for deformed objects. Background Art

[0002] Digital volume correlation (DVC) is an advanced three-dimensional deformation analysis technique that aims to analyze digital images to determine the microscopic motion and changes of materials during deformation. This technology is currently widely used in research fields such as materials science, biology, and geology. Traditional strain measurement methods, such as optical interferometry and digital image correlation (DIC), are often limited by the experimental environment and require the destruction of the specimen structure and measurement of the cross-section. In contrast, DVC has low requirements for the experimental environment and offers advantages such as high resolution, non-contact, and full-field measurement, allowing for quantitative analysis of microscopic internal deformations of materials.

[0003] DVC is an extension of DIC from a two-dimensional plane to a three-dimensional space. The DVC method has a wider range of applicable measurements than the DIC method. It can not only perform displacement analysis on the surface of an object, but also measure the deformation field inside the object. The data object processed by the DIC method is a two-dimensional plane image, while the data image processed by the three-dimensional DVC method is a three-dimensional stereo image, also known as a digital volume image. The basic principles of the two methods are the same. The three-dimensional DVC method analyzes the stereo images of the object being measured before and after deformation, and the method for acquiring stereo images generally comes from X-ray Computer Tomography (X-CT). Using the DVC method to calculate the stereo images before and after deformation, the displacement field and strain field inside the object can be obtained.

[0004] Research on DVC algorithms is a key component of the digital volumetric field, with the goal of improving computational accuracy and efficiency. To achieve higher precision, researchers have proposed algorithms such as multi-scale analysis and subvoxel-level methods based on Newton's iteration method to achieve more accurate deformation calculations. However, current image matching and subvoxel displacement algorithms still have significant deficiencies in computational efficiency and accuracy. Given the increasingly broad application areas and growing demand for DVC, improving the efficiency and accuracy of DVC calculations is crucial. Summary of the Invention

[0005] The present application provides a three-dimensional strain calculation method and system for deformable objects, which can solve the technical problem that the current image matching and subvoxel displacement algorithms in the prior art still have great deficiencies in computational efficiency and accuracy.

[0006] In a first aspect, the present application provides a method for calculating three-dimensional strain of a deformed object, comprising the following steps:

[0007] For a set of 3D images of the input object after strain deformation, the zero-normalized cross-correlation function is used to calculate the pixel displacement and deformation gradient of all pixels in the 3D image after deformation;

[0008] The alternating minimization algorithm is used to decompose the global minimization problem of pixel displacement and random field after deformation of all pixels in the three-dimensional image into two sub-problems, and the augmented Lagrangian function is defined;

[0009] The inverse synthesis Gauss-Newton method is used to solve the first subproblem and obtain the solution of the first subproblem;

[0010] The finite difference method is used to solve the second subproblem and obtain the solution of the second subproblem;

[0011] According to the solution of the first subproblem and the solution of the second subproblem, the first dual variable and the second dual variable in the Lagrangian function are updated to obtain the Lagrangian function after the variables are updated;

[0012] The Lagrangian function after variable update is calculated by alternating minimization iteration. When the preset iteration stopping condition is met, the iteration stops and the three-dimensional strain random field of the object strain deformation is obtained as the global displacement field of the last iteration.

[0013] In combination with the first aspect, in one embodiment, the step of calculating the integer pixel displacement and deformation gradient using a zero-normalized cross-correlation function for a set of three-dimensional images of an input object after strain deformation specifically includes:

[0014] Select pixels in the reference image;

[0015] Based on the selected pixel points, the zero-normalized correlation function is solved to obtain the matching correlation coefficient between the reference image and the deformed image;

[0016] When the correlation coefficient reaches an extreme value, the coordinates corresponding to the pixel point in the target image are obtained;

[0017] The pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation are calculated based on the coordinate value of the pixel in the reference image and the coordinate value in the target image.

[0018] In combination with the first aspect, in one embodiment, the alternating minimization algorithm (AMA) is used to decompose the global minimization problem into two sub-problems, and in the step of defining the augmented Lagrangian function:

[0019] The first sub-problem is:

[0020] Given Fi k ,u i k , W i k , v i k , fixed variable u i k , W i k , v i k , solve for F i k+1 ,u i k+1 ;

[0021] The second sub-problem is:

[0022] Fixed variable F i k ,u i k , W i k , v i k , solve

[0023] Among them, u i is the displacement of the ith pixel sub-block, W i is the first dual variable of the ith pixel sub-block, v i is the second dual variable of the i-th pixel sub-block, F i is the deformation gradient of the ith pixel sub-block, u i is the displacement of the ith pixel sub-block, F i is the deformation gradient of the ith pixel sub-block, is the global displacement field of the i-th pixel sub-block;

[0024] The Lagrangian function is:

[0025]

[0026] Where L is the Lagrangian, p i is the ith pixel sub-block, X i0 is the center point of the i-th pixel sub-block, is the global displacement field, is the finite difference operator of the global displacement field, and defines the phase dual variable W i and v i Can initially perform independent settings.

[0027] In conjunction with the first aspect, in one embodiment, the inverse synthetic Gauss-Newton method is used to solve the first subproblem to obtain a solution to the first subproblem, as shown in the following formula:

[0028]

[0029] In the formula, the superscript k and k+1 are the number of iterations, F i is the deformation gradient of the ith pixel sub-block, u i is the displacement of the ith pixel sub-block, p i is the ith pixel sub-block, the f function is the grayscale calculation value of the reference image, the g function is the grayscale calculation value of the deformed image, X is the coordinate value of the center point of the reference image, X i0 is the coordinate value of the ith pixel sub-block in the deformed image, is the finite difference operator of the i-th pixel sub-block, λ is the coefficient value, is the convergence threshold, is the global displacement field of the i-th pixel sub-block.

[0030] In combination with the first aspect, in one embodiment, the finite difference method is used to solve the second subproblem to obtain a solution to the second subproblem, as shown in the following formula:

[0031]

[0032] In the formula, the superscript k and k+1 are the number of iterations, is the global displacement field of the ith pixel sub-block, p i is the i-th pixel sub-block, λ is the coefficient value, is the finite difference operator of the ith pixel sub-block, F i is the deformation gradient of the ith pixel sub-block, W i is the first dual variable of the i-th pixel sub-block, is the convergence threshold, is the global displacement field of the ith pixel sub-block, u i The displacement of the i-th pixel sub-block, v i is the second dual variable of the i-th pixel sub-block.

[0033] In combination with the first aspect, in one embodiment, the first dual variable and the second dual variable in the Lagrangian function are updated according to the solution of the first subproblem and the solution of the second subproblem to obtain the Lagrangian function after the variables are updated, as shown in the following formula:

[0034]

[0035]

[0036] Where, superscript k and k+1 are the number of iterations, W i is the first dual variable of the i-th pixel sub-block, is the finite difference operator of the ith pixel sub-block, F i is the deformation gradient, v i is the second dual variable of the i-th pixel sub-block, is the global displacement field, u i is the displacement of the i-th pixel sub-block.

[0037] In combination with the first aspect, in one embodiment, an alternating minimization iterative calculation of the Lagrangian function after variable update is performed, and the iteration stops when a preset iteration stopping condition is met. The three-dimensional strain random field of the object strain deformation is obtained as the global displacement field of the last iteration, specifically comprising the following steps:

[0038]

[0039] In the formula, the superscript k and k+1 are the number of iterations, is the global displacement field, is the convergence threshold.

[0040] In a second aspect, the present application provides a three-dimensional strain calculation system for a deformed object, comprising:

[0041] The whole pixel displacement and deformation gradient acquisition module is used to calculate the pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation using the zero-normalized cross-correlation function.

[0042] a problem decomposition and function definition module, in communication with the integer pixel displacement and deformation gradient acquisition module, for decomposing the global minimization problem of the pixel displacement and random field after deformation of all pixels of the three-dimensional image into two sub-problems using an alternating minimization algorithm, and defining an augmented Lagrangian function;

[0043] a first solving module, in communication with the problem decomposition and function definition module, configured to solve the first subproblem using an inverse synthetic Gauss-Newton method to obtain a solution to the first subproblem;

[0044] a second solving module, in communication with the problem decomposition and function definition module, configured to solve the second subproblem using a finite difference method to obtain a solution to the second subproblem;

[0045] a variable updating module, communicatively connected to the first solving module and the second solving module, configured to update the first dual variable and the second dual variable in the Lagrangian function according to the solution of the first subproblem and the solution of the second subproblem, and obtain the Lagrangian function after the variables are updated;

[0046] The deformation field acquisition module is in communication with the problem decomposition and function definition module, and is used to calculate the Lagrangian function after variable update by alternating minimization iteration. When the preset iteration stop condition is met, the iteration stops, and the three-dimensional strain random field of the object strain deformation is obtained as the global displacement field of the last iteration.

[0047] In conjunction with the second aspect, in one embodiment, the displacement and deformation gradient acquisition module includes:

[0048] A pixel selection unit, used to select pixels in a reference image;

[0049] a correlation coefficient solving unit, in communication with the pixel point selection unit, for solving a zero-normalized correlation function based on the selected pixel points to obtain a matching correlation coefficient between the reference image and the deformed image;

[0050] a unit for acquiring coordinates of a pixel point after deformation, communicating with the correlation coefficient solving unit, and configured to acquire the coordinates corresponding to the pixel point in the target image when the correlation coefficient reaches an extreme value;

[0051] The displacement and deformation gradient acquisition module is in communication with the pixel point acquisition unit and the deformed pixel point coordinate acquisition unit, and is used to calculate the pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation based on the coordinate value of the pixel in the reference image and the coordinate value in the target image.

[0052] In a third aspect, the present application provides a computer-readable storage medium, on which a three-dimensional strain calculation program for a deformed object is stored. When the three-dimensional strain calculation program for a deformed object is executed by a processor, the steps of the three-dimensional strain calculation method for a deformed object as described above are implemented.

[0053] The beneficial effects of the technical solutions provided in the embodiments of the present application include at least:

[0054] The high-efficiency three-dimensional strain calculation method for deformed objects provided in this application is based on the augmented Lagrangian digital volume related technology, and is optimized. An alternating minimization algorithm is used for iterative calculation to finally obtain the deformation field inside the object.

[0055] Compared with the existing DVC technology, this method has higher computational efficiency and stronger noise resistance.

[0056] The alternating minimization algorithm transforms a multi-optimization variable problem into a single-optimization variable problem, greatly improving computational efficiency and having the advantages of fast convergence speed and good convergence performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1A flowchart of a method for calculating three-dimensional strain of a deformed object provided in an embodiment of the present application;

[0058] Figure 2 (a) is a computer-generated 3D speckle grayscale image before deformation; Figure 2 (b) is a computer-generated 3D speckle grayscale image after deformation; Figure 2 (c) is a computer-generated slice of the 3D image before deformation; Figure 2 (d) is a computer-generated slice of the 3D image before deformation;

[0059] Figure 3 The mean error distribution curves of deformation data calculated by three DVC algorithms are shown in Figure 2.

[0060] Figure 4 Line graphs of three DVC algorithms and their computation time. DETAILED DESCRIPTION

[0061] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0062] The terms "including" and "having" and any variations thereof in the specification and claims of this application and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices. The terms "first", "second" and "third" are used to distinguish different objects, etc., and do not represent a sequence, nor do they limit the "first", "second" and "third" to different types.

[0063] In the description of the embodiments of this application, the words "exemplary," "for example," or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary," "for example," or "for example" in the embodiments of this application should not be construed as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary," "for example," or "for example" is intended to present the relevant concepts in a concrete manner.

[0064] In the description of the embodiments of the present application, unless otherwise specified, “ / ” means or, for example, A / B can mean A or B; “and / or” in the text is merely a description of the association relationship of associated objects, indicating that three relationships may exist, for example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, in the description of the embodiments of the present application, “multiple” refers to two or more than two.

[0065] In some processes described in the embodiments of the present application, multiple operations or steps are included that appear in a specific order. However, it should be understood that these operations or steps may not be performed in the order in which they appear in the embodiments of the present application or may be performed in parallel. The sequence numbers of the operations are only used to distinguish between different operations, and the sequence numbers themselves do not represent any order of execution. In addition, these processes may include more or fewer operations, and these operations or steps may be performed in sequence or in parallel, and these operations or steps may be combined.

[0066] DVC: Digital volume correlation, digital volume correlation;

[0067] DIC: Digital image correlation, digital image correlation;

[0068] AMA: Alternating Minimization Algorithm, alternating minimization algorithm;

[0069] IC-GN: Inverse compositional Gauss-Newton method, inverse compositional Gauss-Newton method;

[0070] ADMM:Alternating Direction Method of Multipliers, alternating direction multiplier method.

[0071] In order to make the objectives, technical solutions and advantages of this application clearer, the implementation methods of this application will be further described in detail below with reference to the accompanying drawings.

[0072] First, please refer to Figure 1 , the present application provides a three-dimensional strain calculation method for a deformed object, comprising the following steps:

[0073] Step S1: for a set of three-dimensional images of an input object after strain deformation, use a zero-normalized cross-correlation function to calculate the pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation;

[0074] Step S2, using an alternating minimization algorithm to decompose the global minimization problem of pixel displacement and random field after deformation of all pixels in the three-dimensional image into two sub-problems, and defining an augmented Lagrangian function;

[0075] Step S31: solve the first subproblem by using the inverse synthesis Gauss-Newton method to obtain a solution to the first subproblem;

[0076] Step S32: using the finite difference method to solve the second sub-problem and obtain a solution to the second sub-problem;

[0077] Step S4: updating the first dual variable and the second dual variable in the Lagrangian function according to the solution of the first subproblem and the solution of the second subproblem, and obtaining the Lagrangian function after the variables are updated;

[0078] Step S5: using alternating minimization to iteratively calculate the Lagrangian function after variable update, the iteration stops when a preset iteration stop condition is met, and the three-dimensional strain random field of the object strain deformation is obtained as the global displacement field of the last iteration.

[0079] The high-efficiency three-dimensional strain calculation method for deformed objects provided in this application is based on the augmented Lagrangian digital volume related technology, and is optimized. An alternating minimization algorithm is used for iterative calculation to finally obtain the deformation field inside the object.

[0080] Compared with the existing DVC technology, this method has higher computational efficiency and stronger noise resistance.

[0081] The alternating minimization algorithm transforms a multi-optimization variable problem into a single-optimization variable problem, greatly improving computational efficiency and having the advantages of fast convergence speed and good convergence performance.

[0082] In this application, when calculating the displacement field, in order to facilitate the calculation of the displacement of each pixel point after the object is strained and deformed, a cubic sub-area is set at the center of each pixel point. Specifically, it is set to a sub-block of the cubic sub-area with a size of (2N+1)×(2N+1)×(2N+1) the size of each pixel point.

[0083] In one embodiment, step S1, calculating the integer pixel displacement and deformation gradient using a zero-normalized cross-correlation function for a set of three-dimensional images of the input object after strain deformation, specifically includes:

[0084] Select a pixel point in the reference image, denoted as P, with coordinates (x0, y0, z0);

[0085] Solve based on the following zero-normalized correlation function formula to obtain the solved correlation coefficient;

[0086]

[0087] Where, f(X i ), g(X i ) are the grayscale values ​​of the ith pixel sub-block of the reference image and the deformed image, respectively, f m , g m is the average gray value of all pixel sub-blocks in the reference image and the deformed image, C ZNCC is the correlation coefficient.

[0088] When the correlation coefficient reaches a maximum value, the coordinates (x0', y0', z0') corresponding to the pixel point P in the target image are obtained;

[0089] The pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation are calculated based on the coordinate value of the pixel in the reference image and the coordinate value in the target image.

[0090] The purpose of the zero-normalized correlation function is to evaluate the matching degree of the sub-regions before and after deformation. When the correlation coefficient reaches an extreme value, the matching degree of the sub-regions before and after deformation is the highest, thereby calculating the displacement and deformation gradient of all pixels in all reference images after deformation.

[0091] Figure 2 (a)- Figure 2 (d) is a computer-generated three-dimensional speckle grayscale image before and after deformation.

[0092] In one embodiment, in step S2, the global minimization problem is decomposed into two sub-problems using the alternating minimization algorithm (AMA), and the augmented Lagrangian function is defined:

[0093] The first sub-problem is:

[0094] Given F i k ,u i k , W i k , v i k , fixed variable u i k , W i k , v i k , use the inverse synthesis Gauss-Newton method to solve F according to the following formula i k+1 ,u i k+1 :

[0095]

[0096] In the formula, the superscript k and k+1 are the number of iterations, F i is the deformation gradient of the ith pixel sub-block, u i is the displacement of the ith pixel sub-block, p i is the ith pixel sub-block, the f function is the grayscale calculation value of the reference image, the g function is the grayscale calculation value of the deformed image, X is the coordinate value of the center point of the reference image, X i0 is the coordinate value of the ith pixel sub-block in the deformed image, is the finite difference operator of the i-th pixel sub-block, λ is the coefficient value, is the convergence threshold, is the global displacement field of the i-th pixel sub-block;

[0097] The second sub-problem is:

[0098] Fixed variable F i k ,u i k , W i k , v i k , using the finite difference method to solve the following equation

[0099] In the formula, the superscript k and k+1 are the number of iterations, is the global displacement field of the ith pixel sub-block, p i is the i-th pixel sub-block, λ is the coefficient value, is the finite difference operator of the ith pixel sub-block, F i is the deformation gradient of the ith pixel sub-block, W i is the first dual variable of the i-th pixel sub-block, is the convergence threshold, is the global displacement field of the ith pixel sub-block, u i The displacement of the i-th pixel sub-block, v i is the second dual variable of the i-th pixel sub-block;

[0100] The Lagrangian function is:

[0101]

[0102] Where L is the Lagrangian, p i is the ith pixel sub-block, X i0 is the center point of the i-th pixel sub-block, is the global displacement field, is the finite difference operator of the global displacement field, and defines the phase dual variable W i and v i Can initially perform independent settings.

[0103] Based on the solution of the first and second subproblems above, the global displacement field is updated. That is, the updated global displacement field of the i-th and i+1-th pixel sub-blocks.

[0104] In one embodiment, in step S4, the first dual variable and the second dual variable in the Lagrangian function are updated according to the solution of the first subproblem and the solution of the second subproblem to obtain the Lagrangian function after the variables are updated, as shown in the following formula:

[0105]

[0106]

[0107] Where, superscript k and k+1 are the number of iterations, W i is the first dual variable of the i-th pixel sub-block, is the finite difference operator of the ith pixel sub-block, F i is the deformation gradient, v i is the second dual variable of the i-th pixel sub-block, is the global displacement field, u i is the displacement of the i-th pixel sub-block.

[0108] In one embodiment, in step S5, the Lagrangian function after variable update is calculated by alternating minimization iteration. When the following preset iteration stopping condition is met, the iteration stops, and the three-dimensional strain random field of the object strain deformation is obtained as the global displacement field of the last iteration, that is, The specific steps include:

[0109]

[0110] In the formula, the superscript k and k+1 are the number of iterations, is the global displacement field, is the convergence threshold.

[0111] This application uses an alternating minimization algorithm for iterative optimization, transforming a multi-optimization variable problem into a single-optimization variable problem, which greatly improves the computational efficiency and has the advantages of fast convergence speed and good convergence performance.

[0112] In order to verify the advantages of the three-dimensional strain calculation method for deformed objects provided by this application, the AMA algorithm provided by this application, as well as the ADMM algorithm and local DVC algorithm of the prior art, are used to calculate the three-dimensional strain of a three-dimensional image of a deformed object after being subjected to strain. The calculation results are as follows: Figure 3 and Figure 4 As shown, the mean error of the X-axis position obtained by the three-dimensional strain calculation using the AMA algorithm provided in this application is comparable to that of the ADMM algorithm and the AMA algorithm, but the calculation time is significantly shorter.

[0113] In a second aspect, the present application provides a three-dimensional strain calculation system for a deformed object, comprising:

[0114] The whole pixel displacement and deformation gradient acquisition module is used to calculate the pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation using the zero-normalized cross-correlation function.

[0115] a problem decomposition and function definition module, in communication with the integer pixel displacement and deformation gradient acquisition module, for decomposing the global minimization problem of the pixel displacement and random field after deformation of all pixels of the three-dimensional image into two sub-problems using an alternating minimization algorithm, and defining an augmented Lagrangian function;

[0116] a first solving module, in communication with the problem decomposition and function definition module, configured to solve the first subproblem using an inverse synthetic Gauss-Newton method to obtain a solution to the first subproblem;

[0117] a second solving module, in communication with the problem decomposition and function definition module, configured to solve the second subproblem using a finite difference method to obtain a solution to the second subproblem;

[0118] a variable updating module, communicatively connected to the first solving module and the second solving module, configured to update the first dual variable and the second dual variable in the Lagrangian function according to the solution of the first subproblem and the solution of the second subproblem, and obtain the Lagrangian function after the variables are updated;

[0119] The deformation field acquisition module is in communication with the problem decomposition and function definition module, and is used to calculate the Lagrangian function after variable update by alternating minimization iteration. When the preset iteration stop condition is met, the iteration stops, and the three-dimensional strain random field of the object strain deformation is obtained as the global displacement field of the last iteration.

[0120] In one embodiment, the displacement and deformation gradient acquisition module includes:

[0121] A pixel selection unit, used to select pixels in a reference image;

[0122] a correlation coefficient solving unit, in communication with the pixel point selection unit, for solving a zero-normalized correlation function based on the selected pixel points to obtain a matching correlation coefficient between the reference image and the deformed image;

[0123] a unit for acquiring coordinates of a pixel point after deformation, communicating with the correlation coefficient solving unit, and configured to acquire the coordinates corresponding to the pixel point in the target image when the correlation coefficient reaches an extreme value;

[0124] The displacement and deformation gradient acquisition module is in communication with the pixel point acquisition unit and the deformed pixel point coordinate acquisition unit, and is used to calculate the pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation based on the coordinate value of the pixel in the reference image and the coordinate value in the target image.

[0125] In a third aspect, an embodiment of the present application provides a three-dimensional strain calculation device for a deformable object. The three-dimensional strain calculation device for a deformable object can be a personal computer (PC), a laptop computer, a server, or other device with data processing capabilities.

[0126] In the embodiment of the present application, a three-dimensional strain calculation device for a deformable object may include a processor, a memory, a communication interface, and a communication bus.

[0127] The communication bus may be of any type and is used to interconnect the processor, memory, and communication interface.

[0128] Communication interfaces include input / output (I / O) interfaces, physical interfaces, and logical interfaces. These interfaces interconnect components within the device for calculating the three-dimensional strain of deformable objects, as well as interfaces that interconnect the device with other devices (such as other computing devices or user devices). Physical interfaces can include Ethernet, fiber, or ATM interfaces; user devices can include displays and keyboards.

[0129] The memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.

[0130] The processor may be a general-purpose processor that can invoke a three-dimensional strain calculation program for a deformable object stored in a memory and execute the three-dimensional strain calculation method for a deformable object provided in the embodiments of the present application. For example, the general-purpose processor may be a central processing unit (CPU). The method executed when the three-dimensional strain calculation program for a deformable object is invoked can be referenced from the various embodiments of the three-dimensional strain calculation method for a deformable object provided in the present application and will not be further described here.

[0131] In a fourth aspect, an embodiment of the present application also provides a readable storage medium.

[0132] The readable storage medium of the present application stores a three-dimensional strain calculation program for a deformable object, wherein when the three-dimensional strain calculation program for a deformable object is executed by a processor, the steps of the three-dimensional strain calculation method for a deformable object as described above are implemented.

[0133] The method implemented when the three-dimensional strain calculation program for a deformable object is executed can refer to the various embodiments of the three-dimensional strain calculation method for a deformable object in this application, and will not be repeated here.

[0134] It should be noted that the serial numbers of the above-mentioned embodiments of the present application are for description only and do not represent the advantages or disadvantages of the embodiments.

[0135] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus the necessary general hardware platform, of course, it can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes a number of instructions for enabling a terminal device to execute the methods described in each embodiment of the present application.

[0136] The above are only preferred embodiments of the present application and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A three-dimensional strain calculation method for a deformed object, characterized in that: The following steps are involved: For a set of 3D images of the input object after strain deformation, the zero-normalized cross-correlation function is used to calculate the pixel displacement and deformation gradient of all pixels in the 3D image after deformation; The alternating minimization algorithm is used to decompose the global minimization problem of pixel displacement and random field after deformation of all pixels in the three-dimensional image into the first subproblem and the second subproblem, and the augmented Lagrangian function is defined. The first sub-problem is: Given F i k ,u i k , û i k , W i k , v i k , fixed variable u i k , W i k , v i k , solve for F i k+1 ,u i k+1 ; The second sub-problem is: Fixed variable F i k ,u i k , W i k , v i k , solve for û i k+1 ; Among them, the superscript k and k+1 are the number of iterations, u i is the displacement of the ith pixel sub-block, W i is the first dual variable of the ith pixel sub-block, v i is the second dual variable of the i-th pixel sub-block, F i is the deformation gradient of the ith pixel sub-block, u i is the displacement of the ith pixel sub-block, F i is the deformation gradient of the ith pixel sub-block, û i is the global displacement field of the i-th pixel sub-block; The inverse synthesis Gauss-Newton method is used to solve the first subproblem and obtain the solution of the first subproblem; The finite difference method is used to solve the second subproblem and obtain the solution of the second subproblem; According to the solution of the first subproblem and the solution of the second subproblem, the first dual variable and the second dual variable in the Lagrangian function are updated to obtain the Lagrangian function after the variables are updated; The Lagrangian function after variable update is calculated by alternating minimization iteration. When the preset iteration stopping condition is met, the iteration stops and the three-dimensional strain random field of the object strain deformation is obtained as the global displacement field of the last iteration.

2. The three-dimensional strain calculation method for a deformed object according to claim 1, wherein: The method of calculating the integer pixel displacement and deformation gradient using a zero-normalized cross-correlation function for a set of three-dimensional images of the input object after strain deformation specifically includes: Select pixels in the reference image; Based on the selected pixel points, the zero-normalized correlation function is solved to obtain the matching correlation coefficient between the reference image and the deformed image; When the correlation coefficient reaches an extreme value, the coordinates corresponding to the pixel point in the target image are obtained; The pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation are calculated based on the coordinate value of the pixel in the reference image and the coordinate value in the target image.

3. The three-dimensional strain calculation method for a deformed object according to claim 1, wherein: The inverse synthesis Gauss-Newton method is used to solve the first subproblem, and the solution of the first subproblem is obtained as shown in the following formula: In the formula, the superscript k and k+1 are the number of iterations, F i is the deformation gradient of the ith pixel sub-block, u i is the displacement of the ith pixel sub-block, p i is the ith pixel sub-block, the f function is the grayscale calculation value of the reference image, the g function is the grayscale calculation value of the deformed image, X is the coordinate value of the center point of the reference image, X i0 is the coordinate value of the ith pixel sub-block in the deformed image, (Dû) i is the finite difference operator of the i-th pixel sub-block, λ is the coefficient value, is the convergence threshold, i is the global displacement field of the i-th pixel sub-block.

4. The three-dimensional strain calculation method for a deformed object according to claim 1, wherein: The finite difference method is used to solve the second sub-problem, and the solution of the second sub-problem is obtained as shown in the following formula: In the formula, the superscript k and k+1 are the number of iterations, i is the global displacement field of the ith pixel sub-block, p i is the i-th pixel sub-block, λ is the coefficient value, (Dû) i is the finite difference operator of the ith pixel sub-block, F i is the deformation gradient of the ith pixel sub-block, W i is the first dual variable of the i-th pixel sub-block, is the convergence threshold, i is the global displacement field of the ith pixel sub-block, u i The displacement of the i-th pixel sub-block, v i is the second dual variable of the i-th pixel sub-block.

5. The three-dimensional strain calculation method for a deformed object according to claim 1, wherein: According to the solution of the first subproblem and the solution of the second subproblem, the first dual variable and the second dual variable in the Lagrangian function are updated to obtain the Lagrangian function after the variables are updated, as shown in the following formula: Where, superscript k and k+1 are the number of iterations, W i is the first dual variable of the i-th pixel sub-block, (Dû) i is the finite difference operator of the ith pixel sub-block, F i is the deformation gradient, v i is the second dual variable of the i-th pixel sub-block, û is the global displacement field, u i is the displacement of the i-th pixel sub-block; The Lagrangian function is: Where L is the Lagrangian, p i is the ith pixel sub-block, X is the coordinate value of the center point of the reference image, X i0 is the coordinate of the center point of the ith pixel sub-block, û is the global displacement field, Dû is the finite difference operator of the global displacement field, W i and v i are the first dual variable and the second dual variable, respectively, which are the initial setting values.

6. The three-dimensional strain calculation method for a deformed object according to claim 1, wherein: The Lagrangian function after variable update is calculated by alternating minimization iteration. When the preset iteration stop condition is met, the iteration stops and the three-dimensional strain random field of the object strain deformation is obtained as the global displacement field of the last iteration. The specific steps include the following: Where, the superscripts k and k+1 are the number of iterations, û is the global displacement field, is the convergence threshold.

7. A three-dimensional strain calculation system for a deformed object, characterized in that: include: The whole pixel displacement and deformation gradient acquisition module is used to calculate the pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation using the zero-normalized cross-correlation function. a problem decomposition and function definition module, in communication with the integer pixel displacement and deformation gradient acquisition module, for decomposing the global minimization problem of the pixel displacement and random field after deformation of all pixels of the three-dimensional image into a first subproblem and a second subproblem using an alternating minimization algorithm, and defining an augmented Lagrangian function; The first sub-problem is: Given F i k ,u i k , û i k , W i k , v i k , fixed variable u i k , W i k , v i k , solve for F i k+1 ,u i k+1 ; The second sub-problem is: Fixed variable F i k ,u i k , W i k , v i k , solve for û i k+1 ; Among them, the superscript k and k+1 are the number of iterations, u i is the displacement of the ith pixel sub-block, W i is the first dual variable of the ith pixel sub-block, v i is the second dual variable of the i-th pixel sub-block, F i is the deformation gradient of the ith pixel sub-block, u i is the displacement of the ith pixel sub-block, F i is the deformation gradient of the ith pixel sub-block, û i is the global displacement field of the i-th pixel sub-block; a first solving module, in communication with the problem decomposition and function definition module, configured to solve the first subproblem using an inverse synthetic Gauss-Newton method to obtain a solution to the first subproblem; a second solving module, in communication with the problem decomposition and function definition module, configured to solve the second subproblem using a finite difference method to obtain a solution to the second subproblem; a variable updating module, communicatively connected to the first solving module and the second solving module, configured to update the first dual variable and the second dual variable in the Lagrangian function according to the solution of the first subproblem and the solution of the second subproblem, and obtain the Lagrangian function after the variables are updated; The deformation field acquisition module is in communication with the problem decomposition and function definition module, and is used to calculate the Lagrangian function after variable update by alternating minimization iteration. When the preset iteration stop condition is met, the iteration stops, and the three-dimensional strain random field of the object strain deformation is obtained as the global displacement field of the last iteration.

8. The three-dimensional strain calculation system for a deformable object according to claim 7, wherein: The displacement and deformation gradient acquisition module includes: A pixel selection unit, used to select pixels in a reference image; a correlation coefficient solving unit, in communication with the pixel point selection unit, for solving a zero-normalized correlation function based on the selected pixel points to obtain a matching correlation coefficient between the reference image and the deformed image; a unit for acquiring coordinates of a pixel point after deformation, communicating with the correlation coefficient solving unit, and configured to acquire the coordinates corresponding to the pixel point in the target image when the correlation coefficient reaches an extreme value; The displacement and deformation gradient acquisition module is in communication with the pixel point acquisition unit and the deformed pixel point coordinate acquisition unit, and is used to calculate the pixel displacement and deformation gradient of all pixels in the three-dimensional image after deformation based on the coordinate value of the pixel in the reference image and the coordinate value in the target image.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a three-dimensional strain calculation program for a deformable object, wherein when the three-dimensional strain calculation program for a deformable object is executed by a processor, the steps of the three-dimensional strain calculation method for a deformable object according to any one of claims 1 to 6 are implemented.

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