High speed global deformation measurement method and system

Abstract

The application provides a high-speed global deformation measurement method and system, comprising the following steps: S1, the camera and the lens optical axis are perpendicular to the sample surface, the digital images of the sample in different states are recorded by using the camera, an auxiliary global continuous displacement field and a constraint condition are introduced during image processing, and the displacement and displacement gradient of the field in each subset area are consistent with the local DIC calculation result; S2, the related function is modified based on the augmented Lagrangian function and the constraint condition; S3, the solution of the global problem is found by using the alternating direction multiplier method (ADMM) to coordinate the local sub-problems, so that the problem is iteratively solved; and S4, the fields of the quantities of interest including strain and velocity are derived according to the global displacement field. The application uses the augmented Lagrangian function, the calculation efficiency is much higher than that of the global DIC algorithm based on FEM, and the global displacement field obtained by introducing the constraint condition through the augmented Lagrangian function has continuity.

Description

Technical Field

[0001] This invention relates to the fields of image processing and metrology, and more specifically, to a high-speed global deformation measurement method and system. Background Technology

[0002] Digital image correlation (DIC) is an image-based, non-contact optical measurement method used to measure the constantly changing coordinates of an object's surface. The measured coordinate field can be used to further derive fields of interest such as displacement, strain, and velocity. As long as the object's surface has a suitable speckle pattern, it can measure the shape, motion, and deformation of almost any object, even under extreme experimental conditions. Essentially an image processing technique, DIC possesses unique characteristics beyond its non-contact, full-field measurement capabilities, including simple and inexpensive experimental setups, ease of implementation, and robustness. Theoretically, regardless of the imaging method used, as long as the image exhibits significant intensity changes and has a unique correspondence with each point on the object's surface, DIC can be used for measurement. In fact, DIC has been applied to common metals, polymer materials, composite materials, biological tissues, and surface deformation, ranging from a few micrometers (e.g., fibers) to tens of kilometers (e.g., ground deformation).

[0003] Over the past few decades, researchers have proposed various Deformation-Induced Conversion (DIC) algorithms based on their own approaches. Most algorithms can be categorized into two types: subset-based local DIC algorithms and FEM (Finite Element Method)-based global DIC algorithms. In local subset DIC, the region of interest (ROI) of the reference image is first decomposed into multiple subsets, and then the deformation of each subset is calculated separately. Since each subset in local DIC is of finite size, the deformation of each subset can be solved quickly. Because the calculation processes for each subset are independent, parallel computing can be used to improve efficiency. However, precisely because the deformation of each subset is obtained independently, the overall deformation may be discontinuous, and the strain field may contain significant noise disturbances. In FEM-based global DIC, a base set (usually based on finite element discretization) is typically used to represent the global deformation. Then, the global image is analyzed to obtain the parameters of this base set, and the overall deformation field of the object can be obtained from these parameters. Global DIC calculates object deformation based on FEM, therefore the obtained deformation field is consistent throughout. However, global DIC requires a very large amount of computation, often taking ten times longer than local DIC under the same conditions.

[0004] Patent document CN108956310B (application number: CN201810347552.8) discloses a geomembrane hydroswell deformation testing device and method based on three-dimensional DIC, including a pressure testing system, a pressure control system, and a three-dimensional DIC measurement system. The pressure testing system includes a pressure chamber on the membrane, a geomembrane diameter adjustment device, a pressure chamber below the membrane, and a base arranged coaxially from top to bottom. The upper surface of the geomembrane is uniformly sprayed with speckle patterns, and the digital image of the speckle patterns recorded in the three-dimensional DIC measurement system is no less than 3 pixels. The pressure control system includes an upper membrane pressure control system and a lower membrane pressure control system. The three-dimensional DIC measurement system includes a halogen lamp, a computer, and two CCD cameras, both connected to the computer. In one step, when performing time-series matching of a series of digital images of speckle deformation on the geomembrane surface captured by a single camera, the calculated displacements of each region are discontinuous and contain a lot of noise, which reduces the accuracy of subsequent calculation results, due to the use of subset-based local DIC principles. If the algorithm of this patent is used, a globally continuous displacement field can be obtained, and more accurate results can be obtained in subsequent calculations. Summary of the Invention

[0005] In view of the deficiencies in the prior art, the purpose of this invention is to provide a high-speed global deformation measurement method and system.

[0006] The high-speed global deformation measurement method provided by the present invention includes:

[0007] Step S1: Align the camera and lens optical axis with the sample surface, and use the camera to record digital images of the sample under different conditions. In the image processing, introduce an auxiliary global continuous displacement field and constraint conditions to keep the displacement and displacement gradient of the field in each subset region consistent with the local DIC calculation results.

[0008] Step S2: Modify the relevant functions based on the augmented Lagrangian function and constraints;

[0009] Step S3: Use the Alternating Direction Multiplier Method (ADMM) to coordinate local subproblems to find a solution to the global problem, thereby iteratively solving the problem;

[0010] Step S4: Derive the field of interest, including strain and velocity, from the global displacement field.

[0011] Preferably, step S1 includes:

[0012] When the displacement field is globally continuous, the displacement u and the displacement gradient F are not independent and satisfy the global constraints:

[0013] {F}=D{u}

[0014] The formula uses the discrete gradient operator D to calculate the displacement gradient, employs the first-order finite difference method with a uniform square grid, and introduces an auxiliary global continuous displacement field. Processing this condition yields two constraints:

[0015]

[0016] For gradient operators, The gradient of the global continuous displacement field is used as an auxiliary.

[0017] Preferably, step S2 includes:

[0018] The objective function for subset DIC is:

[0019]

[0020] Subset DIC only needs to satisfy its respective subset Ω i The objective function is to minimize it. A globally continuous displacement field is introduced, and the objective function is modified using the augmented Lagrangian function and constraints. The goal is to find the globally optimal solution. The objective function is as follows:

[0021]

[0022] In the formula ∑ i To represent the entire subset region, we need to obtain the global displacement field. Therefore, the global objective function must be minimized;

[0023] u i X represents i0 Displacement; F i Represented as a subset Ω i The uniform displacement gradient; the reference image is divided into multiple subsets in the subset DIC, where i is the index of each subset; f(X) represents the gray value at point X on the reference image; X represents the coordinates of a point in the digital image; g(X) represents the gray value at point X on the deformed image; X i0 Representing a subset Ω i The center; β is the corresponding constraint. The coefficient of the quadratic penalty term; W i It is a correspondence constraint The Lagrange multipliers; μ is the correspondence constraint. The coefficient of the secondary penalty term; V represents the introduced global continuous displacement field, a quantity to be determined; i It is a correspondence constraint Lagrange multipliers.

[0024] Preferably, step S3 includes:

[0025] Step S3.1: Let Wi V i , Unchanged, first solve u i F i The expression for the k-th iteration is as follows:

[0026]

[0027] Step S3.2: Only put As variables, the objective function is as follows:

[0028]

[0029] And based on the results obtained through iteration, update the Lagrange multiplier W. i V i Repeat this step until the iteration stopping criterion is met, i.e. Small enough.

[0030] Preferably, step S4 includes:

[0031] Let the bottom left corner of the image be the origin, the bottom edge be the x-axis, and the left edge be the y-axis, establish a Cartesian coordinate system, and derive the strain using the following formula:

[0032]

[0033] e xy This represents the change in the angle between two small line segments in mutually perpendicular directions after deformation; e yy The value represents the ratio of the length increment of a small line segment along the y-axis due to deformation to its original length; it is positive when the segment is elongated. u represents the displacement along the x-axis. v represents the displacement along the y-axis.

[0034] The high-speed global deformation measurement system provided by the present invention includes:

[0035] Module M1: The camera and lens optical axes are perpendicular to the sample surface. The camera records digital images of the sample under different conditions. During image processing, an auxiliary global continuous displacement field and constraint conditions are introduced to keep the displacement and displacement gradient of the field in each subset region consistent with the local DIC calculation results.

[0036] Module M2: Modifies related functions based on augmented Lagrangian functions and constraints;

[0037] Module M3: Uses the Alternating Direction Multiplier Method (ADMM) to coordinate local subproblems to find a solution to the global problem, thereby iteratively solving the problem;

[0038] Module M4: Derives the field of interest, including strain and velocity, from the global displacement field.

[0039] Preferably, the module M1 includes:

[0040] When the displacement field is globally continuous, the subset's local displacement u and local displacement gradient F are not independent and satisfy the global constraint:

[0041] {F}=D{u}

[0042] The formula uses the discrete gradient operator D to calculate the displacement gradient, employs the first-order finite difference method with a uniform square grid, and introduces an auxiliary global continuous displacement field. Processing this condition yields two constraints:

[0043]

[0044] For gradient operators, The gradient of the global continuous displacement field is used as an auxiliary.

[0045] Preferably, the module M2 includes:

[0046] The objective function for subset DIC is:

[0047]

[0048] Subset DIC only needs to satisfy its respective subset Ω i The objective function is to minimize it. A globally continuous displacement field is introduced, and the objective function is modified using the augmented Lagrangian function and constraints. The goal is to find the globally optimal solution. The objective function is as follows:

[0049]

[0050] In the formula ∑ i To represent the entire subset region, we need to obtain the global displacement field. Therefore, the global objective function must be minimized;

[0051] u i X represents i0 Displacement; F i Represented as a subset Ω i The uniform displacement gradient; the reference image is divided into multiple subsets in the subset DIC, where i is the index of each subset; f(X) represents the gray value at point X on the reference image; X represents the coordinates of a point in the digital image; g(X) represents the gray value at point X on the deformed image; X i0 Representing a subset Ω i The center; β is the corresponding constraint. The coefficient of the quadratic penalty term; W i It is a correspondence constraint The Lagrange multipliers; μ is the correspondence constraint. The coefficient of the secondary penalty term; V represents the introduced global continuous displacement field, a quantity to be determined; i It is a correspondence constraint Lagrange multipliers.

[0052] Preferably, the module M3 includes:

[0053] Module M3.1: Let W i V i , Unchanged, first solve u i F i The expression for the k-th iteration is as follows:

[0054]

[0055] Module M3.2: Only put As variables, the objective function is as follows:

[0056]

[0057] And based on the results obtained through iteration, update the Lagrange multiplier W. i V i Repeat this step until the iteration stopping criterion is met, i.e. Small enough.

[0058] Preferably, the module M4 includes:

[0059] Let the bottom left corner of the image be the origin, the bottom edge be the x-axis, and the left edge be the y-axis, establish a Cartesian coordinate system, and derive the strain using the following formula:

[0060]

[0061] e xy This represents the change in the angle between two small line segments in mutually perpendicular directions after deformation; e yy The value represents the ratio of the length increment of a small line segment along the y-axis due to deformation to its original length; it is positive when the segment is elongated. u represents the displacement along the x-axis. v represents the displacement along the y-axis.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] (1) This invention does not use a base set to force continuity, but uses an augmented Lagrangian function, which has a much higher computational efficiency than the global DIC algorithm based on FEM. By introducing constraints through the augmented Lagrangian function, the obtained global displacement field has continuity.

[0064] (2) This invention combines the advantages of local DIC (fast) and global DIC (strain coordination) algorithms. Compared with local subset DIC and global DIC, it has higher running efficiency without losing continuity.

[0065] (3) The present invention uses the Alternating Direction Multiplier Method (ADMM) to decompose the problem into several simpler problems. First, the local subproblems, i.e. the displacement fields of each subset, are solved, and then the solution to the global problem is found. Therefore, parallel computing can be used to reduce the overall algorithm running time when solving subproblems. Attached Figure Description

[0066] 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:

[0067] Figure 1 Images of the specimens from the shear test;

[0068] Figure 2 shows the strain field calculated by the subset DIC;

[0069] Figure 3 shows the strain field calculated by global DIC based on the finite element method;

[0070] Figure 4 shows the strain field calculated by the algorithm of this invention;

[0071] Figure 5 A time comparison chart for each algorithm;

[0072] Figure 6 This is a flowchart of the method of the present invention. Detailed Implementation

[0073] 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.

[0074] Example:

[0075] This invention proposes a novel DIC algorithm, a high-speed global deformation measurement technique. This algorithm combines the advantages of local subset DIC (velocity and parallel computation) and global DIC (displacement continuity and strain coordination). The basic idea is to calculate object deformation using subset-based local DIC, but using continuity as a constraint. Specifically, an auxiliary global continuous displacement field is introduced, along with the constraint that this auxiliary global continuous displacement field and its gradient are equal to the local correlation value. This constraint is implemented using an augmented Lagrangian function. Finally, the alternating direction multiplier method (ADMM) is used to coordinate local subproblems to find a solution to a large global problem, thereby iteratively solving the problem.

[0076] like Figure 6 According to the present invention, a high-speed global deformation measurement technology includes the following steps:

[0077] Step S1: Introduce an auxiliary globally continuous displacement field and constraints. Since each subset in the subset DIC is matched independently, the local displacement u and local displacement gradient F of each subset are independent of each other and independent for each subset. This leads to potential overlap of matched subsets, thus failing to guarantee deformation compatibility. However, if the displacement field is globally continuous, then the displacement and displacement gradient are not independent but satisfy a global constraint:

[0078] {F}=D{u}

[0079] The displacement gradient is calculated using the discrete gradient operator D, which depends on the discretization method. This invention uses a first-order finite difference method with a uniform square grid. An auxiliary global continuous displacement field is introduced here. To handle this condition, we can obtain two constraints:

[0080]

[0081] Global continuous displacement field Under the condition of continuity, the displacement and displacement gradient should be as similar as possible to the subset DIC results. The core idea of ​​this invention is to add global continuity constraints to the subset DIC results to calculate a globally continuous displacement field.

[0082] Step S2: Modify the correlation function based on the augmented Lagrangian function and constraints. The augmented Lagrangian function adds a quadratic penalty term to the Lagrangian function; this method combines the Lagrangian function method and the penalty function method. Detailed information about this method is readily available online and will not be elaborated here. The objective function for subset DIC is:

[0083]

[0084] Subset DIC only needs to satisfy its respective subset Ω i The objective function is to minimize it. This invention introduces a globally continuous displacement field and modifies the objective function by using an augmented Lagrangian function and constraints. The goal is to find the globally optimal solution. The objective function is as follows:

[0085]

[0086] In the formula ∑ i Unlike subset DIC, which satisfies the minimum objective function of each subset, this invention requires the calculation of the global displacement field, representing the entire subset region. Therefore, the objective function must be minimized globally (for all subset regions).

[0087] Step S3: Use the Alternating Direction Multiplier Method (ADMM) to coordinate local subproblems to find a solution to a large global problem, and then iteratively solve the problem.

[0088] The first step is to let W i V i , Unchanged, first solve u i F i The expression for the k-th iteration is as follows:

[0089]

[0090] This step is essentially similar to subset DIC and can be solved using the subset DIC algorithm.

[0091] The second step only involves... As variables, the objective function is as follows:

[0092]

[0093] And based on the results obtained through iteration, update the Lagrange multiplier W. i V i Repeat this step until the iteration stopping criterion is met, i.e. Small enough.

[0094] Step S4: Derive the field of interest based on the global displacement field. The strain is derived using the following formula:

[0095]

[0096] The following example uses a shear test, where the sample surface has suitable artificial speckle patterns, such as... Figure 1 As shown, the results are verified by comparing the results of subset DIC, FEM-based global DIC, and the algorithm of this invention.

[0097] Strain was calculated using subset DIC, finite element-based global DIC, and the algorithm of this patent, respectively. The results of subset DIC are as follows: Figures 2a-2c As shown, the global DIC results based on the finite element method are as follows: Figures 3a-3c As shown, the results of this patent are as follows: Figures 4a-4c As shown. Figures 2-4 each contain 3 sub-figures, representing e from left to right. xx e xy e yy The results show that the strain calculation results of the subset DIC contain a lot of noise, while the results of the global DIC based on the finite element method and the results of this patent are more continuous. The running time of each algorithm is also recorded. Figure 5 As shown, the running time of this patent is significantly shorter than that of global DIC based on finite element method. This example verifies that this patent combines the running speed of local DIC with the deformation coordination of global DIC.

[0098] The high-speed global deformation measurement system provided by the present invention includes: Module M1: aligning the camera and lens optical axes perpendicular to the sample surface, using the camera to record digital images of the sample under different states, and introducing an auxiliary global continuous displacement field and constraint conditions during image processing to maintain consistency between the displacement and displacement gradient of the field in each subset region and the local DIC calculation results; Module M2: modifying the correlation function based on the augmented Lagrangian function and constraint conditions; Module M3: using the Alternating Direction Multiplier Method (ADMM) to coordinate local subproblems to find the solution to the global problem, thereby iteratively solving the problem; Module M4: deriving the field of interest, including strain and velocity, based on the global displacement field.

[0099] The module M1 includes: when the displacement field is globally continuous, the subset local displacement u and local displacement gradient F are not independent, satisfying the global constraint: {F}=D{u}, where the discrete gradient operator D is used to calculate the displacement gradient, and a first-order finite difference method with a uniform square grid is used to introduce an auxiliary globally continuous displacement field. Processing this condition yields two constraints: For gradient operators, The gradient of the global continuous displacement field is used as an auxiliary.

[0100] The module M2 includes: the objective function of the subset DIC is: The subset DIC only needs to satisfy the minimum objective function of its respective subset Ωi. By introducing a globally continuous displacement field and modifying the objective function through the augmented Lagrangian function and constraints, the global optimal solution needs to be obtained. The objective function is as follows:

[0101]

[0102] In the formula ∑ iTo represent the entire subset region, we need to obtain the global displacement field. Therefore, the global objective function must be minimized; u i X represents i0 Displacement; F i Represented as a subset Ω i The uniform displacement gradient; the reference image is divided into multiple subsets in the subset DIC, where i is the index of each subset; f(X) represents the gray value at point X on the reference image; X represents the coordinates of a point in the digital image; g(X) represents the gray value at point X on the deformed image; X i0 Representing a subset Ω i The center; β is the corresponding constraint. The coefficient of the quadratic penalty term; W i It is a correspondence constraint The Lagrange multipliers; μ is the correspondence constraint. The coefficient of the secondary penalty term; V represents the introduced global continuous displacement field, a quantity to be determined; i It is a correspondence constraint Lagrange multipliers.

[0103] The module M3 includes:

[0104] Module M3.1: Let W i V i , Unchanged, first solve u i F i The expression for the k-th iteration is as follows:

[0105]

[0106] Module M3.2: Only put As variables, the objective function is as follows:

[0107]

[0108] And based on the results obtained through iteration, update the Lagrange multiplier W. i V i Repeat this step until the iteration stopping criterion is met, i.e. Small enough.

[0109] The module M4 includes: establishing a Cartesian coordinate system with the lower left corner of the image as the origin, the lower edge as the x-axis, and the left edge as the y-axis, and deriving the strain using the following formula:

[0110]

[0111] e xy This represents the change in the angle between two small line segments in mutually perpendicular directions after deformation; eyy The value represents the ratio of the length increment of a small line segment along the y-axis due to deformation to its original length; it is positive when the segment is elongated. u represents the displacement along the x-axis. v represents the displacement along the y-axis.

[0112] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0113] 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 high-speed global deformation measurement method, characterized in that, include: Step S1: Align the camera and lens optical axis with the sample surface, and use the camera to record digital images of the sample under different conditions. In the image processing, introduce an auxiliary global continuous displacement field and constraint conditions to keep the displacement and displacement gradient of the field in each subset region consistent with the local DIC calculation results. Step S2: Modify the relevant functions based on the augmented Lagrangian function and constraints; Step S3: Use the Alternating Direction Multiplier Method (ADMM) to coordinate local subproblems to find a solution to the global problem, thereby iteratively solving the problem; Step S4: Derive the field containing the quantities of interest, including strain and velocity, from the global displacement field; Step S2 includes: The objective function for subset DIC is: Subset DIC only needs to satisfy its respective subset The objective function is to minimize it. A globally continuous displacement field is introduced, and the objective function is modified using the augmented Lagrangian function and constraints. The goal is to find the globally optimal solution. The objective function is as follows: In the formula To represent the entire subset region, we need to obtain the global displacement field. Therefore, the global objective function must be minimized. express The displacement; Represented as a subset The uniform displacement gradient; the reference image is divided into multiple subsets in the subset DIC, where i is the index of each subset; This represents the grayscale value at point X in the reference image; Represents the coordinates of a point in a digital image; This represents the gray value at point X in the deformed image; Representing a subset The center; It is a correspondence constraint The coefficient of the secondary penalty term; It is a correspondence constraint Lagrange multipliers; It is a correspondence constraint The coefficient of the secondary penalty term; This represents the introduced global continuous displacement field, a quantity to be determined; It is a correspondence constraint Lagrange multipliers; Step S3 includes: Step S3.1: Let , , Unchanged, solve first , The expression for the k-th iteration is as follows: Step S3.2: Only put As variables, the objective function is as follows: And update the Lagrange multipliers based on the results obtained through iteration. , Repeat this step until the iteration stopping criterion is met, i.e. Small enough.

2. The high-speed global deformation measurement method according to claim 1, characterized in that, Step S1 includes: When the displacement field is globally continuous, the displacement and displacement gradient Not independent, but satisfies global constraints: The discrete gradient operator is used in the formula. The displacement gradient is calculated using a first-order finite-difference method with a uniform square grid, and an auxiliary global continuous displacement field is introduced. Processing this condition yields two constraints: For gradient operators, The gradient of the global continuous displacement field is used as an auxiliary.

3. The high-speed global deformation measurement method according to claim 1, characterized in that, Step S4 includes: Let the bottom left corner of the image be the origin, the bottom edge be the x-axis, and the left edge be the y-axis, establish a Cartesian coordinate system, and derive the strain using the following formula: It represents the change in the angle between two small line segments in mutually perpendicular directions after deformation; It represents the ratio of the increase in length of a small line segment along the y-axis due to deformation to its original length; it is positive when the line segment is stretched. This represents the displacement along the x-axis. This represents the displacement along the y-axis.

4. A high-speed global deformation measurement system, characterized in that, include: Module M1: The camera and lens optical axes are perpendicular to the sample surface. The camera records digital images of the sample under different conditions. During image processing, an auxiliary global continuous displacement field and constraint conditions are introduced to keep the displacement and displacement gradient of the field in each subset region consistent with the local DIC calculation results. Module M2: Modifies related functions based on augmented Lagrangian functions and constraints; Module M3: Uses the Alternating Direction Multiplier Method (ADMM) to coordinate local subproblems to find a solution to the global problem, thereby iteratively solving the problem; Module M4: Derives the field of interest, including strain and velocity, from the global displacement field; The module M2 includes: The objective function for subset DIC is: Subset DIC only needs to satisfy its respective subset The objective function is to minimize it. A globally continuous displacement field is introduced, and the objective function is modified using the augmented Lagrangian function and constraints. The goal is to find the globally optimal solution. The objective function is as follows: In the formula To represent the entire subset region, we need to obtain the global displacement field. Therefore, the global objective function must be minimized. express The displacement; Represented as a subset The uniform displacement gradient; the reference image is divided into multiple subsets in the subset DIC, where i is the index of each subset; This represents the grayscale value at point X in the reference image; Represents the coordinates of a point in a digital image; This represents the gray value at point X in the deformed image; Representing a subset The center; It is a correspondence constraint The coefficient of the secondary penalty term; It is a correspondence constraint Lagrange multipliers; It is a correspondence constraint The coefficient of the secondary penalty term; This represents the introduced global continuous displacement field, a quantity to be determined; It is a correspondence constraint Lagrange multipliers; The module M3 includes: Module M3.1: Command , , Unchanged, solve first , The expression for the k-th iteration is as follows: Module M3.2: Only put As variables, the objective function is as follows: And update the Lagrange multipliers based on the results obtained through iteration. , Repeat this step until the iteration stopping criterion is met, i.e. Small enough.

5. The high-speed global deformation measurement system according to claim 4, characterized in that, The module M1 includes: When the displacement field is globally continuous, the displacement and displacement gradient Not independent, but satisfies global constraints: The discrete gradient operator is used in the formula. The displacement gradient is calculated using a first-order finite-difference method with a uniform square grid, and an auxiliary global continuous displacement field is introduced. Processing this condition yields two constraints: For gradient operators, The gradient of the global continuous displacement field is used as an auxiliary.

6. The high-speed global deformation measurement system according to claim 4, characterized in that, The module M4 includes: Let the bottom left corner of the image be the origin, the bottom edge be the x-axis, and the left edge be the y-axis, establish a Cartesian coordinate system, and derive the strain using the following formula: It represents the change in the angle between two small line segments in mutually perpendicular directions after deformation; It represents the ratio of the increase in length of a small line segment along the y-axis due to deformation to its original length; it is positive when the line segment is stretched. This represents the displacement along the x-axis. This represents the displacement along the y-axis.

Images