A surface shape measurement method based on implicit neural modeling and meta-learning

Abstract

The application discloses a surface shape measurement method based on implicit neural modeling and meta-learning, and belongs to the technical field of optical measurement. The method comprises the following steps: dividing a three-dimensional point cloud used for modeling into multiple local regions; performing surface shape modeling calculation through an implicit neural network and generating intermediate hidden features; extracting geometric features of each local region to obtain a local embedding vector; inputting the local embedding vector into a meta-learning network to generate a local adaptive modulation parameter; in the modeling calculation process, the intermediate hidden features are dynamically modulated according to the modulation parameter to obtain a modulated modeling result; a distance field is constructed based on the result, and a high-precision curved surface coordinate of a to-be-measured aspheric mirror surface is obtained by extracting a zero-equal-surface. The application only relies on point cloud coordinates, and combines global implicit modeling with local adaptive meta-learning, thereby significantly improving the restoration precision of local subtle features while maintaining the global consistency of the curved surface, and having high precision and strong engineering practicability.

Description

A method for measuring face shape based on implicit neural modeling and meta-learning Technical Field

[0001] This application relates to the field of optical measurement technology, and more specifically to a method for measuring surface shape based on implicit neural modeling and meta-learning. Background Technology

[0002] Large-aperture aspherical mirrors are core components of high-end optical systems. In the flatness inspection of large-aperture aspherical mirrors, non-contact optical probes based on spectral confocal technology have become the mainstream method for acquiring three-dimensional point clouds of the mirror surface. Spectral confocal non-contact optical probe technology can efficiently acquire high-precision, large-scale discrete points on the surface, laying a data foundation for subsequent surface shape evaluation. However, the point clouds acquired by non-contact optical probes are inherently disordered, sparse, and potentially noisy discrete samples, lacking explicit topological connections and continuous geometric information. Therefore, how to stably reconstruct a high-fidelity continuous surface from these points is the core challenge for achieving high-precision flatness measurement. This task not only requires the algorithm to accurately reconstruct the macroscopic contour of the mirror surface but also to preserve key features such as local minute undulations, placing extremely high demands on the accuracy, robustness, and detail preservation capabilities of the reconstruction method.

[0003] While traditional surface fitting methods and some deep learning-based point cloud reconstruction techniques have achieved certain results in specific scenarios, they still have significant shortcomings when dealing with large-scale, irregular, and topologically unstructured point cloud data. First, traditional explicit modeling methods typically rely on the regular distribution of point clouds or pre-assumed surface parameters, making them difficult to adapt to actual measurement data with uneven point cloud density, complex local structures, or missing data. In complex free-form surfaces or high-precision detection scenarios, they often require extensive manual intervention and post-processing, resulting in poor engineering adaptability. Second, some deep learning-based point cloud reconstruction methods often use a globally unified model to model the entire point cloud, lacking the ability to characterize the differences in geometric complexity across different spatial regions. When the surface exhibits high-frequency details, abrupt changes, or systematic error differences in local areas, insufficient local reconstruction accuracy can easily occur. Furthermore, many existing methods rely on assumptions about normal vectors, topological structures, or closed surfaces, which are often difficult to obtain stably in actual industrial measurement scenarios, limiting their application scope.

[0004] Therefore, there is an urgent need for a surface shape measurement method based on implicit neural modeling and meta-learning to solve the technical problem of inaccurate measurement of the surface shape of large-aperture aspherical mirrors in existing technologies. Summary of the Invention

[0005] The purpose of this application is to provide a method for measuring surface shape based on implicit neural modeling and meta-learning, which can solve at least one of the aforementioned technical problems. The specific solution is as follows:

[0006] According to a specific embodiment of this application, this application provides a method for measuring face shape based on implicit neural modeling and meta-learning, including the following steps:

[0007] Based on spatial location or neighborhood relationships, the 3D point cloud measurement data used for surface modeling is divided into multiple local point cloud regions;

[0008] Based on the spatial coordinates in the three-dimensional point cloud measurement data, surface modeling calculation is performed through an implicit neural network, and intermediate hidden features are generated layer by layer during the surface modeling calculation process.

[0009] Based on each of the local point cloud regions, local geometric features representing local surface features are extracted, and corresponding local geometric embedding feature vectors are obtained.

[0010] The local geometric embedding feature vector is input into the meta-learning network to generate locally adaptive modulation parameters corresponding to the intermediate hidden features;

[0011] During the surface modeling calculation process, the intermediate hidden features are locally adaptively modulated according to the modulation parameters to obtain the modulated surface modeling result;

[0012] The distance values ​​of spatial points are calculated based on the modulated surface modeling results, a distance field is constructed, and the zero isosurface is extracted to obtain the surface coordinates of the aspherical mirror surface to be measured.

[0013] Furthermore, the surface modeling calculation using an implicit neural network includes:

[0014] The spatial coordinates are position-encoded and mapped to encoded features containing multi-frequency spatial information.

[0015] The encoded features are input into the backbone network of the implicit neural network to perform a mapping calculation from coordinates to distance values;

[0016] In the backbone network, the encoded features are transformed layer by layer nonlinearly to generate the intermediate hidden features;

[0017] Based on the final generated intermediate hidden features, output the unsigned distance value corresponding to the spatial coordinates.

[0018] Furthermore, the step of encoding the spatial coordinates into Fourier position codes includes:

[0019] Each coordinate component is encoded using a set of sine and cosine functions with preset frequencies.

[0020] The encoding results of each coordinate component are concatenated to form an encoded feature containing multi-frequency spatial information.

[0021] Further, obtaining the corresponding local geometric embedding feature vector includes:

[0022] Each of the local point cloud regions is sampled to form a region point set with a fixed number of points;

[0023] The region point set is subjected to hierarchical feature aggregation using a PointNet++-based encoder;

[0024] Global pooling is performed on the aggregated features to output a fixed-length local geometric embedding feature vector.

[0025] Further, the step of inputting the local geometric embedding feature vector into the meta-learning network to generate locally adaptive modulation parameters corresponding to the intermediate hidden features includes:

[0026] The local geometric embedding feature vector is input into a meta-learning network composed of multilayer perceptrons;

[0027] The meta-learning network outputs multiple sets of modulation parameters, each set of modulation parameters including a scaling vector and a bias vector;

[0028] The multiple sets of modulation parameters correspond to the intermediate hidden features generated layer by layer during the surface modeling calculation process of the implicit neural network.

[0029] Further, the step of performing local adaptive modulation on the intermediate hidden features according to the modulation parameters includes:

[0030] During the surface modeling calculation process, the intermediate hidden features are obtained;

[0031] The intermediate hidden feature is multiplied element-wise with the corresponding scaling vector, and the multiplication result is added element-wise with the corresponding bias vector to obtain the modulated intermediate hidden feature.

[0032] The surface modeling calculation is performed based on the modulated intermediate hidden features.

[0033] Further, the step of obtaining the modulated surface modeling result and calculating the distance value of spatial points includes:

[0034] The surface points in the 3D point cloud measurement data used for surface modeling are used as reference points;

[0035] A random perturbation is applied to the reference point to generate a near-surface query point;

[0036] Calculate the Euclidean norm of the perturbation vector corresponding to the random perturbation, and use the Euclidean norm as the true value of the unsigned distance to the corresponding near-surface query point.

[0037] Furthermore, the construction of the distance field includes:

[0038] The three-dimensional point cloud of the aspherical mirror surface under test is spatially divided into multiple local regions of the aspherical mirror surface under test.

[0039] Based on the modulated surface modeling results, modulation parameters corresponding to local regions of the surface of each of the aspherical mirrors under test are obtained.

[0040] The local region of the aspherical mirror surface to be tested is determined based on the location of the spatial point, and the distance value of the spatial point is calculated by calling the corresponding modulation parameters.

[0041] Calculate the distance values ​​for all spatial query points to construct the distance field.

[0042] Further, the extraction of the zero isosurface includes:

[0043] A regular voxel grid is established within the surface space of the aspherical mirror to be tested;

[0044] Obtain the distance values ​​of each vertex of the regular voxel grid;

[0045] The zero isosurface is extracted based on the distance values ​​of each vertex to obtain the surface coordinates of the aspherical mirror surface to be measured.

[0046] Furthermore, the process of dividing the 3D point cloud measurement data used for surface modeling into multiple local point cloud regions includes:

[0047] The three-dimensional point cloud measurement data is subjected to coordinate normalization processing to transform the point cloud coordinates to a preset standard coordinate space;

[0048] After the point cloud has been normalized, it is divided into multiple local point cloud regions by regular grids on the two-dimensional projection plane of the point cloud. Based on the projection coordinates of each point, the point is assigned to the corresponding grid cell. All points belonging to the same grid cell are defined as a local point cloud region.

[0049] Compared with the prior art, the above-described solutions of this application have at least the following beneficial effects:

[0050] 1. This application presents a surface shape measurement method based on implicit neural modeling and meta-learning. Through the architecture of implicit neural networks and meta-learning, it effectively solves the problem that traditional methods struggle to simultaneously capture both overall shape and local details. The globally shared implicit neural network ensures the smoothness, continuity, and geometric consistency of the reconstructed surface on a large scale. Simultaneously, the modulation parameters dynamically generated based on local geometric features enable the same model to perform feature-level differentiated processing on regions of varying complexity, thereby significantly improving the accuracy of capturing and reconstructing local features such as minute undulations and high-frequency details.

[0051] 2. This application presents a surface shape measurement method based on implicit neural modeling and meta-learning. Employing an unsigned distance value supervision strategy, it requires only the original point cloud 3D coordinates to complete model training and surface reconstruction. It eliminates the need for point cloud normals, internal / external labels, or closed surface assumptions, enabling the method to be directly applied to the most common industrial measurement scenarios such as open surfaces, one-sided scans, and missing point clouds. This significantly reduces the data preprocessing threshold and system complexity, enhancing the robustness and practical feasibility of the technology.

[0052] 3. This application presents a surface shape measurement method based on implicit neural modeling and meta-learning. Through the lightweight feature extraction network PointNet++ and parameter modulation mechanism, it achieves leading performance in all-around accuracy metrics, including RMSE and curvature error, while keeping the number of model parameters at a low level, far lower than comparable models with similar accuracy. Furthermore, its inference process requires only a single forward computation, eliminating the need for real-time gradient updates, and achieving millisecond-level reconstruction speed. This fully meets the stringent requirements of industrial online inspection for both efficiency and accuracy, providing a feasible technical path for real-time, high-precision 3D measurement of complex surfaces. Attached Figure Description

[0053] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings:

[0054] Figure 1 is a flowchart illustrating a face shape measurement method based on implicit neural modeling and meta-learning provided in an embodiment of this application.

[0055] Figure 2 is a schematic diagram of the algorithm of a face shape measurement method based on implicit neural modeling and meta-learning provided in an embodiment of this application. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0057] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a product or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a product or device. Without further limitation, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the product or device that includes that element.

[0058] The embodiments of this application are described in detail below with reference to the accompanying drawings.

[0059] This application provides a method for measuring surface shapes based on implicit neural modeling and meta-learning. The data acquisition hardware employs a spectral confocal measurement system to acquire point cloud data. The communication scheme is RS232 communication, and an FPGA chip with customized logic ensures the data transmission of point cloud data to a host computer. The host computer then implements this technical solution for measuring surface shapes based on implicit neural modeling and meta-learning.

[0060] This application aims to address the technical challenge of reconstructing a continuous surface with both global consistency and local detail fidelity from sparse, disordered, and potentially noisy point cloud data in 3D measurement of high-precision complex surfaces such as large-aperture aspherical mirrors, where traditional methods struggle. To this end, the technical solution of this application integrates Implicit Neural Representation (INR) and Meta-Learning networks. The core idea is to construct a globally shared implicit neural network to learn the continuous mapping from spatial coordinates to surface distances, while simultaneously introducing a meta-learning network framework. This allows the implicit neural network to dynamically adjust its internal feature representation based on the geometric features of local regions of the input point cloud, thereby achieving locally adaptive high-precision modeling. The measurement method of this application uses only 3D point cloud coordinates as input, without relying on point cloud normals, topological structures, or closure assumptions, thus possessing strong engineering applicability.

[0061] As shown in Figures 1 and 2, a method for measuring face shape based on implicit neural modeling and meta-learning includes the following steps:

[0062] S1. Based on spatial location or neighborhood relationship, divide the 3D point cloud measurement data used for surface modeling into multiple local point cloud regions.

[0063] S101. This application provides a preferred technical solution, which performs coordinate normalization processing on the 3D point cloud measurement data used for surface modeling, transforming the point cloud coordinates to a preset standard coordinate space. In this application embodiment, the obtained original 3D point cloud measurement data is... First, calculate the centroid and maximum distribution radius of the point cloud. The specific expressions are as follows:

[0064]

[0065] in, Represents the set of original 3D point clouds; Represents the three-dimensional coordinates of the i-th point; Let X, Y, and Z represent the coordinates of the i-th point, respectively. The centroid of the point cloud is represented by ; N represents the original number of points in the point cloud, i.e., the global number of points; s represents the scale normalization factor, i.e., the maximum distribution radius or the maximum norm; i represents the point index. This represents the L2 norm, also known as the Euclidean norm. Subsequently, each point cloud is normalized, expressed as:

[0066]

[0067] in, This represents the normalized point coordinates. In this embodiment... Represents any numerical value. The number in the upper right corner represents the dimension.

[0068] After processing, all point cloud coordinates were normalized to a coordinate system centered at the origin with a range of approximately [missing information]. Within the standard coordinate space.

[0069] In this embodiment, the technical problem of potentially large differences in absolute size and spatial position of point clouds obtained from different aspherical mirrors or different batches of the same aspherical mirror is avoided. By normalizing the coordinates of the 3D point cloud measurement data used for surface modeling, scale and translation differences are eliminated, greatly improving the numerical stability and convergence speed of subsequent implicit neural network training.

[0070] S102. This application provides a preferred technical solution: after the point cloud has been normalized, it is divided into multiple local point cloud regions by regular grids on the two-dimensional projection plane of the point cloud. Based on the projection coordinates of each point, the point is assigned to the corresponding grid cell, and all points belonging to the same grid cell are defined as a local point cloud region.

[0071] The range of the normalized point coordinates on the XY plane, i.e., the projection plane. Divide the data into a two-dimensional regular mesh with equal spacing, and set the mesh resolution as . In the embodiments of this application, The cell mesh size is expressed as:

[0072] in, Indicates the side length of the X-axis mesh cell; This indicates the side length of the Y-axis mesh cell.

[0073] When the mesh is too coarse, meaning the mesh resolution is too low, local geometric features in different regions are easily over-smoothed, making it difficult to reflect local differences in the surface. Conversely, when the mesh is too fine, meaning the mesh resolution is too high, the number of points within a single mesh is insufficient, which can easily lead to instability in local feature extraction and meta-learning modulation. In the embodiments of this application, the following is taken: A 32×32 mesh division ensures that each local region contains a sufficient number of points to stably represent local geometric characteristics while effectively distinguishing geometric differences between different spatial regions, thereby achieving efficient and stable local adaptive modeling. It should be noted that the number of mesh divisions can be adjusted according to the point cloud density and actual application requirements. Such adjustments do not affect the overall technical concept of this application; therefore, this application does not impose any limitations on this, and the mesh division can be determined based on specific circumstances.

[0074] The m-th grid cell is denoted as This defines a local region in space. Each point is assigned to the corresponding grid cell based on its coordinates. All points belonging to the same grid cell constitute a local point cloud region, which is expressed as:

[0075]

[0076] in, This represents the m-th grid cell; Indicates falling into Local point cloud region; They represent falling into X-axis and Y-axis coordinates of a local point cloud region.

[0077] Local point cloud region The number of points in the cloud is N m To avoid empty blocks or blocks with very few points affecting training, this application sets a minimum number of points threshold N. min If N is 128, then... m If the value is less than 128, then it is merged with its four neighboring grids or the local point cloud region is skipped directly.

[0078] Define a local task for each grid. In the embodiments of this application, that is This allows us to obtain all local point cloud regions and construct a task set for each local point cloud region. .

[0079] in, The set of tasks represents a local point cloud region; M represents the number of valid local point cloud regions. This represents the m-th local task.

[0080] The technical solution of this application decomposes the globally complex surface reconstruction task into spatially local and geometrically simple sub-tasks, allowing subsequent surface modeling calculations to focus on local geometry. This provides a spatial basis and operational units for subsequent local feature extraction and meta-learning modulation. Regular mesh partitioning avoids the problems of high computational cost and unstable results when partitioning by spatial location or neighborhood relationships. Setting a minimum point threshold ensures that each "local task" carries sufficient effective geometric information to support feature learning and meta-learning modulation, avoiding technical problems such as sparse or missing point clouds that cause inaccurate subsequent measurements.

[0081] S2. Based on the spatial coordinates in the 3D point cloud measurement data, surface modeling calculation is performed through an implicit neural network, and intermediate hidden features are generated layer by layer during the surface modeling calculation process.

[0082] In this embodiment, a multilayer perceptron (MLP) is used to form the backbone network of the implicit neural network. In order to improve the MLP's ability to represent high-frequency geometric details, spatial coordinates are first encoded in position before being input into the MLP, and the spatial coordinates are mapped into encoded features containing multi-frequency spatial information.

[0083] This application provides a preferred technical solution for spatial coordinate position encoding using Fourier position encoding, including: encoding each coordinate component separately using a set of preset frequency sine and cosine functions; and concatenating the encoding results of each coordinate component to form an encoded feature containing multi-frequency spatial information. For a three-dimensional coordinate... Each component is encoded using a set of preset fixed frequencies. In this embodiment, the fixed frequency L=10, and the expression for the Fourier encoding is:

[0084]

[0085] Where t represents Any single component of x, y, or z in the equation, that is, t, can be replaced by x, y, z in turn; represents the Fourier code of t; L represents the number of frequency layers, which is the number of fixed frequency bands.

[0086] Then, the codes of the three components x, y, and z are concatenated to obtain the coded feature containing multi-frequency spatial information, expressed as:

[0087]

[0088] in, This represents a coding feature that contains multi-frequency spatial information; These represent the codes for the three components x, y, and z, respectively. In this embodiment of the application, the dimension after encoding is represented as follows: In this embodiment, 3 represents the three components of the three-dimensional spatial coordinates X-axis, Y-axis, and Z-axis; 2 represents a set of sine and cosine functions corresponding to each frequency.

[0089] The technical solution of this application employs Fourier encoding to explicitly provide basis functions of different frequencies by mapping the input to a high-frequency space, making it easier for the MLP to combine high-frequency signals. This solves the technical problem that ordinary MLPs exhibit spectral bias when fitting high-frequency signals, tending to learn low-frequency components first, leading to insufficient reconstruction of subtle undulations and sharp features of curved surfaces. It significantly improves the implicit neural network's ability to model and reconstruct local high-frequency details of complex curved surfaces, such as the minute surface shape errors of aspherical mirrors.

[0090] The encoded features are input into the backbone of the implicit neural network to perform a mapping calculation from coordinates to distance values.

[0091] In the backbone network, the encoded features undergo layer-by-layer nonlinear transformation to generate intermediate hidden features.

[0092] Based on the final generated intermediate hidden features, output the unsigned distance value corresponding to the spatial coordinates.

[0093] The technical solution of this application embodiment constructs a multilayer perceptron with 8 hidden layers as the backbone network of the implicit neural network. The hidden width C of each layer is 256. The Softplus activation function is used to enhance numerical stability and avoid the gradient vanishing problem. A skip connection is set in the 4th layer of the network to encode the Fourier-encoded features containing multi-frequency spatial information. The features from the fourth layer are concatenated with the output features from the fifth layer and then input into the fifth layer to alleviate the vanishing gradient problem during deep network training. Implicit neural networks use... As input, through layer-by-layer nonlinear transformations, intermediate hidden features are generated layer by layer. Finally, through a linear output layer, the last layer of hidden features is mapped to a scalar value. The scalar value represents the unsigned distance from the coordinates to the surface to be reconstructed.

[0094] The expression is:

[0095]

[0096]

[0097] in, This indicates the Softplus activation function; This represents the output of a linear layer, an intermediate variable calculated internally by the neural network, and is a numerical value in the feature space. This represents the hidden feature of the (l+1)th layer, and the value of h represents the corresponding layer. This represents the first layer of hidden features; This represents the third layer of hidden features; This represents the 4th layer hidden feature used for skip-input concatenation; This represents the 5th layer hidden feature; , represent the weights and biases of the (l+1)th layer, respectively, and the values ​​on W and b represent the corresponding layers; , These represent the weights and biases of the first layer, respectively. , These represent the weights and biases of the 4th layer, respectively. , These represent the weights and biases of the 5th layer, respectively. These represent the weights and biases of the 8th layer, which is the last layer in this embodiment. This represents a scalar value indicating the output distance field of the implicit neural function, which is also suitable for unsigned distance values. This represents the backbone parameters of the implicit neural network.

[0098] The technical solution of this application, after completing the local point cloud region division, employs an implicit neural network method to perform global geometric modeling of the aspherical mirror-shaped surface. Unlike explicit surface representation methods in the prior art, such as triangular meshes or parametric surfaces, the implicit neural representation in this application describes the surface morphology by learning a continuous function, independent of the explicit topological structure of the point cloud, making it suitable for processing large-scale, irregular point cloud data. Furthermore, the technical solution of this application uses an implicit neural network based on an unsigned distance value function as the global geometric expression, mapping any spatial location to a corresponding distance value through a differentiable neural network function, and using a zero isosurface as the surface representation.

[0099] The technical solution of this application embodiment outputs an unsigned distance value corresponding to the spatial coordinates. Unlike the traditional signed distance function, which must assign a sign to each spatial point, typically positive values ​​are outside the surface and negative values ​​are inside the surface, this solution can effectively solve the technical problem of not being able to stably and reliably determine the inside or outside of points for open surfaces, such as the back of an aspherical mirror that has not been scanned or is an incomplete point cloud.

[0100] S3. Based on each local point cloud region, extract local geometric features that characterize the local surface features and obtain the corresponding local geometric embedding feature vector.

[0101] Each local point cloud region is sampled to form a region point set with a fixed number of points. In this embodiment of the application, each local point cloud region... First, a fixed number of sampling points K is performed, where K = 256. If N m If N > 256, random sampling is used; if N m <256, use repeated sampling to complete, that is, form a region point set with a fixed number of points. This transforms irregular, variable-length real-world data into regular, fixed-length tensors that can be directly processed by neural networks.

[0102] In this embodiment, the value of K directly affects the expressive power of local geometric features and the computational complexity of the system. When K is too small, the local point cloud is too sparse, making it difficult to fully describe the curvature changes and high-frequency details within the region; when K is too large, although the local geometric information is more complete, it will significantly increase the computational and storage overhead of the feature extraction module, and the accuracy improvement tends to saturate. In this embodiment, considering the integrity of local geometry, the stability of model training, and the efficiency of engineering implementation, the number of sampling points K is fixed at 256. The fixed number of points K can be adjusted according to the actual application requirements. The adjustment does not affect the overall technical concept of this application, so this application does not limit it and can choose a value according to the specific situation.

[0103] Hierarchical feature aggregation is performed on a fixed-number region point set using a PointNet++-based encoder. Then, a lightweight PointNet++-based encoder is used to process the randomly sampled point set and the point set padded with repeated samples.

[0104] Will The input is fed into the lightweight PointNet++ encoder. In this embodiment, the PointNet++ encoder includes two levels of set abstraction operations:

[0105] First-level set abstraction (SA1): In the context of... Of the 256 points, local neighborhood information is aggregated through farthest point sampling and radius search, and a tensor of [128, 128] is output, which is 128 center points, each with 128-dimensional features.

[0106] Second-level set abstraction (SA2): Sampling and neighborhood aggregation are performed again on the output of SA1, outputting a tensor of [32, 256], which is 32 center points, each with 256-dimensional features.

[0107] Global pooling: Max pooling is performed along the dimensions of the 32 points of the 256-dimensional features output by SA2, taking the maximum value in each feature dimension, and finally obtaining a tensor of [1, 256], which is a 256-dimensional local geometric embedding feature vector. .

[0108] The technical solution of this application embodiment performs neighborhood aggregation on the original point set through the first stage of the PointNet++ encoder, outputting a small number of feature points with local contextual information; the second stage further aggregates, and finally compresses the features of all points into a fixed-length vector, namely the local geometric embedding feature vector, through global max pooling. The PointNet++ network can effectively learn hierarchical geometric features from the unordered point set, capture the shape characteristics of local regions, and automatically learn and extract deep features that can represent the overall geometric shape of the local region.

[0109] The technical solution of this application embodiment effectively learns hierarchical geometric features from disordered local point cloud regions through the encoder of PointNet++, captures the shape characteristics of local regions, and enables the implicit neural network to perceive the geometric differences between different local regions, such as flatness, curvature, the presence of pits or protrusions, and obtains surface shape information in a more detailed and realistic manner.

[0110] S4. Input the local geometric embedding feature vector into the meta-learning network to generate locally adaptive modulation parameters corresponding to the intermediate hidden features.

[0111] The local geometric embedding feature vectors are input into a meta-learning network composed of multilayer perceptrons.

[0112] In this embodiment, the meta-learning network is specifically a meta-conditional network composed of multi-layer perceptrons, with a fixed structure of 3 fully connected layers to ensure its lightweight and efficiency. Local geometry is embedded into the feature vector. Input meta-learning network.

[0113] The meta-learning network outputs multiple sets of modulation parameters, each set including a scaling vector and a bias vector.

[0114] The meta-learning network executes the following sequentially:

[0115] The first fully connected layer (FC1) maps the 256-dimensional input to 512 dimensions and uses the ReLU activation function.

[0116] The second fully connected layer (FC2) maintains 512 dimensions and uses the ReLU activation function for nonlinear transformation.

[0117] The third fully connected layer (FC3): linearly maps the 512-dimensional features to 2048 dimensions, serving as the direct output of the meta-learning network. .

[0118] Multiple sets of modulation parameters correspond to the intermediate hidden features generated layer by layer during the surface modeling calculation process of the implicit neural network.

[0119] In this embodiment of the application, the 2048-dimensional vector output by the third fully connected layer... It contains all the modulation information. The parameters are rearranged and analyzed into four sets of modulation parameters, each containing a scaling vector. and a bias vector The rearranged expression is: Each scaling vector and bias vector All are 256-dimensional vectors, consistent with the hidden feature dimensions of the corresponding layers to be modulated in the implicit neural network backbone. In this embodiment, multiple sets of modulation parameters correspond in advance to the intermediate hidden features to be generated in layers 2, 4, 6, and 8 of the implicit neural network backbone, respectively, preparing for subsequent targeted modulation.

[0120] S5. During the surface modeling calculation, the intermediate hidden features are locally adaptively modulated according to the modulation parameters to obtain the modulated surface modeling result.

[0121] During the surface modeling calculation process, intermediate hidden features are obtained. First, the standard calculation for this layer is completed to obtain the original features after activation.

[0122] In this embodiment, the generated multiple sets of modulation parameters are not arbitrarily specified, but strictly correspond to the selected intermediate hidden features generated layer by layer during the surface modeling calculation of the implicit neural network. The output features of the four representative intermediate layers in the backbone of the implicit neural network—layers 2, 4, 6, and 8—are used as modulation targets. This layered modulation strategy allows the meta-learning network mechanism to exert influence on feature levels at different depths and abstraction levels, thereby achieving more refined and powerful adaptive control of the network's representation capabilities. This provides a key control mechanism for achieving high-precision local surface reconstruction.

[0123] The intermediate hidden features are multiplied element-wise with the corresponding scaling vector, and the result of the multiplication is added element-wise with the corresponding bias vector to obtain the modulated intermediate hidden features.

[0124] Taking the second layer as an example, the same logic applies to the remaining layers. The expression for the second layer is:

[0125]

[0126] in, This represents the second layer intermediate hidden feature output after modulation; These represent the modulation parameters corresponding to the second layer, namely the scaling vector and the bias vector; , These represent the weights and biases of the second layer, respectively. This represents the hidden features in the middle of the first layer; It represents the Hadamardi (or Hadama) stack.

[0127] In other words, the first set of parameters output by the meta-learning network corresponds to the intermediate hidden features generated by the second layer of the implicit neural network; the second set of parameters output by the meta-learning network corresponds to the intermediate hidden features generated by the fourth layer of the implicit neural network. Similarly, the third and fourth sets of parameters correspond to the intermediate hidden features of the sixth and eighth layers, respectively.

[0128] Finally, the output of this layer is replaced with modulated features, expressed as:

[0129]

[0130] in, This represents the k-th layer intermediate hidden feature output after modulation; These represent the modulation parameters corresponding to the k-th layer, and are the scaling vector and bias vector, respectively. , These represent the weights and biases of the k-th layer, respectively. This represents the hidden features in the (k-1)th layer.

[0131] Surface modeling calculations are performed based on the modulated intermediate hidden features. This process is repeated for each preset modulation layer. Finally, a scalar value is output.

[0132] The final output expression is:

[0133]

[0134] in, This represents the equivalent implicit function of the m-th local block after modulation, which is the unsigned distance value predicted for the input coordinate x; x represents the coordinates of a query point in the input three-dimensional space; and m represents the index of the local region.

[0135] Surface modeling calculations are performed based on the modulated intermediate hidden features. This means that the modulated features... This value will be used as input to the next layer, the (k+1)th layer, and will continue to participate in the forward propagation of the network. This process is repeated at each pre-defined modulation layer. Finally, after computation by all layers (including modulated and unmodulated layers), the network outputs a scalar value. That is, the modulated surface modeling result integrates the surface distance value with global geometric prior and local adaptive information.

[0136] The technical solution of this embodiment utilizes a globally shared backbone network to address the different modulation parameters inputted into different local regions. This generates differentiated internal feature representations and final outputs, thereby achieving high-precision, adaptive modeling of local geometric features of complex surfaces.

[0137] The technical solution in this embodiment achieves the transformation from local geometric perception to model behavior regulation through a dedicated meta-conditional network. The generated modulation parameters are precisely linked to the key intermediate layers of the implicit neural network, enabling the implicit neural network to dynamically and discriminatively adjust its internal feature representation based on the local features of different regions of the input point cloud. This architecture of globally shared backbone and local parameter modulation can achieve high-precision local adaptive reconstruction while maintaining model compactness and generalization ability.

[0138] S6. Calculate the distance values ​​of spatial points based on the modulated surface modeling results, construct the distance field, extract the zero isosurface, and obtain the surface coordinates of the aspherical mirror surface to be measured.

[0139] Surface points in the 3D point cloud measurement data used for surface modeling are used as reference points. For each reference point, a random 3D Gaussian perturbation is applied to generate near-surface query points located nearby, expressed as:

[0140]

[0141] in, This represents the near-surface query point of the k-th perturbation at the i-th surface point; Represents the i-th surface point; Represents a three-dimensional Gaussian perturbation vector; This indicates that the expression follows a pattern with a mean of 0 and a covariance of . The three-dimensional Gaussian distribution; Represents a 3×3 identity matrix; This represents the standard deviation of the disturbance, which is 0.01 in this embodiment.

[0142] Calculate the Euclidean norm of the perturbation vector corresponding to the random perturbation, and use the Euclidean norm as the ground truth of the unsigned distance value for the corresponding near-surface query point. The ground truth of the unsigned distance value corresponding to the query point is the Euclidean norm of the perturbation vector. In this embodiment, four perturbation points are sampled for each surface point, and the expression is:

[0143]

[0144] in, This represents the true value of the unsigned distance, which is the Euclidean norm of the perturbation vector.

[0145] The core objective of the above steps is to ensure that the predicted values ​​of the implicit neural network meet the following requirements. The technical solution of this application embodiment uses unsigned distance value function training for greater stability, i.e., the supervision target is... It relies solely on point cloud coordinates, requiring no normal vectors or closure assumptions, and exhibits strong adaptability to open surfaces. Among these, express The predicted distance to the surface to be reconstructed is the true value of the unsigned distance.

[0146] This application provides a preferred technical solution. To ensure that the proposed surface shape measurement method based on implicit neural modeling and meta-learning can stably obtain high-precision surface reconstruction results with geometric consistency, this application constructs a comprehensive loss function that minimizes multiple loss functions. This comprehensive loss function is composed of the weighted sum of the following four losses: near-surface unsigned distance loss function, Eikonal regularization loss function, local consistency loss function, and feature-level linear modulation regularization loss function, with the following expressions:

[0147]

[0148]

[0149]

[0150]

[0151] in, Represents the loss function for unsigned distance values ​​near the surface; Let j represent the j-th near-surface query point, which is obtained by adding random Gaussian perturbation to the surface point; This indicates that the implicit neural network is at the point The truth value of the unsigned distance at that location; The true perturbation distance corresponding to the query point is represented by the Euclidean norm of the perturbation vector; This indicates the number of query points participating in each local region, which is 4096 in this embodiment. Represents the Eikonal regularized loss function; In normalized space Points uniformly and randomly sampled within the area; This represents the gradient of the implicit function with respect to the input coordinates; This indicates the number of random sampling points in the Eikonal regularization term, which is 2048 in this embodiment. Represents the local consistency loss function; This indicates sampling points located near the common boundary of adjacent grids; These represent two spatially adjacent local grid indices; These represent the implicit function responses obtained under different local modulation parameters; Indicates the number of boundary sampling points; This represents the characteristic-level linear modulation regularization loss function; This represents the scaling parameter of the feature-level linear modulation regularized loss function of the m-th local point cloud region at the k-th layer; The bias parameter represents the characteristic-level linear modulation regularization loss function. This indicates the index of the implicit network layer selected for modulation.

[0152] In this embodiment of the application, the expression for the comprehensive loss function L is:

[0153]

[0154] The weight combination in the embodiments of this application, The weight is 1, which is used as the core fitting term; The weight is 0.1, used to balance geometric constraints and fitting accuracy; A weight of 0.05 is used to suppress inter-block discontinuities; Weight is It prevents the modulation parameters from diverging in a weak constraint manner; while ensuring training stability, it does not weaken the effect of local adaptive modeling, and is suitable for implicit modeling tasks of complex freeform surfaces and large-scale point cloud data.

[0155] The technical solution provided in this application uses the near-surface unsigned distance loss function as the dominant loss term to directly constrain the consistency between the unsigned distance value function output by the implicit neural network and the true near-surface distance. Since it is difficult to stably obtain internal and external sign information in open surface or non-closed point cloud scenarios, this application adopts an unsigned distance value supervision method, requiring only that the absolute value of the predicted distance matches the true distance, thereby significantly improving training stability and applicability. The Eikonal regularization loss function is used to constrain the gradient norm of the implicit function in space to be close to 1, thus satisfying the basic geometric properties of the distance function. This constraint can effectively avoid problems such as gradient explosion, collapse, or discontinuity in the implicit field, making the implicit representation closer to the true Euclidean distance field. The Eikonal regularization loss function significantly improves the numerical stability and geometric consistency of the implicit neural field without relying on surface normals or closed topological information. Because this application's technical solution introduces a meta-learning-based local adaptive modulation mechanism in different spatial regions, slight differences may exist in the implicit representation of different local blocks. Therefore, a hetero-local consistency loss function is introduced to avoid geometric breaks or discontinuities at grid boundaries. This consistency regularization term constrains the implicit function output of adjacent regions, ensuring that local adaptation only operates at the detail level while maintaining the continuity and global consistency of the overall surface. A feature-level linear modulation regularization loss function is used to stabilize the modulation parameters of the meta-learning network output.

[0156] A joint loss function, consisting of near-surface distance loss, Eikonal regularization term, local consistency loss, and modulation parameter regularization term, is calculated. The learnable parameters of the implicit neural network, feature extraction module, and meta-learning network are then updated synchronously via backpropagation. This process collaboratively optimizes all steps, enabling the implicit neural network, under the control of the meta-learning network, to adaptively and accurately model different local point cloud regions, ultimately achieving high-precision, high-generalization 3D surface reconstruction.

[0157] The 3D point cloud of the aspherical mirror surface under test is spatially divided into multiple local regions of the aspherical mirror surface. First, the 3D point cloud of the aspherical mirror surface under test undergoes the same data preprocessing as in the surface modeling stage. Then, the 3D point cloud of the aspherical mirror surface under test is spatially divided into multiple local regions of the aspherical mirror surface. The division rules are exactly the same as in the surface modeling stage, that is, regular meshing is performed on the normalized XY projection plane, and points are assigned to corresponding mesh cells based on their projected coordinates, forming multiple local point cloud regions.

[0158] Based on the modulated surface modeling results in step S5, Fourier position encoding is performed on each local point cloud region to extract local geometric features representing local surface features. These local geometric features are then input into a meta-learning network to obtain modulation parameters corresponding to the local regions of each aspherical mirror surface under test. These parameters are a set of scaling and bias vectors, corresponding to the intermediate hidden features of the implicit neural network.

[0159] The distance values ​​of all spatial query points are calculated to construct a distance field. Based on the location of each spatial point, the local region on the surface of the aspherical mirror under test is determined, and the corresponding modulation parameters are called to calculate the distance value of the spatial point. Then, query points are densely sampled within the space under test. For each query point, its region is determined based on its location, and the corresponding modulation parameters are called to calculate its distance value. The distance values ​​of all points are then aggregated to form a continuous implicit distance field covering the space under test.

[0160] To obtain explicit surfaces from implicit distance fields, in normalized three-dimensional space... Within the surface space of the aspherical mirror to be tested, a regular voxel grid is established with a fixed resolution of R=256, meaning that in this embodiment, the number of sampling grid points is [missing information]. The distance value at each vertex of the regular voxel mesh is calculated. Then, the traveling cube algorithm is applied to traverse all voxel meshes, interpolating and constructing triangular patches based on the distance values ​​of their eight vertices. The set of these triangular patches is the zero isosurface, which is the high-precision triangular mesh surface model of the aspherical mirror surface to be tested, i.e., the surface coordinate representation of the aspherical mirror surface to be tested.

[0161] This application's embodiments verify the effectiveness of its technical solution through comparative experiments. Four methods are compared: the classic point cloud processing network PointNet, the improved PointNet++, and the dynamic graph convolutional network DGCNN. The core evaluation metrics are root mean square error (RMSE), mean absolute error (MAE), peak-to-valley ratio (PV), curvature error, chamfer distance (CD), normal consistency (NMD), number of model parameters, and reconstruction time. Specific data for the four methods are shown in Table 1.

[0162] Table 1 Comparison of Experimental Results

[0163]

[0164] Comparative experiments show that RMSE and MAE are the core indicators for measuring the overall deviation between the reconstructed surface and the real surface. The proposed method achieves optimal values ​​of 2.47 μm and 2.05 μm for RMSE and MAE, respectively, demonstrating that the implicit neural field of the proposed method is superior to existing methods based on discrete points or graphs in modeling the global continuous shape of the surface. It exhibits a more concentrated error distribution, better robustness, insensitivity to outliers and noise, and more stable predictions. The PV value is 10.9 μm, and the curvature error is 3.47 × 10⁻³, both of which are optimal and significantly superior. The PV value reflects the maximum possible local distortion in the reconstructed surface, indicating that the proposed method significantly improves average accuracy while suppressing the maximum error, resulting in a more uniform reconstructed surface quality. The lowest curvature error demonstrates that the proposed method utilizes meta-learning local adaptation to dynamically adapt to the geometric complexity of different regions, thus unparalleled in restoring the minute undulations, inflection points, and curvature changes of the surface, which is crucial for optical mirror detection. The lowest CD value indicates that the reconstructed surface in this application has the highest overall shape matching degree with the real surface. The chamfer distance considers the bidirectional nearest point distance between the two surfaces, and its significant reduction indicates that the reconstruction result is closer to the real object in terms of topology and overall shape, avoiding overall deformation or shrinkage. The reduction in NMD normal error directly reflects the greater accuracy of the tangent plane direction of the reconstructed surface in this application. While achieving the above-mentioned comprehensive accuracy breakthroughs, the model parameter count (15.1M) is far lower than that of the comparative methods with the same accuracy level, and the single reconstruction time is only 17.6 milliseconds. This shows that the model complexity control of this application is still excellent, and the design is efficient and lightweight, reducing the computational resource requirements and improving deployment flexibility. A perfect balance between high accuracy and high efficiency is achieved. Under the premise of achieving a significant improvement in comprehensive accuracy, the speed is still maintained at the millisecond level, which can be easily deployed in actual engineering, fully meeting the real-time requirements of industrial online inspection.

[0165] In summary, the technical solution of this application, by integrating implicit neural representation and meta-learning local adaptive mechanisms, successfully solves the long-standing technical challenges of balancing global accuracy and local detail in complex surface reconstruction, as well as the contradiction between model performance and computational efficiency. It provides an innovative solution with higher accuracy, richer detail, and ease of engineering deployment for the measurement of surfaces with high-quality requirements, such as large-aperture aspherical mirrors.

[0166] Finally, it should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0167] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for measuring surface shape based on implicit neural modeling and meta-learning, characterized in that, Includes the following steps: Based on spatial location or neighborhood relationships, the 3D point cloud measurement data used for surface modeling is divided into multiple local point cloud regions; Based on the spatial coordinates in the 3D point cloud measurement data, surface modeling calculations are performed using an implicit neural network, generating intermediate hidden features layer by layer during the surface modeling calculation process. Local geometric features characterizing local surface features are extracted from each local point cloud region, and corresponding local geometric embedding feature vectors are obtained. These local geometric embedding feature vectors are input into a meta-learning network to generate locally adaptive modulation parameters corresponding to the intermediate hidden features. During the surface modeling calculation process, the intermediate hidden features are locally adaptively modulated according to the modulation parameters to obtain the modulated surface modeling result. The distance values ​​of spatial points are calculated based on the modulated surface modeling results, a distance field is constructed, and the zero isosurface is extracted to obtain the surface coordinates of the aspherical mirror surface to be measured.

2. The measurement method according to claim 1, characterized in that, The surface modeling calculation using an implicit neural network includes: encoding the spatial coordinates to map them into encoded features containing multi-frequency spatial information; inputting the encoded features into the backbone network of the implicit neural network to perform a mapping calculation from coordinates to distance values; in the backbone network, the encoded features undergo layer-by-layer nonlinear transformation to generate intermediate hidden features; and based on the finally generated intermediate hidden features, outputting the unsigned distance value corresponding to the spatial coordinates.

3. The measurement method according to claim 2, characterized in that, The spatial coordinates are encoded into Fourier position codes, which includes: encoding each coordinate component separately using a set of sine and cosine functions of preset frequencies; and concatenating the encoding results of each coordinate component to form an encoding feature containing multi-frequency spatial information.

4. The measurement method according to claim 1, characterized in that, The step of obtaining the corresponding local geometric embedding feature vector includes: sampling each local point cloud region to form a region point set with a fixed number of points; performing hierarchical feature aggregation on the region point set through a PointNet++-based encoder; and performing global pooling on the aggregated features to output the local geometric embedding feature vector of fixed length.

5. The measurement method according to claim 1, characterized in that, The step of inputting the local geometric embedding feature vector into a meta-learning network to generate locally adaptive modulation parameters corresponding to the intermediate hidden features includes: inputting the local geometric embedding feature vector into a meta-learning network composed of a multilayer perceptron; the meta-learning network outputting multiple sets of modulation parameters, each set of modulation parameters including a scaling vector and a bias vector; the multiple sets of modulation parameters respectively corresponding to the intermediate hidden features generated layer by layer during the surface modeling calculation of the implicit neural network.

6. The measurement method according to claim 5, characterized in that, The step of performing local adaptive modulation of the intermediate hidden features according to the modulation parameters includes: obtaining the intermediate hidden features during the surface modeling calculation; multiplying the intermediate hidden features element-wise with the corresponding scaling vector, and adding the multiplication result element-wise with the corresponding bias vector to obtain the modulated intermediate hidden features; and performing the surface modeling calculation based on the modulated intermediate hidden features.

7. The measurement method according to claim 1, characterized in that, The step of obtaining the distance value of spatial points from the modulated surface modeling results includes: using surface points in the 3D point cloud measurement data used for surface modeling as reference points; applying random perturbation to the reference points to generate near-surface query points; calculating the Euclidean norm of the perturbation vector corresponding to the random perturbation, and using the Euclidean norm as the true value of the unsigned distance value of the corresponding near-surface query point.

8. The measurement method according to claim 1, characterized in that, The construction of the distance field includes: spatially dividing the three-dimensional point cloud of the aspherical mirror surface to be tested into multiple local regions of the aspherical mirror surface to be tested; based on the modulated surface modeling results, obtaining modulation parameters corresponding to each of the local regions of the aspherical mirror surface to be tested; determining the local region of the aspherical mirror surface to which the spatial point belongs according to the position of the spatial point, and calling the corresponding modulation parameters to calculate the distance value of the spatial point; calculating the distance values ​​of all spatial query points to construct the distance field.

9. The measurement method according to claim 1 or 8, characterized in that, The extraction of the zero isosurface includes: establishing a regular voxel grid in the space of the surface of the aspherical mirror to be tested; obtaining the distance value of each vertex of the regular voxel grid; extracting the zero isosurface based on the distance value of each vertex to obtain the surface coordinates of the surface of the aspherical mirror to be tested.

10. The measurement method according to claim 1, characterized in that, The step of dividing the 3D point cloud measurement data used for surface modeling into multiple local point cloud regions includes: performing coordinate normalization processing on the 3D point cloud measurement data to transform the point cloud coordinates to a preset standard coordinate space; dividing the point cloud after normalization processing into multiple local point cloud regions by regular grids on the 2D projection plane of the point cloud; assigning each point to the corresponding grid cell according to the projection coordinates of each point; and defining all point sets belonging to the same grid cell as one local point cloud region.

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