A method and apparatus for phase unpacking of multi-scale anisotropic dynamic elastoplastic meshes

Abstract

This invention relates to the field of optical interferometry technology and discloses a multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method and apparatus. The method involves obtaining the gradient field of the encapsulated phase matrix as the initial prestress; establishing a discrete node mesh corresponding to the image; initializing the anisotropic stiffness coefficient tensor based on residual point detection; constructing and solving a multi-scale mechanical equilibrium equation based on the minimum potential energy principle; calculating the difference between the current unpacked phase gradient and the prestress to obtain the local lattice strain field; dynamically updating the stiffness coefficients according to the strain magnitude based on a nonlinear plastic constitutive relation to simulate the plastic softening and fracture behavior in the shear region; iterating until the system potential energy converges, and outputting the target unpacked phase matrix. This invention accelerates convergence through multi-scale solving, suppresses noise and preserves phase discontinuity characteristics by utilizing anisotropic elastoplastic mechanisms, solves the problem of traditional algorithms easily producing stringing or excessive smoothing, and improves the accuracy of phase unpacking.

Description

Technical Field

[0001] This invention relates to the field of optical interferometry technology, and in particular to a method and apparatus for unpacking phase of a multi-scale anisotropic dynamic elastoplastic grid. Background Technology

[0002] Optical interferometry techniques, such as electronic speckle interferometry, digital holography, and moiré fringe techniques, are characterized by non-contact, high precision, and full-field measurement capabilities. They are widely used in deformation measurement, non-destructive testing, optical component surface shape inspection, and topographic mapping. In these applications, the measured physical quantity (such as displacement, height, and deformation) is typically modulated into the phase information of the interference fringes. Due to the periodicity of light waves and the properties of the arctangent function, the phase value extracted directly from the interferogram is truncated. Within the principal value interval, a discontinuous "wrapped phase" is formed. To obtain a continuous phase distribution that reflects the true physical quantity, the lost phase must be recovered. The process of unpacking is called phase unpacking, where the number of cycles is an integer multiple of the number of cycles.

[0003] Phase unpacking is one of the key and most challenging steps in the optical measurement data processing workflow. The difficulties stem primarily from two aspects: first, unavoidable noise in the measurement system (such as speckle noise and electronic noise) reduces the signal-to-noise ratio of the phase data; second, the measurement object itself may possess complex topological structures (such as steep steps, cracks, holes, or shear layers), resulting in an inherently discontinuous phase distribution.

[0004] Traditional phase unpacking algorithms are mainly divided into three categories: path-following algorithms and minimum norm algorithms. The core idea of ​​path-following algorithms is to select an integration path based on a certain strategy, integrating the phase gradient along the path to recover continuous phase; this type of algorithm assumes that the phase difference along the integration path is less than... The classic example of the branch-cutting method is the Goldstein branch-cutting method. This method first identifies residual points in the phase diagram, which usually appear in pairs with opposite polarities. Then, the algorithm connects positive and negative residual points by setting branch-cutting lines, preventing the integration path from crossing these branches-cutting lines, thereby achieving the purpose of "balancing" the residual charge. However, the generation strategy of branch-cutting lines is often based on heuristic rules (such as the nearest neighbor principle). In noisy regions, the number of residual points is huge, which can easily form complex closed "dead zones" or incorrect branch-cutting line connections, resulting in some regions being unable to unpack or the unpacking result deviating significantly from the true value.

[0005] The quality map-guided method introduces phase quality maps (such as phase derivative variance, modulation depth, pseudocoherence coefficients, etc.) to quantify the reliability of each pixel. The unpacking process is similar to flood filling, prioritizing integration in high-quality regions and processing low-quality regions last. Although this method can suppress error propagation to some extent, in regions with high noise or phase shearing, the quality map often fails to accurately reflect the true topology. Once the path is chosen incorrectly, the error will spread rapidly along the integration path, producing a large-scale stringing error, and this error is globally destructive.

[0006] In summary, in the field of optical interferometry, existing traditional phase unpacking algorithms struggle to simultaneously achieve noise robustness, computational efficiency, and the ability to preserve phase break / shearing features. Path-following methods are prone to producing string-like patterns, least squares methods tend to blur edges, and norm methods are computationally too time-consuming. Therefore, a new unpacking mechanism is urgently needed that possesses global convergence like least squares methods while allowing for local discontinuities like path-following methods, thereby effectively solving the phase unpacking challenge in complex scenarios. Summary of the Invention

[0007] Therefore, the technical problem to be solved by the present invention is to overcome the problem in the prior art that it is difficult to simultaneously take into account noise resistance, computational efficiency and the ability to preserve phase break / shear features, resulting in inaccurate phase unpacking.

[0008] To address the aforementioned technical problems, this invention provides a method for phase unpacking of multi-scale anisotropic dynamic elastoplastic meshes, comprising: The horizontal and vertical wrapping gradient fields of the discrete two-dimensional wrapping phase matrix of the input image are obtained to form the initial prestress field. Construct a discrete node grid corresponding to the pixels of the input image and define the adjacency relationship between nodes in the discrete node grid; Based on the wrapping phase gradient at each node in the discrete node mesh, residual points are identified and obtained. Based on the location of the residual points, the stiffness coefficients of each connecting edge in the discrete node mesh are initialized, and the stiffness coefficient tensor of each node is obtained. Based on the initial stress field and the stiffness coefficient tensor of all nodes in the discrete nodal mesh, a multi-scale mechanical equilibrium equation for the discrete nodal mesh is constructed. The multi-scale mechanical equilibrium equations are solved at multiple scales to obtain the current unpacked phase field of the discrete node mesh; Calculate the difference between the gradient of the current unpacking phase field and the initial prestress field to obtain the local lattice strain field of the discrete node mesh; The stiffness coefficient tensor is adjusted based on the real-time updated local lattice strain field. The updated stiffness coefficient tensor is obtained, and the multi-scale mechanical equilibrium equation is reconstructed. The current unpacking phase field is calculated until the change in the total potential energy of the discrete node grid is less than a preset threshold. The target unpacking phase matrix of the input image is then obtained.

[0009] Preferably, the horizontal and vertical wrapping gradient fields of the discrete two-dimensional wrapping phase matrix of the input image are obtained to form the initial prestress field. , is represented as: ; This represents the horizontally wrapped gradient field, with coordinates as follows: Horizontal gradient at pixel ; This represents the gradient field wrapped in the vertical direction, with coordinates as follows: Vertical gradient at pixel ; in, Indicates coordinates as Discrete two-dimensional wrapper phase at the pixel; Indicates the mapping of numerical values ​​to Interval phase wrapper operator; , , and These represent the number of rows and columns of the input image, respectively.

[0010] Preferably, residual points are identified and obtained based on the wrapping phase gradient at each node in the discrete node mesh. Based on the location of the residual points, the stiffness coefficients of each connecting edge in the discrete node mesh are initialized, and the stiffness coefficient tensor of each node is obtained, including: Based on the residual point detection strategy, the wrapping phase gradient at each node in the discrete node mesh is calculated to identify the residual points; Based on the identified residual points, the discrete node mesh is divided into regions without residual points and regions with residual points and their neighborhoods. Initialize the stiffness coefficient of the connecting edges in the region without residual points to a unit value, and initialize the stiffness coefficient of the connecting edges in the residual points and their neighboring regions to a preset smaller value. For each node, obtain the stiffness coefficients of its connecting edges to form the stiffness coefficient tensor of each node.

[0011] Preferably, the stiffness coefficient tensor is expressed as: ; in, Indicates the first The updated stiffness coefficient tensor , This indicates the initialization of the stiffness coefficient tensor; Indicates the first The horizontal stiffness coefficient after the next update Indicates the first Vertical stiffness coefficient after the next update.

[0012] Preferably, based on the initial stress field and the stiffness coefficient tensors of all nodes in the discrete nodal mesh, a multi-scale mechanical equilibrium equation for the discrete nodal mesh is constructed, including: Based on nodes horizontal gradient Vertical gradient and the The updated horizontal stiffness coefficient Vertical stiffness coefficient Build nodes Net prestressed flow , is represented as: ; Obtain the net prestress flow at all nodes in the discrete node mesh and form a generalized force vector. ; Construct a weighted Laplace matrix based on the stiffness coefficient tensor of all nodes. ; Based on the weighted Laplace matrix and the current unpacking phase field to be solved The product of these equals the generalized force vector, constructing the first... The updated multiscale mechanical equilibrium equations are expressed as follows: ; Among them, the elements of the weighted Laplace matrix Defined as: if ,but For connecting nodes The sum of the stiffness coefficients of all connected edges; if the node For nodes The adjacent nodes, then It is the negative value of the stiffness coefficient of the connecting edge between the two; otherwise, it is 0. , ; , , and These represent the number of rows and columns of the input image, respectively.

[0013] Preferably, the multi-scale mechanical equilibrium equations are solved using the explicit dynamic relaxation method or the damped Verlet integral method to obtain the current unpacked phase field of the discrete node grid.

[0014] Preferably, the difference between the gradient of the current unpacking phase field and the initial prestress field is calculated to obtain the local lattice strain field of the discrete node mesh. , is represented as: ; No. After the next update, the nodes in the discrete node mesh Local lattice strain field at , is represented as: ; Indicates the first After the next update, the node The horizontal strain component at a given location is expressed as: ; Indicates the first After the next update, the node The vertical strain component at a given location is expressed as: ; in, , , and These represent the number of rows and columns of the input image, respectively. Indicates the first After the next update, the node Phase at that point, Represents a node The horizontal gradient at that point Represents a node The vertical gradient at that point.

[0015] Preferably, the full-field potential energy function of the discrete node grid , is represented as: ; in, , , and These represent the number of rows and columns of the input image, respectively. and They represent the first After the next update, the node The horizontal stiffness coefficient and the vertical stiffness coefficient at the location and They represent the first After the next update, the node The horizontal strain component and the vertical strain component at the location.

[0016] Preferably, adjusting the stiffness coefficient tensor based on the real-time updated local lattice strain field to obtain the updated stiffness coefficient tensor includes: No. After the next update, the node Horizontal stiffness coefficient , is represented as: ; No. After the next update, the node Vertical stiffness coefficient , is represented as: ; in, This indicates the preset damage sensitivity parameter. and They represent the first After the next update, the node The horizontal strain component and the vertical strain component at the location.

[0017] This embodiment provides an apparatus based on the multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method as described above, comprising: An anisotropic elastic mesh construction module is used to obtain the horizontal and vertical wrapping gradient fields of the discrete two-dimensional wrapping phase matrix of the input image, forming the initial prestress field; construct a discrete node mesh corresponding to the pixels of the input image, and define the adjacency relationship between nodes in the discrete node mesh; based on the wrapping phase gradient at each node in the discrete node mesh, identify and obtain residual points; based on the position of the residual points, initialize the stiffness coefficients of each connecting edge in the discrete node mesh, and obtain the stiffness coefficient tensor of each node; The multi-scale mechanical equilibrium equation construction module is used to construct the multi-scale mechanical equilibrium equations of the discrete node mesh based on the initial stress field and the stiffness coefficient tensor of all nodes in the discrete node mesh. The solver module is used to solve the multi-scale mechanical equilibrium equations at multiple scales and obtain the current unpacked phase field of the discrete node mesh. The local lattice strain field construction module is used to calculate the difference between the gradient of the current unpacked phase field and the initial prestress field, and to obtain the local lattice strain field of the discrete node mesh. The iterative update module is used to adjust the stiffness coefficient tensor based on the real-time updated local lattice strain field, obtain the updated stiffness coefficient tensor, return to reconstruct the multi-scale mechanical equilibrium equation, and calculate the current unpacking phase field until the total potential energy change of the discrete node grid is less than a preset threshold, and obtain the target unpacking phase matrix of the input image.

[0018] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method described in this invention establishes a discrete node mesh model corresponding to the wrapped phase image. It uses the curl of the wrapped phase gradient to detect residual points and initializes the anisotropic stiffness tensor. Through the residual points, an index with clear topological significance, the mesh connection edges are divided into strongly connected and weakly connected regions, achieving precise pre-positioning of the fracture region and providing a reasonable initial state for subsequent elastoplastic evolution. This effectively avoids the slow convergence or getting trapped in local extrema problems caused by improper initial weight settings in traditional methods. Furthermore, it constructs a mechanical equilibrium equation based on the minimum potential energy principle to address the phase unpacking problem. The problem is transformed into a global energy minimization problem, ensuring the theoretical convergence of the solution process. During the iteration process, a strain-based nonlinear plastic constitutive relation is introduced, and the stiffness coefficient of the mesh connection edge is dynamically updated according to the magnitude of the local lattice strain. In the shear region with severe phase jumps, the plastic softening and fracture behavior of the material are simulated, realizing the adaptive distinction between continuous and fracture regions. When the local strain is small, the system maintains elastic behavior to ensure unpacking continuity. When the strain exceeds the threshold, the stiffness coefficient decays exponentially and automatically releases the inter-node constraints, allowing the real phase jump to occur, avoiding the loss of key features caused by the excessive smoothing of the traditional least squares method.

[0019] This invention accelerates convergence through a multi-scale solution strategy, effectively suppresses noise and preserves the true discontinuities of the phase field by utilizing anisotropic elastoplastic mechanisms, and forms a positive feedback synergy among residual-guided initialization, global energy optimization, dynamic relaxation solution and plastic constitutive update, enabling the mesh system to continuously improve itself during the iteration process. This improves the system's noise robustness, discontinuity preservation, global convergence and computational efficiency, and solves the problem of traditional algorithms easily producing stringing or smoothing overlays in complex topologies. Attached Figure Description

[0020] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein: Figure 1 This is a flowchart of the steps of the multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method of the present invention; Figure 2 It is the original phase distribution map including noise; Figure 3 It is a discrete encapsulated phase diagram of local shear fracture; Figure 4 This is the unpacked phase diagram after phase unpacking according to the present invention. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0022] Reference Figure 1 The flowchart shown is a step-by-step diagram of the multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method of the present invention, and the specific steps are shown in S101 to S107.

[0023] S101: Obtain the discrete two-dimensional wrapping phase matrix of the input image. The horizontal and vertical gradient fields together form the initial prestress field. , is represented as: ; This represents the horizontally wrapped gradient field, with coordinates as follows: Horizontal gradient at pixel ; This represents the gradient field wrapped in the vertical direction, with coordinates as follows: Vertical gradient at pixel ; in, Indicates coordinates as Discrete two-dimensional wrapper phase at the pixel; Indicates the mapping of numerical values ​​to Interval phase wrapper operator; , , and These represent the number of rows and columns of the input image, respectively.

[0024] S102: Construct a discrete node grid corresponding to the pixels of the input image and define the adjacency relationships between nodes in the discrete node grid.

[0025] S103: Based on the wrapper phase gradient at each node in the discrete node mesh, identify and obtain residual points. Based on the residual point locations, initialize the stiffness coefficients of each connecting edge in the discrete node mesh, and obtain the stiffness coefficient tensor of each node, including: S103-1: Based on the residual point detection strategy, calculate the wrapping phase gradient at each node in the discrete node mesh and identify the residual points; S103-2: Based on the identified residual points, the discrete node mesh is divided into regions without residual points and regions with residual points and their neighborhoods; S103-3: Initialize the stiffness coefficient of the connecting edges in the region without residual points to a unit value, and initialize the stiffness coefficient of the connecting edges in the residual points and their neighboring regions to a preset smaller value. S103-4: For each node, obtain the stiffness coefficients of its connecting edges to form the stiffness coefficient tensor of each node, represented as: ; in, Indicates the first The updated stiffness coefficient tensor , This indicates the initialization of the stiffness coefficient tensor; Indicates the first The horizontal stiffness coefficient after the next update Indicates the first Vertical stiffness coefficient after the next update.

[0026] This embodiment initializes the stiffness coefficient of each connecting edge in the mesh based on the local quality index of the wrapped phase, forming the stiffness coefficient tensor of each node. Specifically, a residual point detection strategy is adopted to calculate the curl of the wrapped phase gradient and identify the location of residual points where the phase is discontinuous. For the region near the residual point, its initial connection stiffness coefficient is reduced to a small value, while for the continuous region without residuals, the initial stiffness coefficient is set to a unit value.

[0027] S104: Based on the initial stress field and the stiffness coefficient tensors of all nodes in the discrete nodal mesh, construct the multi-scale mechanical equilibrium equations for the discrete nodal mesh, including: S104-1: Node-based horizontal gradient Vertical gradient and the The updated horizontal stiffness coefficient Vertical stiffness coefficient Build nodes Net prestressed flow , is represented as: ; For nodes where there is no net prestressed flow at the boundary, this term is set to 0; S104-2: Obtain the net prestressed flow of all nodes in the discrete node mesh and form a generalized force vector. ; S104-3: Construct a weighted Laplace matrix based on the stiffness coefficient tensors of all nodes. ; S104-4: Based on the weighted Laplacian matrix and the current unpacking phase field to be solved The product of these equals the generalized force vector, constructing the first... The updated multiscale mechanical equilibrium equations are expressed as follows: ; Among them, the elements of the weighted Laplace matrix Defined as: if ,but For connecting nodes The sum of the stiffness coefficients of all connected edges; if the node For nodes The adjacent nodes, then It is the negative value of the stiffness coefficient of the connecting edge between the two; otherwise, it is 0. , ; , , and These represent the number of rows and columns of the input image, respectively.

[0028] S105: Solve the multi-scale mechanical equilibrium equations at multiple scales to obtain the current unpacked phase field of the discrete node mesh.

[0029] In this embodiment, the multi-scale mechanical equilibrium equations are solved using the explicit dynamic relaxation method or the damped Verlet integral method to obtain the current unpacked phase field of the discrete node mesh.

[0030] S106: Calculate the difference between the gradient of the current unpacking phase field and the initial prestress field to obtain the local lattice strain field of the discrete node mesh, expressed as: ; No. After the next update, the nodes in the discrete node mesh Local lattice strain field at , is represented as: ; Indicates the first After the next update, the node The horizontal strain component at a given location is expressed as: ; Indicates the first After the next update, the node The vertical strain component at a given location is expressed as: ; in, , , and These represent the number of rows and columns of the input image, respectively. Indicates the first After the next update, the node Phase at that point, Represents a node The horizontal gradient at that point Represents a node The vertical gradient at that point.

[0031] S107: Adjust the stiffness coefficient tensor based on the real-time updated local lattice strain field, obtain the updated stiffness coefficient tensor, return to reconstruct the multi-scale mechanical equilibrium equation, and calculate the current unpacking phase field until the total potential energy change of the discrete node grid is less than the preset threshold, and obtain the target unpacking phase matrix of the input image.

[0032] Among them, the full-field potential energy function of the discrete node grid , is represented as: ; in, , , and These represent the number of rows and columns of the input image, respectively. and They represent the first After the next update, the node The horizontal stiffness coefficient and the vertical stiffness coefficient at the location and They represent the first After the next update, the node The horizontal strain component and the vertical strain component at the location.

[0033] This embodiment describes the full-field potential function. Regarding the phase of each node By taking the derivative and setting it to zero, the multi-scale mechanical equilibrium equations of the discrete nodal mesh constructed in step S104 can be derived. .

[0034] The process involves adjusting the stiffness coefficient tensor based on the real-time updated local lattice strain field to obtain the updated stiffness coefficient tensor, including: No. After the next update, the node Horizontal stiffness coefficient , is represented as: ; No. After the next update, the node Vertical stiffness coefficient , is represented as: ; in, This represents a preset damage sensitivity parameter, which in this embodiment is typically set between 2.0 and 5.0; and They represent the first After the next update, the node The horizontal strain component and the vertical strain component at the location.

[0035] In this embodiment, the target unpacking phase matrix of the input image is obtained by using the update amount of the unpacking phase being less than a preset threshold as the iteration cutoff condition.

[0036] This invention presents a multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method. Using two-dimensional compressed phase distribution data containing noise and complex topology as input, it constructs and solves a multi-scale anisotropic elastoplastic network to calculate the phase unpacking of the two-dimensional compressed phase image. This embodiment establishes a discrete node mesh model corresponding to the compressed phase image, uses the curl of the compressed phase gradient to detect residual points and initialize the anisotropic stiffness tensor, constructs a mechanical equilibrium equation based on the minimum potential energy principle, and employs an explicit dynamic relaxation method for multi-scale iterative solution. During the iteration process, a strain-based nonlinear plastic constitutive relation is introduced, dynamically updating the stiffness coefficients of the mesh connection edges according to the magnitude of local lattice strain, simulating the plastic softening and fracture behavior of the material in shear regions with drastic phase jumps. This invention accelerates convergence through a multi-scale solution strategy, effectively suppresses noise and preserves the true discontinuities of the phase field using anisotropic elastoplastic mechanisms, and solves the problem of traditional algorithms easily producing stringing or smoothing overlays in complex topologies.

[0037] Based on the above embodiments, in this embodiment of the invention, taking the processing of a noisy sheared phase map of 256x256 pixels as an example, it demonstrates how to utilize the multi-scale anisotropic dynamic elastoplastic mesh method of the present invention to process a noisy sheared phase map of size 256x256 pixels. , The pixel-level, discretely wrapped phase map containing Gaussian noise, with a signal-to-noise ratio (SNR) of 5dB, and exhibiting localized shearing breaks is unpacked. (Refer to...) Figure 2 The image shown is the original phase distribution diagram including noise; refer to... Figure 3 The image shown is a discrete encapsulated phase diagram of local shear fracture; refer to... Figure 4 The figure shown is the unpacked phase diagram after phase unpacking according to the present invention; the color scale unit in the figure is radians.

[0038] S201: Data Input and Prestress Calculation: S201-1: Reading the Discrete Two-Dimensional Wrapping Phase Matrix Its size is The numerical range is between; S201-2: Calculate the gradient field of the package ;in: Horizontal prestressing : ; Vertical prestressing : ; in, The imaginary unit, To perform the phase angle operation, ensure that the difference result falls within the range of... Interval.

[0039] S202: Anisotropic elastic mesh initialization, establish a A node mesh, each node It represents one pixel.

[0040] S203: The residual point detection strategy is used to initialize the mesh to determine the initial stiffness coefficients, including: S203-1: Calculate the curl of the gradient field of the package, expressed as: ; S203-2: If If so, mark that position as a residual point; S203-3: Based on the identified residual points, set the initial stiffness: For residual points and their neighborhoods determined by the dilation operation, set the initial stiffness coefficient of their connecting edges to a smaller value of 0.1; for other continuous regions, set the initial stiffness coefficient to a unit value of 1.0.

[0041] S204: Constructing multi-scale mechanical equilibrium equations, in the... In the next iteration, a discrete linear equation system is constructed: ; In this embodiment, The elemental structure includes: Using a four-neighborhood system, It could be the right neighbor Left neighbor Neighbor or the neighbor ; stiffness coefficient tensor In the finite difference implementation of discrete meshes, it is concretized as scalar stiffness coefficients defined on the mesh connection edges, including: off-diagonal elements and diagonal elements; Among them, the off-diagonal elements are: For connecting nodes with neighbors The negative values ​​of the scalar stiffness coefficients on the edges; the specific correspondence is as follows: like right neighbor ,but ; like downstairs neighbor ,but ; like left neighbor ,but ; like For the upper neighbor ,but ; Among them, the diagonal elements are: The sum of the scalar stiffness coefficients of all variables connecting the node is the sum of the scalar values ​​in the four directions (if they exist). In summary, for nodes Matrix-vector product The discrete form of is expressed as: ; in, This indicates that the center pixel of the force calculation is currently being performed. express Belongs to the current node The neighborhood of.

[0042] For boundary nodes, if A node located at the edge of an image and having fewer than four neighbors is called a boundary node. For example, the vertex (1,1) at the top left corner of the image has only two neighbors: its right neighbor (1,2) and its bottom neighbor (2,1).

[0043] Specifically, calculate the generalized force vector: .

[0044] S205: Multi-scale solution of equilibrium displacement: due to the matrix Due to the large dimensionality, this embodiment employs an explicit dynamic relaxation method to solve the problem. .

[0045] In this embodiment, grid nodes are considered to have virtual mass. The particles undergo time-stepping iterations, including: Calculate the resultant force: Calculate the total elastic force acting on each node. That is, the negative value of the potential energy gradient; Update speed: The damping coefficient Time step ; Update location: ; Repeat the above steps until the system's kinetic energy is completely dissipated and a static equilibrium state is reached, thus obtaining the current unpacking phase estimate. .

[0046] S206: Calculate the current unpacking phase The actual gradient, and with prestress By comparison, the lattice strain was obtained. .

[0047] S207: Dynamic plastic evolution, updating the stiffness coefficient tensor, expressed as: ; ; in, As the damage sensitivity parameter, in this embodiment, we take... .

[0048] S208: Repeat steps S203 to S207 a total of 10 times, and finally output the result. This yields the target unpacking phase distribution.

[0049] This invention achieves self-organized evolution of a grid system through a closed-loop iterative structure that constructs equilibrium equations, solves for the displacement field, calculates the strain field, updates the stiffness coefficients, and reconstructs the equations. In each iteration, the stiffness coefficients are dynamically adjusted based on the current unpacking state, and the system gradually approaches the true solution. The iteration terminates when the change in the total potential energy is less than a preset threshold, ensuring the stability and reliability of the output results. Compared with the traditional method of fixing weights, the dynamic feedback mechanism of this invention gives the system a strong self-correcting ability. Even if the initial stiffness coefficient settings are not ideal, they can be gradually corrected through subsequent iterations, improving the robustness of the algorithm.

[0050] Based on the above embodiments, this invention provides an apparatus for a multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method, the specific apparatus including: An anisotropic elastic mesh construction module is used to obtain the horizontal and vertical wrapping gradient fields of the discrete two-dimensional wrapping phase matrix of the input image, forming the initial prestress field; construct a discrete node mesh corresponding to the pixels of the input image, and define the adjacency relationship between nodes in the discrete node mesh; based on the wrapping phase gradient at each node in the discrete node mesh, identify and obtain residual points; based on the position of the residual points, initialize the stiffness coefficients of each connecting edge in the discrete node mesh, and obtain the stiffness coefficient tensor of each node; The multi-scale mechanical equilibrium equation construction module is used to construct the multi-scale mechanical equilibrium equations of the discrete node mesh based on the initial stress field and the stiffness coefficient tensor of all nodes in the discrete node mesh. The solver module is used to solve the multi-scale mechanical equilibrium equations at multiple scales and obtain the current unpacked phase field of the discrete node mesh. The local lattice strain field construction module is used to calculate the difference between the gradient of the current unpacked phase field and the initial prestress field, and to obtain the local lattice strain field of the discrete node mesh. The iterative update module is used to adjust the stiffness coefficient tensor based on the real-time updated local lattice strain field, obtain the updated stiffness coefficient tensor, return to reconstruct the multi-scale mechanical equilibrium equation, and calculate the current unpacking phase field until the total potential energy change of the discrete node grid is less than a preset threshold, and obtain the target unpacking phase matrix of the input image.

[0051] The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking device of this embodiment is used to implement the aforementioned multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method. Therefore, the specific implementation of the multi-scale anisotropic dynamic elastoplastic mesh phase unpacking device can be found in the embodiment section of the multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method above. For example, the anisotropic elastic mesh construction module is used to implement steps S101, S102 and S103 in the aforementioned multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method; the multi-scale mechanical equilibrium equation construction module, the solution module, the local lattice strain field construction module and the iterative update module are used to implement steps S104, S105, S106 and S107 in the aforementioned multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method, respectively. Therefore, its specific implementation can be referred to the description of the corresponding embodiments, and will not be repeated here.

[0052] The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method described in this invention establishes a discrete node mesh model corresponding to the wrapped phase image. It uses the curl of the wrapped phase gradient to detect residual points and initializes the anisotropic stiffness tensor. Through the residual points, an index with clear topological significance, the mesh connection edges are divided into strongly connected and weakly connected regions, achieving precise pre-positioning of the fracture region and providing a reasonable initial state for subsequent elastoplastic evolution. This effectively avoids the slow convergence or getting trapped in local extrema problems caused by improper initial weight settings in traditional methods. Furthermore, it constructs a mechanical equilibrium equation based on the minimum potential energy principle to address the phase unpacking problem. The problem is transformed into a global energy minimization problem, ensuring the theoretical convergence of the solution process. During the iteration process, a strain-based nonlinear plastic constitutive relation is introduced, dynamically updating the stiffness coefficients of the mesh connection edges according to the magnitude of local lattice strain. This simulates the plastic softening and fracture behavior of the material in shear regions with drastic phase jumps, achieving adaptive differentiation between continuous and fracture regions. When the local strain is small, the system maintains elastic behavior to ensure unpacking continuity; when the strain exceeds a threshold, the stiffness coefficients decay exponentially, automatically releasing the inter-node constraints and allowing true phase jumps to occur, avoiding the loss of key features caused by excessive smoothing in traditional least squares methods. This invention accelerates convergence through a multi-scale solution strategy, effectively suppressing noise and preserving the true discontinuities of the phase field using an anisotropic elastoplastic mechanism. Simultaneously, residual-guided initialization, global energy optimization, dynamic relaxation, and plastic constitutive updating form a positive feedback synergy, enabling the mesh system to continuously improve itself during iteration. This enhances the system's noise robustness, discontinuity feature preservation, global convergence, and computational efficiency, solving the problem of traditional algorithms easily producing stringing or excessive smoothing in complex topologies.

[0053] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0054] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0055] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0056] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0057] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A phase unpacking method for multi-scale anisotropic dynamic elastoplastic meshes, characterized in that, include: The horizontal and vertical wrapping gradient fields of the discrete two-dimensional wrapping phase matrix of the input image are obtained to form the initial prestress field. Construct a discrete node grid corresponding to the pixels of the input image and define the adjacency relationship between nodes in the discrete node grid; Based on the wrapping phase gradient at each node in the discrete node mesh, residual points are identified and obtained. Based on the location of the residual points, the stiffness coefficients of each connecting edge in the discrete node mesh are initialized, and the stiffness coefficient tensor of each node is obtained. Based on the initial stress field and the stiffness coefficient tensor of all nodes in the discrete nodal mesh, a multi-scale mechanical equilibrium equation for the discrete nodal mesh is constructed. The multi-scale mechanical equilibrium equations are solved at multiple scales to obtain the current unpacked phase field of the discrete node mesh; Calculate the difference between the gradient of the current unpacking phase field and the initial prestress field to obtain the local lattice strain field of the discrete node mesh; The stiffness coefficient tensor is adjusted based on the real-time updated local lattice strain field. The updated stiffness coefficient tensor is obtained, and the multi-scale mechanical equilibrium equation is reconstructed. The current unpacking phase field is calculated until the change in the total potential energy of the discrete node grid is less than a preset threshold. The target unpacking phase matrix of the input image is then obtained.

2. The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method according to claim 1, characterized in that, The horizontal and vertical wrapping gradient fields of the discrete two-dimensional wrapping phase matrix of the input image are obtained to form the initial prestress field. , is represented as: ； This represents the horizontally wrapped gradient field, with coordinates as follows: Horizontal gradient at pixel ; This represents the gradient field wrapped in the vertical direction, with coordinates as follows: Vertical gradient at pixel ; in, Indicates coordinates as Discrete two-dimensional wrapper phase at the pixel; Indicates the mapping of numerical values ​​to Interval phase wrapper operator; , , and These represent the number of rows and columns of the input image, respectively.

3. The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method according to claim 1, characterized in that, Based on the wrapper phase gradient at each node in the discrete node mesh, residual points are identified and obtained. Based on the location of the residual points, the stiffness coefficients of each connecting edge in the discrete node mesh are initialized, and the stiffness coefficient tensor of each node is obtained, including: Based on the residual point detection strategy, the wrapping phase gradient at each node in the discrete node mesh is calculated to identify the residual points; Based on the identified residual points, the discrete node mesh is divided into regions without residual points and regions with residual points and their neighborhoods. Initialize the stiffness coefficient of the connecting edges in the region without residual points to a unit value, and initialize the stiffness coefficient of the connecting edges in the residual points and their neighboring regions to a preset smaller value. For each node, obtain the stiffness coefficients of its connecting edges to form the stiffness coefficient tensor of each node.

4. The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method according to claim 1, characterized in that, The stiffness coefficient tensor is expressed as: ； in, Indicates the first The updated stiffness coefficient tensor , This indicates the initialization of the stiffness coefficient tensor; Indicates the first The horizontal stiffness coefficient after the next update Indicates the first Vertical stiffness coefficient after the next update.

5. The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method according to claim 1, characterized in that, Based on the initial stress field and the stiffness coefficient tensors of all nodes in the discrete nodal mesh, a multi-scale mechanical equilibrium equation for the discrete nodal mesh is constructed, including: Based on nodes horizontal gradient Vertical gradient and the The updated horizontal stiffness coefficient Vertical stiffness coefficient Build nodes Net prestressed flow , is represented as: ； Obtain the net prestress flow at all nodes in the discrete node mesh and form a generalized force vector. ; Construct a weighted Laplace matrix based on the stiffness coefficient tensor of all nodes. ; Based on the weighted Laplace matrix and the current unpacking phase field to be solved The product of these equals the generalized force vector, constructing the first... The updated multiscale mechanical equilibrium equations are expressed as follows: ; Among them, the elements of the weighted Laplace matrix Defined as: if ,but For connecting nodes The sum of the stiffness coefficients of all connected edges; if the node For nodes The adjacent nodes, then It is the negative value of the stiffness coefficient of the connecting edge between the two; otherwise, it is 0. , ; , , and These represent the number of rows and columns of the input image, respectively.

6. The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method according to claim 1, characterized in that, The multi-scale mechanical equilibrium equations are solved using the explicit dynamic relaxation method or the damped Verlet integral method to obtain the current unpacked phase field of the discrete node mesh.

7. The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method according to claim 1, characterized in that, Calculate the difference between the gradient of the current unpacked phase field and the initial prestress field to obtain the local lattice strain field of the discrete node mesh. , is represented as: ； No. After the next update, the nodes in the discrete node mesh Local lattice strain field at , is represented as: ; Indicates the first After the next update, the node The horizontal strain component at a given location is expressed as: ; Indicates the first After the next update, the node The vertical strain component at a given location is expressed as: ; in, , , and These represent the number of rows and columns of the input image, respectively. Indicates the first After the next update, the node Phase at that point, Represents a node The horizontal gradient at that point Represents a node The vertical gradient at that point.

8. The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method according to claim 1, characterized in that, Full-field potential function of discrete nodal mesh , is represented as: ； in, , , and These represent the number of rows and columns of the input image, respectively. and They represent the first After the next update, the node The horizontal stiffness coefficient and the vertical stiffness coefficient at the location and They represent the first After the next update, the node The horizontal strain component and the vertical strain component at the location.

9. The multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method according to claim 1, characterized in that, Based on the real-time updated local lattice strain field, the stiffness coefficient tensor is adjusted to obtain the updated stiffness coefficient tensor, including: No. After the next update, the node Horizontal stiffness coefficient , is represented as: ; No. After the next update, the node Vertical stiffness coefficient , is represented as: ; in, This indicates the preset damage sensitivity parameter. and They represent the first After the next update, the node The horizontal strain component and the vertical strain component at the location.

10. An apparatus based on the multi-scale anisotropic dynamic elastoplastic mesh phase unpacking method as described in any one of claims 1 to 9, characterized in that, include: An anisotropic elastic mesh construction module is used to obtain the horizontal and vertical wrapping gradient fields of the discrete two-dimensional wrapping phase matrix of the input image to form the initial prestress field; construct the discrete node mesh corresponding to the pixels of the input image and define the adjacency relationship between the nodes in the discrete node mesh; Based on the wrapping phase gradient at each node in the discrete node mesh, residual points are identified and obtained. Based on the location of the residual points, the stiffness coefficients of each connecting edge in the discrete node mesh are initialized, and the stiffness coefficient tensor of each node is obtained. The multi-scale mechanical equilibrium equation construction module is used to construct the multi-scale mechanical equilibrium equations of the discrete node mesh based on the initial stress field and the stiffness coefficient tensor of all nodes in the discrete node mesh. The solver module is used to solve the multi-scale mechanical equilibrium equations at multiple scales and obtain the current unpacked phase field of the discrete node mesh. The local lattice strain field construction module is used to calculate the difference between the gradient of the current unpacked phase field and the initial prestress field, and to obtain the local lattice strain field of the discrete node mesh. The iterative update module is used to adjust the stiffness coefficient tensor based on the real-time updated local lattice strain field, obtain the updated stiffness coefficient tensor, return to reconstruct the multi-scale mechanical equilibrium equation, and calculate the current unpacking phase field until the total potential energy change of the discrete node grid is less than a preset threshold, and obtain the target unpacking phase matrix of the input image.

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