Multi-target constrained adaptive triangulation network discrete phase unwrapping method and system

Abstract

The invention relates to the technical field of phase field unwrapping, in particular to a multi-target constrained self-adaptive triangulation network discrete phase unwrapping method and a multi-target constrained self-adaptive triangulation network discrete phase unwrapping system. Comprising the following steps of performing phase quality evaluation on discrete sampling points, calculating a local signal-to-noise ratio, a phase gradient amplitude, a local phase consistency measure and a boundary distance factor of each sampling point so as to comprehensively evaluate the phase quality of each sampling point, and quantifying phase reliability by calculating the local signal-to-noise ratio and a phase gradient amplitude index of the discrete sampling points so as to obtain the phase quality of the discrete sampling points. And as basic input, a quality basis is provided for subsequent network construction. According to the multi-target constraint adaptive triangulation network discrete phase unwrapping method provided by the invention, through organic combination of three core technologies of phase quality guided adaptive triangulation network construction, a multi-target constraint MCF framework and quality guided intelligent path planning, high-precision and high-robustness unwrapping of discrete phase data is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of phase field unwrapping, and in particular to a multi-objective constrained adaptive triangulated discrete phase unwrapping method and system. Background Art

[0002] In recent years, deep learning-based methods have been used for phase unwrapping, but these methods primarily unwrap data in continuous regions using the natural grid layout of the data. Without relying on the physical data structure, traditional deep learning methods rely heavily on large amounts of high-quality data during the learning process. However, practical applications often face challenges with data scarcity, severe noise, and complex striations. In these cases, relying solely on data-driven models makes it difficult to achieve accurate and reliable predictions.

[0003] Therefore, traditional path tracking methods generally rely heavily on the choice of unfolding path, and different paths can lead to different results, especially when noise causes local phase gradients to exceed π, resulting in erroneous 2π jump judgments. Secondly, excessive phase gradients, insufficient sampling, and violations of the Nyquist sampling theorem can also lead to phase unwrapping anomalies. All phase unwrapping methods are extremely sensitive to noise, but their sensitivity manifests differently. In path tracking methods, noise can lead to erroneous 2π jump judgments, with errors accumulating and propagating along the path. In least squares methods, noise affects the accuracy of gradient calculations and diffuses to the entire solution through global optimization. Phase discontinuities at object boundaries and occluded areas in discontinuous regions, phase fields in multiply connected regions with holes or separated regions, regions with high slopes and extremely large phase gradients, and regions with rich textures and drastic changes in local details are solved by assuming a continuous and smooth solution by default, resulting in "missing solutions" in discontinuous regions.

[0004] Based on this, the present invention provides a multi-objective constrained adaptive triangulated discrete phase unwrapping method and system to solve the above-mentioned technical problems. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-objective constrained adaptive triangulated discrete phase unwrapping method and system to solve the problems raised by the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] The first aspect of the present invention:

[0008] The present invention proposes a multi-objective constrained adaptive triangulated discrete phase unwrapping method, comprising the following steps:

[0009] S1. Perform phase quality assessment on discrete sampling points. Calculate the local signal-to-noise ratio, phase gradient amplitude, local phase consistency metric, and boundary distance factor for each sampling point to comprehensively evaluate its phase quality. By calculating the local signal-to-noise ratio and phase gradient amplitude indicators of discrete sampling points, the phase reliability is quantified, providing a quality basis for subsequent network construction as a basic input.

[0010] S2. Dynamically adjust mesh density based on quality assessment results, densify high-quality areas, and thin out low-quality areas, and optimize the triangulation structure through quality-guided edge weights.

[0011] S3. Expand the MCF model based on the triangulated network, integrate phase gradient reliability, spatial continuity, and boundary protection constraints, and construct a multi-objective optimization function. Use the triangulated network as the carrier to define the optimization objectives.

[0012] S4. Screen high-quality integral paths based on signal-to-noise ratio, gradient amplitude, and distance factor, determine the initial expansion starting point, and optimize flow distribution. This is independent of the MCF but provides an efficient initial solution for it.

[0013] S5. Solve the global optimal flow distribution through the dynamic tree acceleration algorithm, combine the path planning results to achieve high-precision phase unfolding, integrate the path planning output, and complete the core unfolding calculation;

[0014] S6. Evaluate the expansion effect based on accuracy and noise resistance indicators, iterate in reverse to adjust the quality assessment threshold or constraint weight, and perform closed-loop feedback to optimize the parameters of the entire process.

[0015] Preferably, the implementation steps of step S2 are:

[0016] S21. Based on the quality assessment results of step S1, a phase quality-guided adaptive triangulation method is used to dynamically adjust the network structure according to the phase quality characteristics of discrete sampling points;

[0017] S22. Introduce a composite quality evaluation function and adopt a quality-adaptive importance sampling mechanism to make the sampling probability positively correlated with the quality score, ensuring that the high-quality areas evaluated in step S1 are densely sampled and the low-quality areas are appropriately sparsely sampled;

[0018] S23. Using the boundary distance factor of step S1 to identify boundary points, identify and specially process the sampling points in the boundary area, and enhance the sampling probability of the boundary points through the boundary detection operator to improve the processing accuracy of the boundary area;

[0019] S24. An improved constrained Delaunay triangulation algorithm is used, and quality-guided edge weights are introduced. The weight parameters are derived from the phase consistency metric in step S1, and the optimized triangulated network structure is finally obtained.

[0020] Preferably, the implementation steps of step S3 are:

[0021] S31. Expand the MCF model based on the triangulated network optimized in step S2, expand the traditional MCF minimum cost flow solving framework, introduce a multi-objective constraint optimization function, and integrate the edge weight definition cost function of step S24;

[0022] S32. Comprehensively balance three types of constraints: phase gradient reliability constraint, spatial continuity constraint, and boundary protection constraint to evaluate the reliability of gradients between discrete points, reduce the impact of unreliable gradients, and promote phase consistency between adjacent triangles. At the same time, it protects structural edges and discontinuous areas to avoid over-smoothing. The gradient reliability constraint depends on the grid density of step S21, the spatial continuity constraint depends on the edge weight of step S24, and the boundary protection constraint depends on the boundary point processing of step S23.

[0023] S33. Define the MCF cost function for multi-objective optimization, and adaptively configure the weight coefficient of the MCF cost function according to the local signal-to-noise ratio distribution in step S1.

[0024] Preferably, the implementation steps of step S4 are:

[0025] S41. Further improve the deployment accuracy and propose a quality-guided integral path selection algorithm, which directly uses the quality assessment results of step S1 to select reliable paths, replacing the traditional path planning method;

[0026] S42. Construct a point-to-point quality metric function to evaluate path quality based on signal-to-noise ratio, phase gradient amplitude, and inter-point Euclidean distance factors;

[0027] S43. Divide the path quality level into high-quality path, medium-quality path and low-quality path, and optimize the path according to the quality metric, integrating the signal-to-noise ratio, gradient amplitude and inter-point distance of step S1 to divide the path quality level;

[0028] S44. Select the most reliable point evaluated in step S1 as the integration starting point, integrate along the mass path to obtain the initial unfolding phase, and construct the MCF initial flow distribution.

[0029] Preferably, the implementation steps of step S5 are:

[0030] S51. Combine the triangulated network structure of step S2 to perform multi-scale decomposition. When the approximate solution of the scale layer is mapped to the fine scale layer, the initial flow distribution of step S44 is loaded, and the network simplex algorithm is accelerated using a dynamic tree data structure to construct a hierarchical representation of the problem. The approximate solution is quickly solved at the coarse scale layer, and the result is then mapped to the fine scale layer as the initial solution, and the optimization is refined layer by layer.

[0031] S52. Under the conditions of satisfying capacity constraints and node balance constraints, the global optimal solution is solved through the multi-objective cost function of step S3 to achieve high-precision expansion of discrete phase data.

[0032] Preferably, the implementation steps of step S6 are:

[0033] S61. Verify the expansion results and evaluate the expansion accuracy, noise resistance and processing speed indicators. The verification results are directly fed back to the quality assessment threshold adjustment in step S1 and the weight coefficient optimization in step S33;

[0034] S62. Based on the verification results, optimize and adjust the method to further improve the performance and stability of phase unwrapping.

[0035] On the other hand, the present invention also proposes an adaptive triangulated network discrete phase unwrapping system for realizing high-precision unwrapping processing of discrete sampled phase data. The system includes a computing device and a phase acquisition array module. The phase acquisition array module is deployed according to the non-uniform spatial distribution rules to form a multi-level sampling network. The computing device is used to execute a multi-objective constrained adaptive triangulated network discrete phase unwrapping method.

[0036] Preferably, the computing device comprises:

[0037] A phase quality assessment module, which is used to generate a multidimensional quality score map of discrete sampling points based on local signal-to-noise ratio, phase gradient amplitude, local phase consistency metric and boundary distance factor;

[0038] An adaptive triangulation generation module, which controls sampling density through a quality-driven dynamic segmentation strategy combined with a quality evaluation function, implements enhanced sampling in boundary areas, and constructs a quality-guided weighted triangulation structure;

[0039] A multi-objective constrained optimization module, which is used to extend the minimum cost flow framework, integrate phase gradient reliability constraints, spatial continuity constraints, and boundary protection constraints, and define a multi-objective cost function with adaptive weight configuration;

[0040] A quality-guided path planning module, which constructs a path quality metric function based on signal-to-noise ratio-gradient amplitude-distance factor to screen the optimal integral path and determine the initial unwrapping phase;

[0041] A hierarchical MCF solver, which implements multi-scale optimization through a dynamic tree acceleration algorithm, and is used to generate an approximate solution at a coarse scale layer and then map it to a fine scale layer for fine adjustment;

[0042] The verification and feedback optimization module is used to form a closed-loop parameter optimization mechanism by evaluating the results of the expansion accuracy, noise suppression capability and computational efficiency indicators.

[0043] The computing device is used to sequentially generate a quality map of discrete phase data through the phase quality assessment module; the adaptive triangulated network generation module dynamically adjusts the mesh topology according to the quality map; the multi-objective constraint optimization module constructs a constraint flow network based on the triangulated network; the quality-guided path planning module generates an initial phase distribution; and finally, the hierarchical MCF solver completes the global optimal phase expansion; and the verification and feedback optimization module continuously optimizes the parameter configuration of each module.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The multi-objective constrained adaptive triangulated network discrete phase unfolding method proposed in the present invention realizes high-precision and high-robustness unfolding of discrete phase data through the organic combination of three core technologies: phase quality-guided adaptive triangulated network construction, multi-objective constrained MCF framework, and quality-guided intelligent path planning. Compared with traditional methods, the phase unfolding method of the present invention has higher phase unfolding accuracy, stronger noise resistance, and faster processing speed. It has significant technical advantages and application prospects. It is particularly suitable for the phase field unfolding of discrete sampling point distribution, and can effectively handle complex scenes such as noise, discontinuous areas, and high gradient areas, providing strong technical support for optical measurement, medical imaging and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 An overview diagram of the system architecture of the present invention is shown;

[0047] Figure 2 shows a diagram of the construction of an adaptive triangulated network of the present invention;

[0048] Figure 3 A schematic diagram of a multi-objective constraint function of the present invention is shown;

[0049] Figure 4 A comparison diagram showing the simulated package of the present invention before and after unfolding is shown;

[0050] Figure 5 A comparison diagram of the effects of the simulated discrete wrapping phase unwrapping of the present invention is shown;

[0051] Figure 6 The error effect diagram of the simulated discrete wrapped phase unwrapping of the present invention is shown;

[0052] Figure 7 2D comparison diagrams before and after discrete wrapping phase unwrapping of the present invention are shown;

[0053] Figure 8 3D comparison diagrams before and after the true discrete wrapping phase unwrapping of the present invention are shown. DETAILED DESCRIPTION

[0054] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described 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 making any creative efforts shall fall within the scope of protection of the present invention.

[0055] Example 1, please refer to Figures 1 to 8 The present invention proposes a multi-objective constrained adaptive triangulated discrete phase unwrapping method, comprising the following steps:

[0056] S1. Perform phase quality assessment on discrete sampling points. Calculate the local signal-to-noise ratio, phase gradient amplitude, local phase consistency metric, and boundary distance factor for each sampling point to comprehensively evaluate its phase quality. By calculating the local signal-to-noise ratio and phase gradient amplitude indicators of discrete sampling points, the phase reliability is quantified, providing a quality basis for subsequent network construction as a basic input.

[0057] S2. Dynamically adjust mesh density based on quality assessment results, densify high-quality areas, and thin out low-quality areas, and optimize the triangulation structure through quality-guided edge weights.

[0058] S3. Expand the MCF model based on the triangulated network, integrate phase gradient reliability, spatial continuity, and boundary protection constraints, and construct a multi-objective optimization function. Use the triangulated network as the carrier to define the optimization objectives.

[0059] S4. Screen high-quality integral paths based on signal-to-noise ratio, gradient amplitude, and distance factor, determine the initial expansion starting point, and optimize flow distribution. This is independent of the MCF but provides an efficient initial solution for it.

[0060] S5. Solve the global optimal flow distribution through the dynamic tree acceleration algorithm, combine the path planning results to achieve high-precision phase unfolding, integrate the path planning output, and complete the core unfolding calculation;

[0061] S6. Evaluate the expansion effect based on accuracy and noise resistance indicators, iterate in reverse to adjust the quality assessment threshold or constraint weight, and perform closed-loop feedback to optimize the parameters of the entire process.

[0062] It should be noted that the implementation steps of step S2 are:

[0063] S21. Based on the quality assessment results of step S1, a phase quality-guided adaptive triangulation method is used to dynamically adjust the network structure according to the phase quality characteristics of discrete sampling points;

[0064] S22. Introduce a composite quality evaluation function and adopt a quality-adaptive importance sampling mechanism to make the sampling probability positively correlated with the quality score, ensuring that the high-quality areas evaluated in step S1 are densely sampled and the low-quality areas are appropriately sparsely sampled;

[0065] S23. Using the boundary distance factor of step S1 to identify boundary points, identify and specially process the sampling points in the boundary area, and enhance the sampling probability of the boundary points through the boundary detection operator to improve the processing accuracy of the boundary area;

[0066] S24. An improved constrained Delaunay triangulation algorithm is used, and quality-guided edge weights are introduced. The weight parameters are derived from the phase consistency metric in step S1, and the optimized triangulated network structure is finally obtained.

[0067] It should be noted that the implementation steps of step S3 are:

[0068] S31. Expand the MCF model based on the triangulated network optimized in step S2, expand the traditional MCF minimum cost flow solving framework, introduce a multi-objective constraint optimization function, and integrate the edge weight definition cost function of step S24;

[0069] S32. Comprehensively balance three types of constraints: phase gradient reliability constraint, spatial continuity constraint, and boundary protection constraint to evaluate the reliability of gradients between discrete points, reduce the impact of unreliable gradients, and promote phase consistency between adjacent triangles. At the same time, it protects structural edges and discontinuous areas to avoid over-smoothing. The gradient reliability constraint depends on the grid density of step S21, the spatial continuity constraint depends on the edge weight of step S24, and the boundary protection constraint depends on the boundary point processing of step S23.

[0070] S33. Define the MCF cost function for multi-objective optimization, and adaptively configure the weight coefficient of the MCF cost function according to the local signal-to-noise ratio distribution in step S1.

[0071] It should be noted that the implementation steps of step S4 are:

[0072] S41. Further improve the deployment accuracy and propose a quality-guided integral path selection algorithm, which directly uses the quality assessment results of step S1 to select reliable paths, replacing the traditional path planning method;

[0073] S42. Construct a point-to-point quality metric function to evaluate path quality based on signal-to-noise ratio, phase gradient amplitude, and inter-point Euclidean distance factors;

[0074] S43. Divide the path quality level into high-quality path, medium-quality path and low-quality path, and optimize the path according to the quality metric, integrating the signal-to-noise ratio, gradient amplitude and inter-point distance of step S1 to divide the path quality level;

[0075] S44. Select the most reliable point evaluated in step S1 as the integration starting point, integrate along the mass path to obtain the initial unfolding phase, and construct the MCF initial flow distribution.

[0076] It should be noted that the implementation steps of step S5 are:

[0077] S51. Combine the triangulated network structure of step S2 to perform multi-scale decomposition. When the approximate solution of the scale layer is mapped to the fine scale layer, the initial flow distribution of step S44 is loaded, and the network simplex algorithm is accelerated using a dynamic tree data structure to construct a hierarchical representation of the problem. The approximate solution is quickly solved at the coarse scale layer, and the result is then mapped to the fine scale layer as the initial solution, and the optimization is refined layer by layer.

[0078] S52. Under the conditions of satisfying capacity constraints and node balance constraints, the global optimal solution is solved through the multi-objective cost function of step S3 to achieve high-precision expansion of discrete phase data.

[0079] It should be noted that the implementation steps of step S6 are:

[0080] S61. Verify the expansion results and evaluate the expansion accuracy, noise resistance and processing speed indicators. The verification results are directly fed back to the quality assessment threshold adjustment in step S1 and the weight coefficient optimization in step S33;

[0081] S62. Based on the verification results, optimize and adjust the method to further improve the performance and stability of phase unwrapping.

[0082] The present invention also proposes an adaptive triangulated network discrete phase unwrapping system for achieving high-precision unwrapping processing of discrete sampled phase data. The system includes a computing device and a phase acquisition array module. The phase acquisition array module is deployed according to non-uniform spatial distribution rules to form a multi-level sampling network. The computing device is used to execute a multi-objective constrained adaptive triangulated network discrete phase unwrapping method.

[0083] It should also be noted that the computing device includes:

[0084] A phase quality assessment module, which is used to generate a multidimensional quality score map of discrete sampling points based on local signal-to-noise ratio, phase gradient amplitude, local phase consistency metric and boundary distance factor;

[0085] An adaptive triangulation generation module, which controls sampling density through a quality-driven dynamic segmentation strategy combined with a quality evaluation function, implements enhanced sampling in boundary areas, and constructs a quality-guided weighted triangulation structure;

[0086] A multi-objective constrained optimization module, which is used to extend the minimum cost flow framework, integrate phase gradient reliability constraints, spatial continuity constraints, and boundary protection constraints, and define a multi-objective cost function with adaptive weight configuration;

[0087] A quality-guided path planning module, which constructs a path quality metric function based on signal-to-noise ratio-gradient amplitude-distance factor to screen the optimal integral path and determine the initial unwrapping phase;

[0088] A hierarchical MCF solver, which implements multi-scale optimization through a dynamic tree acceleration algorithm, and is used to generate an approximate solution at a coarse scale layer and then map it to a fine scale layer for fine adjustment;

[0089] The verification and feedback optimization module is used to form a closed-loop parameter optimization mechanism by evaluating the results of the expansion accuracy, noise suppression capability and computational efficiency indicators.

[0090] The computing device is used to sequentially generate a quality map of discrete phase data through the phase quality assessment module; the adaptive triangulated network generation module dynamically adjusts the mesh topology according to the quality map; the multi-objective constraint optimization module constructs a constraint flow network based on the triangulated network; the quality-guided path planning module generates an initial phase distribution; and finally, the hierarchical MCF solver completes the global optimal phase expansion; and the verification and feedback optimization module continuously optimizes the parameter configuration of each module.

[0091] Example 2, please refer to Figures 1 to 8 In practical applications, the adaptive triangulated discrete phase unwrapping method based on the multi-objective constraints of the above system specifically includes the following steps:

[0092] (1) Dynamically adjust the network structure according to the phase quality characteristics of discrete sampling points;

[0093] The specific technical means include the following: introducing a composite quality evaluation function Q(x,y), and comprehensively considering the following factors:

[0094] Q(x,y)=w1·SNR(x,y)+w2·G -1 (x,y)+w3·C(x,y)+w4·D(x,y)

[0095] Where, SNR(x,y): local signal-to-noise ratio evaluation, G(x,y): phase gradient amplitude, C(x,y): local phase consistency measure, D(x,y) is the boundary distance factor, w1,w2,w3,w4: adaptive weight coefficients;

[0096] Based on the above quality evaluation function, this method adopts a quality-adaptive importance sampling mechanism to make the sampling probability positively correlated with the quality score:

[0097] P(x,y)=Q(x,y) / ∑∑Q(i,j)

[0098] Select the point set by Monte Carlo sampling or importance sampling method to ensure that the high-quality areas have sufficient sampling density and the low-quality areas are appropriately sparse;

[0099] This sampling strategy enables the triangulated network structure to adaptively reflect the complexity distribution of the phase field;

[0100] To further improve the processing accuracy of boundary areas, this method identifies and specially processes the sampling points in the boundary areas, and enhances the sampling probability of boundary points through the boundary detection operator:

[0101]

[0102] Where E(x,y) is the edge detection function based on local variance or Canny operator;

[0103] The sampling probability of the boundary area is additionally enhanced:

[0104] P'(x,y)=P(x,y)+α·B(x,y)

[0105] Where α is the boundary enhancement coefficient, and its value range is [0.5, 2.0];

[0106] In the process of adaptive triangulation construction, an improved constrained Delaunay triangulation (CDT) algorithm is used to introduce quality-guided edge weights:

[0107]

[0108] Where β is the phase difference sensitivity parameter;

[0109] Finally, the triangulation optimization objective function can be obtained:

[0110] F(T)=∑ e w(e)L(e)+λ∑tA(t)[1–Q(t)]

[0111] Where T is the triangulated network, e is the edge in the triangulated network, t is the triangle unit, L(e) is the edge length, A(t) is the triangle area, Q(t) is the triangle quality metric, and λ is the balance coefficient;

[0112] (2) MCF solution framework for multi-objective constraints:

[0113] Based on the construction of adaptive triangulation, this method innovatively expands the traditional MCF solution framework and introduces a multi-objective constraint optimization function to comprehensively balance three types of constraints: phase gradient reliability constraint, spatial continuity constraint, and boundary protection constraint.

[0114] In order to evaluate the reliability of the gradient between discrete points and reduce the impact of unreliable gradients, the first type of constraint is defined as:

[0115]

[0116] in is the actual phase gradient between points i and j, is the locally smoothed estimated phase gradient, σ 2 is the noise variance estimate, α is the sensitivity adjustment parameter;

[0117] This constraint effectively identifies abnormal gradients, reduces their weight in the expansion process, and improves the robustness of the algorithm;

[0118] To promote phase consistency between adjacent triangles, a second type of constraint is added:

[0119] C2(t1,t2)=exp(-β·d(t1,t2) 2 )·(1-|cos(θ 12 )|)

[0120] Where t1, t2 are adjacent triangles, d(t1, t2) is the distance between the triangle centers, θ 12 is the triangle normal vector angle, β is the distance sensitivity parameter;

[0121] This constraint can effectively ensure the smoothness and continuity of the phase field, especially in areas where the phase changes relatively slowly;

[0122] In order to protect the edges and discontinuous areas of the structure and avoid over-smoothing, this method adds a third type of constraint C3(i,j):

[0123] C3(i,j)=γ[1-exp(-λ·E(i,j) 2 )]

[0124] Where e(i,j) is the edge strength function;

[0125] γ,λ are adjustment parameters;

[0126] This constraint provides additional protection at the boundaries, preventing over-smoothing from causing loss of detail;

[0127] Based on the above three types of constraints, the MCF cost function of multi-objective optimization is defined as:

[0128] Cost(i,j)=w1·C1(i,j)+w2·C2(t(i),t(j))+w3C3(i,j)+ε;

[0129] Where w1, w2, w3 are adaptive weight coefficients, t(i), t(j) are triangles containing points i and j, and ε is a small positive number to ensure that the cost function is non-negative;

[0130] The weight coefficient adopts a dynamic adjustment mechanism and is adaptively configured according to the local phase field characteristics:

[0131] w1=k1exp(-SNR -1 )

[0132]

[0133] w3=k3E avg

[0134] Where SNR is the local signal-to-noise ratio, is the local phase variance, E avg is the average edge strength, k1, k2, k3 are positive constants;

[0135] This method effectively maps the relationship between discrete sampling points into a network flow model: each triangle represents a network node, and the shared edges between adjacent triangles constitute network edges. The residual points are identified by the following formula:

[0136]

[0137] Set the capacity cap based on edge quality to:

[0138]

[0139] The cost assignment uses the multi-objective constraint cost function mentioned above;

[0140] During the solution process, this method uses a dynamic tree data structure to accelerate the network simplex algorithm, construct a hierarchical representation of the problem, quickly solve the approximate solution at the coarse-scale layer, and then map the result to the fine-scale layer as the initial solution, and refine the optimization layer by layer.

[0141] The entire solution process satisfies Kirchhoff's law and network flow balance constraints:

[0142] ∑ kflow(k,j)-∑ i flow(j,i)=supply(j)

[0143] The final objective function is:

[0144] min∑ e cost(e)flow(e)

[0145] Solve the global optimal traffic allocation under the conditions of satisfying capacity constraints and node balance constraints;

[0146] (3) Quality-guided path planning:

[0147] In order to further improve the expansion accuracy, this method innovatively proposes a quality-guided integral path selection algorithm to replace the traditional BFS path;

[0148] First, construct the point pair quality measurement function:

[0149]

[0150] Where: SNR(i), SNR(j) are the signal-to-noise ratios at points i and j, is the phase gradient amplitude, d(i,j) is the Euclidean distance between points, and α, β are adjustment parameters;

[0151] Path quality levels are divided into: High Quality Path (HQ) (Q path >T1); Medium Quality Path (MQ)(T2 path ≤T1); low quality path (LQ)(Q path ≤T1) where T1 and T2 are phase quality thresholds, which are dynamically adjusted according to the application scenario;

[0152] This method improves the traditional Dijkstra algorithm and introduces quality metrics for path optimization:

[0153] d(s,v)=min{{u∈pred(v)}{d(s,u)+[1-Q path(u,v) ]}}

[0154] Where d(s,v) is the shortest path cost from the starting point s to the point v, and pred(v) is the set of predecessor nodes of v;

[0155] To ensure the reliability of the starting point of the integration path, this method selects the most reliable point in the phase field as the integration starting point:

[0156]

[0157] Where V is the set of all points, N(v) is the neighborhood point set of v;

[0158] ​The method of generating the initial solution of MCF based on the mass path is as follows: the initial unfolding phase φ0 is obtained by integrating along the mass path;

[0159] Compute the initial integer field:

[0160]

[0161] Construct MCF initial flow distribution:

[0162] flow(e)=k0(head(e))-k0(tail(e))

[0163] Here, k0(head(e)) and k0(tail(e)) represent the initial integer field values ​​of the head and tail nodes of edge e, respectively, and flow(e) is the initial flow assigned to edge e. Based on the initial flow assignments, the algorithm performs a global flow balance check on the triangulated network to ensure that the inflow and outflow of each node meet the network's conservation constraints. For nodes that do not meet flow balance, a flow adjustment strategy is implemented to achieve overall flow balance in the network by modifying the flow of some edges.

[0164] This high-quality initial solution significantly improves the convergence speed and solution quality of the MCF algorithm, and greatly enhances the expansion accuracy and computational efficiency.

[0165] The multi-objective constrained adaptive triangulated discrete phase unwrapping method proposed in this paper achieves high-precision and high-robustness unwrapping of discrete phase data by organically combining three core technologies: phase quality-guided adaptive triangulated network construction, a multi-objective constrained MCF framework, and quality-guided intelligent path planning.

[0166] Compared with traditional methods, this method improves phase unwrapping accuracy by 45-60%, noise resistance by 65%, and processing speed by 3-5 times, showing significant technical advantages and application prospects.

[0167] This method is particularly suitable for phase field expansion with discrete sampling point distribution. It can effectively handle complex scenes such as noise, discontinuous areas, and high-gradient areas, providing strong technical support for optical measurement, medical imaging and other fields.

[0168] Throughout this specification, references to terms such as "one embodiment," "example," or "specific example" indicate that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, schematic representations of these terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0169] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A multi-objective constrained adaptive triangulated discrete phase unwrapping method, characterized in that: The following steps are involved: S1. Perform phase quality assessment on discrete sampling points. Calculate the local signal-to-noise ratio, phase gradient amplitude, local phase consistency metric, and boundary distance factor for each sampling point to comprehensively evaluate its phase quality. By calculating the local signal-to-noise ratio and phase gradient amplitude indicators of discrete sampling points, the phase reliability is quantified, providing a quality basis for subsequent network construction as a basic input. S2. Dynamically adjust mesh density based on quality assessment results, densify high-quality areas, and thin out low-quality areas, and optimize the triangulation structure through quality-guided edge weights. S3. Expand the MCF model based on the triangulated network, integrate phase gradient reliability, spatial continuity, and boundary protection constraints, and construct a multi-objective optimization function. Use the triangulated network as the carrier to define the optimization objectives. S4. Screen high-quality integral paths based on signal-to-noise ratio, gradient amplitude, and distance factor, determine the initial expansion starting point, and optimize flow distribution. This is independent of the MCF but provides an efficient initial solution for it. S5. Solve the global optimal flow distribution through the dynamic tree acceleration algorithm, combine the path planning results to achieve high-precision phase unfolding, integrate the path planning output, and complete the core unfolding calculation; S6. Evaluate the expansion effect based on accuracy and noise resistance indicators, iterate in reverse to adjust the quality assessment threshold or constraint weight, and perform closed-loop feedback to optimize the parameters of the entire process.

2. The multi-objective constrained adaptive triangulated discrete phase unwrapping method according to claim 1, characterized in that: The implementation steps of step S2 are: S21. Based on the quality assessment results of step S1, a phase quality-guided adaptive triangulation method is used to dynamically adjust the network structure according to the phase quality characteristics of discrete sampling points; S22. Introduce a composite quality evaluation function and adopt a quality-adaptive importance sampling mechanism to make the sampling probability positively correlated with the quality score, ensuring that the high-quality areas evaluated in step S1 are densely sampled and the low-quality areas are appropriately sparsely sampled; S23. Using the boundary distance factor of step S1 to identify boundary points, identify and specially process the sampling points in the boundary area, and enhance the sampling probability of the boundary points through the boundary detection operator to improve the processing accuracy of the boundary area; S24. An improved constrained Delaunay triangulation algorithm is used, and quality-guided edge weights are introduced. The weight parameters are derived from the phase consistency metric in step S1, and the optimized triangulated network structure is finally obtained.

3. The multi-objective constrained adaptive triangulated discrete phase unwrapping method according to claim 2, characterized in that: The implementation steps of step S3 are: S31. Expand the MCF model based on the triangulated network optimized in step S2, expand the traditional MCF minimum cost flow solving framework, introduce a multi-objective constraint optimization function, and integrate the edge weight definition cost function of step S24; S32. Comprehensively balance three types of constraints: phase gradient reliability constraint, spatial continuity constraint, and boundary protection constraint to evaluate the reliability of gradients between discrete points, reduce the impact of unreliable gradients, and promote phase consistency between adjacent triangles. At the same time, it protects structural edges and discontinuous areas to avoid over-smoothing. The gradient reliability constraint depends on the grid density of step S21, the spatial continuity constraint depends on the edge weight of step S24, and the boundary protection constraint depends on the boundary point processing of step S23. S33. Define the MCF cost function for multi-objective optimization, and adaptively configure the weight coefficient of the MCF cost function according to the local signal-to-noise ratio distribution in step S1.

4. The multi-objective constrained adaptive triangulated discrete phase unwrapping method according to claim 3, characterized in that: The implementation steps of step S4 are: S41. Further improve the deployment accuracy and propose a quality-guided integral path selection algorithm, which directly uses the quality assessment results of step S1 to select reliable paths, replacing the traditional path planning method; S42. Construct a point-to-point quality metric function to evaluate path quality based on signal-to-noise ratio, phase gradient amplitude, and inter-point Euclidean distance factors; S43. Divide the path quality level into high-quality path, medium-quality path and low-quality path, and optimize the path according to the quality metric, integrating the signal-to-noise ratio, gradient amplitude and inter-point distance of step S1 to divide the path quality level; S44. Select the most reliable point evaluated in step S1 as the integration starting point, integrate along the mass path to obtain the initial unfolding phase, and construct the MCF initial flow distribution.

5. The multi-objective constrained adaptive triangulated discrete phase unwrapping method according to claim 4, characterized in that: The implementation steps of step S5 are: S51. Combine the triangulated network structure of step S2 to perform multi-scale decomposition. When the approximate solution of the scale layer is mapped to the fine scale layer, the initial flow distribution of step S44 is loaded, and the network simplex algorithm is accelerated using a dynamic tree data structure to construct a hierarchical representation of the problem. The approximate solution is quickly solved at the coarse scale layer, and the result is then mapped to the fine scale layer as the initial solution, and the optimization is refined layer by layer. S52. Under the conditions of satisfying capacity constraints and node balance constraints, the global optimal solution is solved through the multi-objective cost function of step S3 to achieve high-precision expansion of discrete phase data.

6. The multi-objective constrained adaptive triangulated discrete phase unwrapping method according to claim 5, characterized in that: The implementation steps of step S6 are: S61. Verify the expansion results and evaluate the expansion accuracy, noise resistance and processing speed indicators. The verification results are directly fed back to the quality assessment threshold adjustment in step S1 and the weight coefficient optimization in step S33; S62. Based on the verification results, optimize and adjust the method to further improve the performance and stability of phase unwrapping.

7. An adaptive triangulated discrete phase unwrapping system for high-precision unwrapping of discrete sampled phase data, characterized in that: The system includes a computing device and a phase acquisition array module. The phase acquisition array module is deployed according to a non-uniform spatial distribution rule to form a multi-level sampling network. The computing device is used to execute a method for adaptive triangulated discrete phase expansion with multi-objective constraints.

8. The system according to claim 7, wherein the computing device comprises: A phase quality assessment module, which is used to generate a multidimensional quality score map of discrete sampling points based on local signal-to-noise ratio, phase gradient amplitude, local phase consistency metric and boundary distance factor; An adaptive triangulation generation module, which controls sampling density through a quality-driven dynamic segmentation strategy combined with a quality evaluation function, implements enhanced sampling in boundary areas, and constructs a quality-guided weighted triangulation structure; A multi-objective constrained optimization module, which is used to extend the minimum cost flow framework, integrate phase gradient reliability constraints, spatial continuity constraints, and boundary protection constraints, and define a multi-objective cost function with adaptive weight configuration; A quality-guided path planning module, which constructs a path quality metric function based on signal-to-noise ratio-gradient amplitude-distance factor to screen the optimal integral path and determine the initial unwrapping phase; A hierarchical MCF solver, which implements multi-scale optimization through a dynamic tree acceleration algorithm, and is used to generate an approximate solution at a coarse scale layer and then map it to a fine scale layer for fine adjustment; The verification and feedback optimization module is used to form a closed-loop parameter optimization mechanism by evaluating the results of the expansion accuracy, noise suppression capability and computational efficiency indicators. The computing device is used to sequentially generate a quality map of discrete phase data through the phase quality assessment module; the adaptive triangulated network generation module dynamically adjusts the mesh topology according to the quality map; the multi-objective constraint optimization module constructs a constraint flow network based on the triangulated network; the quality-guided path planning module generates an initial phase distribution; and finally, the hierarchical MCF solver completes the global optimal phase expansion; and the verification and feedback optimization module continuously optimizes the parameter configuration of each module.

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