Gold and silver coin anti-counterfeiting identification method based on deep learning

Abstract

The present application relates to the cross field of deep learning and precise optical detection. The present application discloses a gold and silver coin anti-counterfeiting identification method based on deep learning, comprising: collecting a multi-frame image sequence of a gold and silver coin to be identified under a multi-angle ring light source array, and calculating a normal vector matrix and a height map matrix through photometric stereo method; inputting the normal vector matrix into a graph convolution feature extraction branch to extract global geometric feature; inputting the height map matrix into a spatial attention feature extraction branch to extract local texture abnormal feature; dynamically calculating a fusion weight matrix according to the gradient amplitude of the local area of the normal vector matrix, weighting and splicing the two types of features, and then inputting them into a full connection classification layer to output a true and false identification result. The present application eliminates the interference of the surface mirror reflection highlight of the gold and silver coin on the microscopic identification feature, reduces the misjudgment rate of the same batch of true coins caused by manufacturing tolerance, and improves the robustness of the identification model for gold and silver coins in different circulation wear states.

Description

Technical Field

[0001] This invention relates to the intersection of deep learning and precision optical inspection, and covers technologies for data processing and pattern recognition using algorithms such as artificial neural networks and deep learning. This invention discloses a method for anti-counterfeiting authentication of gold and silver coins based on deep learning. Background Technology

[0002] Current deep learning-based anti-counterfeiting authentication schemes for gold and silver coins typically involve acquiring two-dimensional images of the coin's surface under a single, fixed light source. These images are then input into a convolutional neural network for feature extraction and classification. In practice, this approach uses an industrial camera to acquire planar image data of the gold and silver coins. After preprocessing, the images are directly fed into a network model containing multiple convolutional and pooling layers. The network model uses convolutional kernels to perform sliding window calculations on the two-dimensional image, extracting the two-dimensional texture features and edge contour features of the coin's surface. Finally, a classifier outputs the authentication result.

[0003] The aforementioned existing technical solutions have a core flaw in application: due to the highly reflective metallic properties of gold and silver coins, under a single fixed light source, the coin surface inevitably produces localized specular reflections of highlights and shadows, resulting in the complete loss of sandblasting textures and embossing details in the highlight-covered areas of the two-dimensional image. Convolutional neural networks directly process two-dimensional images with highlight occlusion, failing to recover the true microscopic three-dimensional morphological information from the pixels obscured by highlights. This leads to missing features extracted by the model, resulting in erroneous authentication results. Summary of the Invention

[0004] The purpose of this invention is to provide a deep learning-based method for authenticating gold and silver coins against counterfeits, which can solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a deep learning-based method for authenticating gold and silver coins, comprising: acquiring a multi-frame image sequence of the gold and silver coin to be authenticated under a multi-angle ring light source array, and calculating the normal vector matrix and height map matrix of the surface of the gold and silver coin to be authenticated by photometric stereo method.

[0006] The normal vector matrix is ​​input into the graph convolution feature extraction branch. A topological graph is constructed using the surface pixels of the gold and silver coins to be identified as nodes and spatial adjacency relationships as edges to extract global geometric features.

[0007] The height map matrix is ​​input into the spatial attention feature extraction branch to filter out high-frequency noise in the specular reflection area and extract local texture anomaly features.

[0008] A cross-modal adaptive feature fusion layer is constructed. The fusion weight matrix of the global geometric features and the local texture anomaly features is dynamically calculated based on the gradient magnitude of the local region in the normal vector matrix. The global geometric features and the local texture anomaly features are then weighted and concatenated. The concatenated feature vector is input into a fully connected classification layer, which outputs the authentication result of the gold and silver coins to be authenticated.

[0009] Preferably, the step of acquiring a multi-frame image sequence of the gold and silver coin to be identified under a multi-angle ring light source array, and calculating the normal vector matrix and height map matrix of the surface of the gold and silver coin to be identified by photometric stereo method, includes: the multi-angle ring light source array containing a preset number of point light sources evenly distributed on the circumference, controlling the preset number of point light sources to be lit sequentially, and acquiring a single-frame grayscale image of the gold and silver coin to be identified under the illumination of each of the point light sources.

[0010] The single-frame grayscale image corresponding to the preset number of point light sources is masked and cropped to retain the effective pixel area containing the main pattern of the gold and silver coins to be identified.

[0011] Based on the gray values, light source direction vector, and camera line-of-sight vector within the effective pixel region, the surface reflection equation is solved to generate the normal vector matrix.

[0012] The height map matrix is ​​generated by performing an integral transformation on the normal vector matrix.

[0013] Preferably, the step of inputting the normal vector matrix into the graph convolution feature extraction branch, constructing a topology graph with the surface pixels of the gold and silver coins to be identified as nodes and spatial adjacency relationships as edges, and extracting global geometric features includes: performing downsampling processing on the normal vector matrix to obtain a gridded node set, and using the node coordinates in the gridded node set as the node attributes of the topology graph.

[0014] Calculate the cosine of the angle between the normal vectors of any two adjacent nodes in the gridded node set, and use the cosine of the angle between the normal vectors as the edge weight of the connecting edge in the topology graph.

[0015] The topology graph is input into the graph convolution feature extraction branch, which consists of multiple graph convolution layers. The graph convolution layers perform message passing and aggregation updates on the node attributes and edge weights, and output the global geometric features that include the coin surface curvature change features and the embossing depth change features.

[0016] Preferably, the step of inputting the height map matrix into the spatial attention feature extraction branch to filter out high-frequency noise in the specular reflection region and extract local texture anomaly features includes: inputting the height map matrix into a U-shaped network structure composed of an encoder and a decoder, wherein the encoder extracts multi-scale height feature maps through multi-level convolution operations.

[0017] The multi-scale height feature map is input into the spatial attention sub-network, the attention weight coefficient of each spatial location in the multi-scale height feature map is calculated, and the attention weight coefficient is multiplied element-wise with the multi-scale height feature map.

[0018] The multiplied multi-scale height feature map is input into the decoder, and deconvolution is performed to restore it to the same resolution as the height map matrix, outputting the local texture anomaly features.

[0019] Preferably, the construction of the cross-modal adaptive feature fusion layer, which dynamically calculates the fusion weight matrix of the global geometric features and the local texture anomaly features based on the gradient magnitude of the local regions in the normal vector matrix, includes: dividing the normal vector matrix into multiple non-overlapping local window regions, calculating the difference between the normal vectors in the horizontal and vertical directions in each local window region, and taking the square root of the sum of the squares of the differences in the horizontal and vertical directions as the gradient magnitude of the local window region.

[0020] The gradient magnitudes of all the local window regions are concatenated to form a gradient feature map. The gradient feature map is then input into a weight prediction subnetwork containing two convolutional kernels, and the fusion weight matrix with the same number of channels as the global geometric feature channels is output.

[0021] Preferably, the step of inputting the spliced ​​feature vector into a fully connected classification layer and outputting the authenticity authentication result of the gold and silver coins to be authenticated includes: inputting the spliced ​​feature vector into a flattening layer, a random deactivation layer and two fully connected layers connected in sequence, wherein the random deactivation layer sets the feature dimension output by the flattening layer to zero according to a preset discard probability.

[0022] The second fully connected layer has two output nodes, and the output values ​​of the two output nodes are mapped to probability values ​​within the interval by an activation function.

[0023] The category corresponding to the maximum value among the probability values ​​is selected as the authenticity authentication result of the gold and silver coins to be authenticated.

[0024] Preferably, the step of solving the surface reflection equation based on the gray values, light source direction vector, and camera line-of-sight vector within the effective pixel region to generate the normal vector matrix includes: constructing the surface reflection equation using a Lambertian diffuse reflection model and transforming the surface reflection equation into a linear overdetermined system of equations.

[0025] By introducing the surface roughness parameter and metal reflectivity parameter of the gold and silver coins to be identified as regularization constraints, the linear overdetermined equations are transformed into a constrained optimization problem.

[0026] The constrained optimization problem is solved iteratively using the alternating direction multiplier method to obtain the three-dimensional normal vector coordinates corresponding to each pixel on the surface of the gold and silver coin to be identified. The three-dimensional normal vector coordinates are then arranged according to the pixel rows and columns on the surface of the gold and silver coin to be identified to generate the normal vector matrix.

[0027] Preferably, the step of performing message passing and aggregation updates on the node attributes and edge weights through the graph convolutional layer includes: in each graph convolutional layer, for each central node in the topology graph, obtaining all first-order neighboring nodes of the central node.

[0028] The node attributes of the central node are concatenated with the node attributes of each of the first-order neighboring nodes, and the concatenated vector is multiplied by the edge weights connecting the central node to each of the first-order neighboring nodes to generate an edge feature message.

[0029] All the edge feature messages are summed and aggregated, and the aggregation result is input into a non-linear activation function. The activated result is then updated to reflect the node attributes of the center node in the current graph convolutional layer.

[0030] Preferably, the step of inputting the multi-scale height feature map into the spatial attention sub-network and calculating the attention weight coefficient of each spatial location in the multi-scale height feature map includes: performing max pooling and average pooling operations on the multi-scale height feature map along the channel dimension to generate max pooling feature maps and average pooling feature maps. The max pooling feature map and the average pooling feature map are concatenated along the channel dimension. The concatenation result is input into a concatenated network containing a convolutional layer with a kernel size of a preset size and an activation function. The attention weight coefficients of the spatial attention subnetwork are output, and the number of channels of the attention weight coefficients is set to 1.

[0031] Preferably, the step of inputting the gradient feature map into a weight prediction subnetwork containing two convolutional kernels and outputting the fused weight matrix with the same number of channels as the global geometric feature channels includes: inputting the gradient feature map into the first convolutional kernel of the weight prediction subnetwork, wherein the kernel size and stride of the first convolutional kernel are set according to the spatial resolution of the gradient feature map, and outputting the first feature map.

[0032] The first layer feature map is input into the second layer convolutional kernel of the weight prediction subnetwork. The kernel size of the second layer convolutional kernel is set to a preset value, and the output is an initial weight matrix with the same number of channels as the global geometric feature channels.

[0033] Each channel dimension in the initial weight matrix is ​​normalized, and the normalized matrix is ​​used as the fusion weight matrix.

[0034] Compared with existing technologies, the beneficial effects of this invention are as follows: 1. This invention acquires multiple image sequences under a multi-angle ring light source array and calculates the normal vector matrix and height map matrix of the surface of the gold and silver coins to be identified using the photometric stereo method, transforming the two-dimensional image domain identification problem affected by specular reflection into a three-dimensional surface morphology domain feature analysis problem. By combining graph convolution feature extraction branches and spatial attention feature extraction branches, global geometric morphology features and local texture anomaly features are extracted respectively, eliminating the interference of specular reflection specular highlights on microscopic identification features and overcoming the problem of detail loss in the highlight coverage area in existing technologies.

[0035] 2. In constructing the topology graph, this invention uses the cosine of the angle between the normal vectors as edge weights for message passing and aggregation updates, quantifying the curvature changes and embossing depth of the coin surface. In spatial attention feature extraction, max pooling and average pooling are performed along the channel dimension, and attention weight coefficients for spatial positions are calculated, filtering out high-frequency noise in the height map. By dividing local window regions, calculating gradient magnitudes, and inputting them into the weight prediction subnetwork to generate a fusion weight matrix, the fusion ratio of the two types of features is dynamically adjusted based on the local gradient, reducing the misjudgment rate caused by manufacturing tolerances in the same batch of genuine coins and improving the robustness of the authentication model to gold and silver coins under different circulation wear conditions. Attached Figure Description

[0036] Figure 1 This is a flowchart of the overall process for a deep learning-based anti-counterfeiting authentication method for gold and silver coins.

[0037] Figure 2 This is a flowchart for calculating the normal vector matrix and height map matrix using the photometric stereo method.

[0038] Figure 3 The flowchart shows the execution process of the graph convolution feature extraction branch.

[0039] Figure 4 Flowchart for the spatial attention feature extraction branch.

[0040] Figure 5 The flowchart shows the execution process of the cross-modal adaptive feature fusion layer.

[0041] Figure 6 Flowchart for outputting identification results for the fully connected classification layer. Detailed Implementation

[0042] The technical solution disclosed in this specific embodiment addresses the problem of loss of two-dimensional image features caused by the highly reflective metallic properties of gold and silver coins. It transforms the anti-counterfeiting authentication of the two-dimensional image domain into feature analysis of the three-dimensional surface morphology domain. The following is a detailed description of the specific implementation process.

[0043] Please refer to the attached document. Figure 1 and 2 This embodiment provides a deep learning-based method for authenticating gold and silver coins. It involves acquiring a multi-frame image sequence of the gold or silver coin to be authenticated under a multi-angle ring light source array. The normal vector matrix and height map matrix of the coin's surface are calculated using a photometric stereo method. The multi-angle ring light source array includes a predetermined number of point light sources evenly distributed on the circumference. The predetermined number is an integer greater than or equal to 3. The plane of the light source array is perpendicular to the camera's optical axis, which passes through the center of the circumference of the light source array. The gold or silver coin to be authenticated is placed at the intersection of the camera's optical axis and the central axis of the light source array, ensuring that the reference plane of the coin's surface is parallel to the camera's imaging plane. A preset number of point light sources are lit sequentially, with only one point light source lit at a time, while the rest remain off. The lighting of the camera and the point light sources are triggered synchronously, acquiring a single-frame grayscale image of the gold or silver coin to be appraised under the illumination of each point light source. All single-frame grayscale images constitute a multi-frame image sequence. The pixel coordinate system of each frame image maintains a fixed mapping relationship with the camera coordinate system. The direction of the camera's line of sight vector is the direction from the camera's optical axis to the surface of the gold or silver coin to be appraised, corresponding to the negative Z-axis direction of the camera coordinate system.

[0044] A mask cropping process is applied to single-frame grayscale images corresponding to a preset number of point light sources, retaining the effective pixel areas containing the main pattern of the gold or silver coin to be authenticated. Specifically, threshold segmentation is performed on any single-frame grayscale image to obtain a segmentation threshold that distinguishes the coin face area from the background area. A binarized image is generated based on the segmentation threshold. Morphological processing is performed on the binarized image to eliminate isolated noise points and internal holes, extracting the continuous circular contour of the coin face. A circular binary mask is generated based on the center and radius of the circular contour. The size of the binary mask is consistent with the size of the single-frame grayscale image. Pixels within the circular area have a value of 1, and pixels outside the circular area have a value of 0. The generated binary mask is then multiplied element-wise with all single-frame grayscale images to obtain a grayscale image containing only the effective pixel areas of the coin face. Pixels within the effective pixel areas retain their original grayscale values, while pixel values ​​in the background area are set to 0 to eliminate interference from the background area in subsequent calculations.

[0045] Based on the grayscale values ​​within the effective pixel region, the light source direction vector, and the camera viewing vector, the surface reflection equation is solved to generate the normal vector matrix. The surface reflection equation is constructed using a Lambertian diffuse reflection model, and the corresponding formula is as follows:

[0046] Where I(p) is the gray value corresponding to pixel p. Let p be the surface albedo. Let p be the unit normal vector. Let be the unit light source direction vector. Both the light source direction vector and the camera view vector are represented uniformly in the camera coordinate system. When there are N light sources with different directions, a system of linear overdetermined equations can be obtained, with the corresponding formulas as follows:

[0047] in, Let be an N-dimensional column vector, where each element corresponds to the grayscale value of a pixel p under a given light source. This is an N×3 light source direction matrix, where each row corresponds to a unit light source direction vector. This is a 3D unit normal vector column vector. The linear overdetermined equations are solved using the least squares method to obtain the 3D normal vector coordinates corresponding to each pixel. These coordinates are then arranged according to the pixel rows and columns on the surface of the gold or silver coin to be authenticated, generating a normal vector matrix. In this matrix, the 3D normal vector corresponding to each pixel is a unit vector.

[0048] An integral transformation is performed on the normal vector matrix to generate a height map matrix. The Poisson equation is then constructed using the components of the normal vectors, as shown in the following formula:

[0049] Where h(x,y) is the height value corresponding to the pixel coordinates (x,y). , , These represent the components of the normal vector along the X, Y, and Z axes of the camera coordinate system. This is the Laplace operator. The Poisson equation is solved using discrete cosine transform to obtain the height value corresponding to each pixel on the surface of the gold or silver coin to be authenticated. A height map matrix is ​​generated according to the pixel row and column arrangement, and the size of the height map matrix is ​​exactly the same as the size of the normal vector matrix.

[0050] The normal vector matrix is ​​input into the graph convolution feature extraction branch. A topology graph is constructed using the surface pixels of the gold and silver coins to be identified as nodes and spatial adjacency relationships as edges to extract global geometric features. The normal vector matrix is ​​downsampled to obtain a gridded node set. Uniform grid sampling is used to divide the pixel plane corresponding to the normal vector matrix into equally sized grid cells. Each grid cell corresponds to a node, whose coordinates are the coordinates of the center pixel of the grid cell, and whose attributes are the three-dimensional components of the normal vector corresponding to the center pixel. A topology graph is constructed using the spatial adjacency relationships of the nodes as edges. Each node's neighboring nodes are its 8-neighbors, i.e., nodes adjacent to the center node in the horizontal, vertical, and diagonal directions. An undirected edge is constructed between any two adjacent nodes. The cosine of the angle between the normal vectors of any two adjacent nodes in the gridded node set is calculated and used as the edge weight of the connecting edges in the topology graph. The corresponding formula is as follows:

[0051] in, Let be the edge weight between node i and node j. Let i be the normal vector corresponding to node i. Let j be the normal vector corresponding to node j.

[0052] The L2 norm is used. Since the normal vector is a unit vector, the formula can be simplified to the dot product of two normal vectors. The edge weight ranges from [-1, 1]. When the normal vectors of two nodes are in the same direction, the edge weight is 1, corresponding to the flat area of ​​the coin surface. The greater the difference in the normal vector directions of the two nodes, the smaller the edge weight, corresponding to the curvature variation area of ​​the coin surface.

[0053] The core parameters for the topology graph construction process in this embodiment are defined in the following table:

[0054] This table clarifies the definition and constraints of the core parameters in the construction of the topology graph, ensuring that the topology graph can accurately map the three-dimensional geometric features of the surface of the gold and silver coins to be identified, and providing standardized input data for subsequent graph convolution feature extraction.

[0055] The topology graph is input into the graph convolutional feature extraction branch, which consists of multiple graph convolutional layers. The graph convolutional layers perform message passing and aggregation updates on node attributes and edge weights, outputting global geometric features including coin surface curvature and embossing depth variations. The graph convolutional feature extraction branch contains three sequentially connected graph convolutional layers. The output of each graph convolutional layer undergoes layer normalization and non-linear activation function processing. In each graph convolutional layer, for each central node in the topology graph, all first-order neighboring nodes are obtained. The node attributes of the central node are concatenated with the node attributes of each of its first-order neighboring nodes. The concatenated vector is then multiplied by the edge weights connecting the central node to each of its first-order neighboring nodes to generate edge feature messages. All edge feature messages are summed and aggregated. The aggregation result is input into a non-linear activation function, and the activated result updates the node attributes of the central node in the current graph convolutional layer. The corresponding formula is as follows:

[0056] in, Let i be the updated node attributes of node i in the (l+1)th graph convolutional layer. Let be the set of all first-order neighbor nodes of node i. Let L be the learnable weight matrix of the l-th graph convolutional layer. This is a vector concatenation operation for the node attributes of node i and node j at the l-th layer. Let l be the bias vector of the l-th graph convolutional layer. The ReLU nonlinear activation function is used. The first graph convolutional layer has 3 input channels, corresponding to the three-dimensional components of the normal vector. The second graph convolutional layer has 64 output channels, and the third graph convolutional layer has 128 output channels. Finally, the output attributes of all nodes are globally averaged and pooled to obtain a global geometric feature with a dimension of 128.

[0057] The height map matrix is ​​input into the spatial attention feature extraction branch to filter out high-frequency noise in the specular reflection region and extract local texture anomaly features. The spatial attention feature extraction branch employs a U-shaped network structure consisting of an encoder and a decoder. The encoder extracts multi-scale height feature maps through multi-level convolutional operations. The encoder contains four levels of convolutional blocks, each containing two 3×3 convolutional layers and one 2×2 max-pooling layer. With each convolutional block, the spatial resolution of the feature map is reduced to half its original value, while the number of channels is doubled. The first level of convolutional block has 1 input channel, corresponding to a single channel of the height map matrix, and 32 output channels. The second level has 64 output channels, the third level has 128 output channels, and the fourth level has 256 output channels, resulting in four different scale height feature maps, forming a multi-scale height feature map.

[0058] The multi-scale height feature map is input into the spatial attention sub-network. The attention weight coefficient for each spatial location in the multi-scale height feature map is calculated, and then the attention weight coefficient is multiplied element-wise with the multi-scale height feature map. The formula for calculating the spatial attention weight coefficient is as follows:

[0059] in, Given the spatial attention weight coefficient matrix corresponding to the input feature map F, This refers to the average pooling operation performed along the channel dimension on the input feature map F. This refers to the max pooling operation performed on the input feature map F along the channel dimension. Here is the learnable weight matrix of the convolutional layers in the spatial attention subnetwork. The Sigmoid activation function maps the output values ​​to the [0,1] interval. Both average pooling and max pooling operations output feature maps with 1 channel, and their spatial resolution is the same as the input feature maps. Figure 1 The concatenated feature map has 2 channels. After passing through a convolutional layer with a kernel size of 7×7, it outputs an attention weight coefficient matrix with 1 channel. The weight value of each spatial location in this matrix reflects the importance of the feature at that location. For high-frequency noise in the specular reflection area, the weight value approaches 0, and for texture abnormal areas on the coin surface, the weight value approaches 1.

[0060] The multiplied multi-scale height feature map is input into the decoder, and deconvolution is performed to restore it to the same resolution as the height map matrix, outputting local texture anomaly features. The decoder contains four levels of deconvolution blocks, each containing one 2×2 deconvolution layer and two 3×3 convolution layers. With each level of deconvolution, the spatial resolution of the feature map is doubled, while the number of channels is halved. The input of each level of deconvolution in the decoder is skip-connected to the output of the corresponding level of convolution in the encoder, fusing the low-level features extracted by the encoder with the high-level features of the decoder. The final feature map output by the decoder has the same spatial resolution as the input height map matrix and 128 channels. Global average pooling is then performed on this feature map to obtain local texture anomaly features with a dimension of 128.

[0061] A cross-modal adaptive feature fusion layer is constructed. The fusion weight matrix of global geometric features and local texture anomaly features is dynamically calculated based on the gradient magnitude of local regions in the normal vector matrix. The global geometric features and local texture anomaly features are then weighted and concatenated. The normal vector matrix is ​​divided into multiple non-overlapping local window regions, each with a size of 8×8 pixels. There is no overlap between adjacent windows. The difference between the normal vectors in the horizontal and vertical directions within each local window region is calculated. The square root of the sum of the squares of these differences is taken as the gradient magnitude of the local window region, as shown in the following formula:

[0062] Where G(x,y) is the gradient magnitude corresponding to the local window region (x,y). This represents the average difference in the horizontal direction of the X-axis component of the normal vector within this local window region. This is the average difference in the vertical direction of the Y-axis component of the normal vector within the local window region. The magnitude of the gradient reflects the degree of change in the geometric shape of the coin surface within the local window region. The larger the gradient magnitude, the more drastic the curvature change in the region; the smaller the gradient magnitude, the flatter the coin surface in the region.

[0063] Gradient magnitudes from all local window regions are concatenated to form a gradient feature map. The spatial resolution of the gradient feature map is consistent with the number of local window regions, and it has one channel. This gradient feature map is then input into a weight prediction subnetwork containing two convolutional kernels. The output is a fusion weight matrix with the same number of channels as the global geometric shape feature. The calculation process for the fusion weight coefficients corresponds to the following formula:

[0064] in, The fusion weight coefficient is the value corresponding to the c-th channel. The learnable weight matrix is ​​the first layer convolutional kernel of the weight prediction subnetwork. Let G be the learnable weight matrix of the second convolutional kernel of the weight prediction subnetwork, where G is the gradient feature map and C is the number of channels for the global geometric features. The first convolutional kernel of the weight prediction subnetwork has a size of 3×3, a stride of 1, padding of 1, and 64 output channels. The second convolutional kernel has a size of 1×1, a stride of 1, padding of 0, and the number of output channels is the same as the number of channels for the global geometric features. After Softmax normalization, the sum of the fusion weight coefficients for each channel is 1, resulting in the fusion weight matrix.

[0065] The global geometric features and local texture anomaly features are weighted and concatenated. The fusion weight matrix is ​​multiplied with the global geometric features channel by channel. The result of subtracting the fusion weight matrix from 1 is multiplied with the local texture anomaly features channel by channel. The two multiplied feature vectors are concatenated along the channel dimension to obtain a concatenated feature vector with dimension 256.

[0066] The concatenated feature vector is input into a fully connected classification layer, which outputs the authentication result of the gold and silver coins to be authenticated. The concatenated feature vector is then sequentially input into a flattening layer, a random deactivation layer, and two sequentially connected fully connected layers. The flattening layer flattens the 256-dimensional feature vector into a one-dimensional vector. The random deactivation layer sets the feature dimension of the output from the flattening layer to zero according to a preset discard probability of 0.5. This preset discard probability is effective during model training but disabled during model inference. The first fully connected layer has an input dimension of 256 and an output dimension of 64. The second fully connected layer has an input dimension of 64 and two output nodes, corresponding to the genuine coin category and the counterfeit coin category, respectively. An activation function maps the output values ​​of the two output nodes to probability values ​​in the interval [0,1], as shown in the following formula:

[0067] in, This represents the category probability value corresponding to the k-th output node. The output value of the kth output node of the second fully connected layer is used as the category corresponding to the maximum value among the probability values, and the authenticity of the gold and silver coins to be identified is selected.

[0068] This embodiment acquires multiple frames of images using a multi-angle ring light source array, and combines photometric stereo method to obtain the three-dimensional normal vector and height information of the coin surface. The authentication problem in the two-dimensional image domain is transformed into feature analysis in the three-dimensional shape domain. A dual-branch feature extraction network is used to obtain global geometric shape features and local texture anomaly features respectively. Adaptive feature fusion is combined to realize dynamic weighting of the two types of features. Finally, the authenticity authentication result is output through the classification layer, eliminating the interference of specular reflection highlights on feature extraction and ensuring the reliability of the authentication result.

[0069] In another embodiment, the acquisition of multiple image sequences and the calculation of the normal vector matrix are refined to address the metallic reflective characteristics of the surface of the gold and silver coins to be authenticated. A multi-angle ring light source array includes a preset number of point light sources evenly distributed on a circumference. The preset number is set to 12. The 12 point light sources are evenly distributed on a circumference of fixed radius. The plane of the circumference is perpendicular to the camera's optical axis. The light emission direction of each point light source points to the center of the circumference, i.e., the placement position of the gold and silver coins to be authenticated. The 12 point light sources are controlled to light up sequentially, with only one point light source lit at a time, while the remaining 11 point light sources are turned off. The camera and the lighting of the point light sources are triggered synchronously, acquiring single-frame grayscale images of the gold and silver coins to be authenticated under the illumination of each point light source. A total of 12 single-frame grayscale images are acquired, forming a multi-frame image sequence.

[0070] Twelve single-frame grayscale images are masked and cropped to retain the effective pixel areas containing the main pattern of the gold and silver coins to be identified. Specifically, Otsu's threshold segmentation method is applied to any single-frame grayscale image to obtain a segmentation threshold that distinguishes the coin face area from the background area. A binarized image is generated based on the segmentation threshold. Morphological opening and closing operations are performed on the binarized image to eliminate isolated noise points and holes, extracting the continuous circular contour of the coin face. A circular binary mask is generated based on the center and radius of the circular contour. The size of the binary mask is consistent with the size of the single-frame grayscale image. Pixels within the circular area have a value of 1, and pixels outside the circular area have a value of 0. The generated binary mask is then multiplied element-wise with each of the 12 single-frame grayscale images to obtain 12 grayscale images containing only the effective pixel areas of the coin face. Pixels within the effective pixel areas retain their original grayscale values, while pixel values ​​in the background area are set to 0 to eliminate interference from the background area in subsequent solving processes.

[0071] Based on the grayscale values ​​within the effective pixel region, the light source direction vector, and the camera viewing vector, the surface reflection equation is solved to generate the normal vector matrix. A Lambertian diffuse reflection model is used to construct the surface reflection equation. Based on this model, the surface roughness parameter and metal reflectivity parameter of the gold and silver coins to be authenticated are introduced as regularization constraints, transforming the surface reflection equation into a linear overdetermined system of equations, which is then further transformed into a constrained optimization problem. The corresponding formulas are as follows:

[0072] The first term is the data fidelity term, which is used to ensure that the normal vector and albedo obtained from the solution can fit the collected gray values. and The regularization coefficient is . The surface roughness parameters of the gold and silver coins to be identified. This is a metal reflectivity constraint term, used to constrain the relationship between the reflectivity and roughness of metallic materials. This is the total variational regularization term for the normal vector, used to constrain the continuity of the normal vectors of adjacent pixels and eliminate abrupt changes in the normal vector caused by specular reflection noise.

[0073] The constrained optimization problem is solved iteratively using the alternating direction multiplier method. The original problem is decomposed into three subproblems, and the normal vector, albedo, and auxiliary variables are solved alternately and iteratively respectively. The corresponding iterative formulas are as follows:

[0074] Where k is the number of iterations. As an auxiliary variable, As dual variables, The penalty coefficient is used to determine the convergence condition of the iterative process. The L2 norm of the difference between the normal vectors of two consecutive iterations is less than a preset convergence threshold, which is set to... When the number of iterations reaches the preset maximum number of iterations, 1000, the iteration will terminate regardless of whether the convergence condition is met.

[0075] The correspondence between the parameters and convergence states in the iterative solution process of the alternating direction multiplier method in this embodiment is shown in the table below:

[0076] This table shows the relationship between the number of iterations and the solution accuracy in solving the surface reflection equation with regularization constraints. By setting reasonable convergence thresholds and maximum number of iterations, the computational load of the solution process can be controlled while ensuring the solution accuracy, so that the normal vector matrix can accurately reflect the true three-dimensional geometry of the coin surface.

[0077] After iterative solving, the 3D normal vector coordinates corresponding to each pixel on the surface of the gold or silver coin to be authenticated are obtained. These coordinates are then arranged according to the pixel rows and columns of the coin's surface to generate a normal vector matrix, where each pixel's 3D normal vector is a unit vector. An integral transformation is performed on the normal vector matrix to generate a height map matrix. The integral transformation uses a Poisson solver, constructing a Poisson equation based on the X-axis and Y-axis components of the normal vectors. The Poisson equation is then solved using discrete cosine transform to obtain the height value corresponding to each pixel, generating a height map matrix with the same dimensions as the normal vector matrix.

[0078] This embodiment acquires multiple frames of images by sequentially illuminating 12 equally spaced point light sources. Background interference is eliminated by combining mask clipping. By introducing regularization constraints on surface roughness and metal reflectivity, a constrained optimization problem is constructed. The normal vector matrix is ​​solved iteratively using the alternating direction multiplier method, which suppresses the interference of the specular reflection component of the metal surface on the solution of the normal vector, improves the solution accuracy of the normal vector matrix and height map matrix, and provides high-quality three-dimensional topography data for subsequent feature extraction.

[0079] refer to Figure 3 In a preferred embodiment, the topology graph construction and node attribute update process of the graph convolution feature extraction branch, and the multi-scale feature extraction and attention weight calculation process of the spatial attention feature extraction branch are refined. The normal vector matrix is ​​input into the graph convolution feature extraction branch, and a topology graph is constructed using the surface pixels of the gold and silver coins to be identified as nodes and spatial adjacency relationships as edges to extract global geometric features. The normal vector matrix is ​​downsampled to obtain a gridded node set. The downsampling process uses bilinear interpolation downsampling, downsampling the original H×W×3 normal vector matrix into a h×w×3 feature map, where h=H / 4 and w=W / 4. Each pixel in the downsampled feature map corresponds to a gridded node, resulting in a total of h×w nodes, forming a gridded node set. The pixel coordinates corresponding to each node are used as the node position attribute of the topology graph, and the three-dimensional components of the normal vector corresponding to each node are used as the node feature attribute of the topology graph.

[0080] Calculate the cosine of the angle between the normal vectors of any two adjacent nodes in the gridded node set, and use this cosine as the edge weight of the connecting edge in the topology graph. For each node in the gridded node set, determine its 8-neighborhood neighbors, i.e., nodes adjacent to the center node in the horizontal, vertical, and diagonal directions. The absolute value of the difference between the coordinates of the adjacent node and the coordinates of the center node does not exceed one grid cell. For each pair of adjacent center node and neighboring nodes, calculate the dot product of the normal vectors of the two nodes, which is used as the edge weight of the edge connecting the two nodes. For non-adjacent nodes, no connecting edge is constructed, and the edge weight is 0. Construct an undirected topology graph based on the node set and edge weights. The adjacency matrix of the topology graph is a sparse matrix of h×w×h×w, with non-zero edge weight values ​​only at the positions corresponding to adjacent nodes.

[0081] The topology graph is input into the graph convolutional feature extraction branch, which consists of multiple graph convolutional layers. The graph convolutional layers perform message passing and aggregation updates on node attributes and edge weights, outputting global geometric features including coin surface curvature and embossing depth variations. The graph convolutional feature extraction branch contains three sequentially connected graph convolutional layers. The output of each layer undergoes layer normalization and non-linear activation function processing. In each graph convolutional layer, for each central node in the topology graph, all first-order neighboring nodes are obtained. The node attributes of the central node are concatenated with the node attributes of each of its first-order neighboring nodes. The concatenated vector is multiplied by the edge weights connecting the central node to each of its first-order neighboring nodes to generate edge feature messages. All edge feature messages are summed and aggregated. The aggregation result is multiplied by the learnable weight matrix of the graph convolutional layer, and after adding a bias vector, it is input into a non-linear activation function. The activated result updates the node attributes of the central node in the current graph convolutional layer. The corresponding formula is as follows:

[0082] in, In the l-th graph convolutional layer, the edge feature message passed from node j to node i is... The aggregation result of the neighborhood messages of node i. For layer normalization operation, This is the ReLU nonlinear activation function, and the definitions of the other parameters are the same as those in the previous formula.

[0083] The mapping relationship between the core parameters and node attributes of each graph convolutional layer in this embodiment is shown in the following table:

[0084] This table clarifies the mapping relationship between the core parameter settings of each graph convolutional layer and the node attributes. By progressively increasing the dimension of node attributes, a wider range of neighborhood messages are aggregated, enabling multi-scale extraction of the global geometric features of the coin surface. This ensures that the features can cover the overall embossed outline and relief depth changes of the coin surface.

[0085] The first graph convolutional layer has an input node attribute dimension of 3 and an output node attribute dimension of 64. The second graph convolutional layer has an input node attribute dimension of 64 and an output node attribute dimension of 128. The third graph convolutional layer has an input node attribute dimension of 128 and an output node attribute dimension of 128. Global average pooling and global max pooling are performed on all node attributes output by the third graph convolutional layer. The two pooled vectors are concatenated to obtain a global geometric shape feature with a dimension of 256.

[0086] refer to Figure 4The height map matrix is ​​input into the spatial attention feature extraction branch to filter out high-frequency noise in the specular reflection area and extract local texture anomaly features. The height map matrix is ​​input into a U-shaped network structure consisting of an encoder and a decoder. The encoder extracts multi-scale height feature maps through multi-level convolutional operations. The encoder contains four levels of convolutional blocks. Each level of convolutional block contains two convolutional layers with a kernel size of 3×3, a stride of 1, and padding of 1, and a max pooling layer with a kernel size of 2×2 and a stride of 2. Each level of convolutional block is followed by a batch normalization layer and a ReLU activation function. The input of the first level of convolutional block is a single-channel height map matrix, and the output has 32 channels and a feature map size of H×W. The output of the second level of convolutional block has 64 channels and a feature map size of H / 2×W / 2. The output of the third level of convolutional block has 128 channels and a feature map size of H / 4×W / 4. The output of the fourth level of convolutional block has 256 channels and a feature map size of H / 8×W / 8. The feature maps output by the four levels of convolutional blocks constitute a multi-scale height feature map.

[0087] The multi-scale height feature map is input into the spatial attention subnetwork, and the attention weight coefficient for each spatial location in the multi-scale height feature map is calculated. For each scale feature map in the multi-scale height feature map, max pooling and average pooling operations are performed along the channel dimension. The kernel size of max pooling and average pooling operations is 1×1, and the stride is 1. The number of channels in the output max pooling feature map and average pooling feature map is 1. The spatial resolution is the same as the input feature map. Figure 1 The max-pooling feature map and the average-pooling feature map are concatenated along the channel dimension to obtain a concatenated feature map with 2 channels. This concatenated feature map is then input into a cascaded network consisting of a 7×7 convolutional layer with a stride of 1 and padding of 3, and a sigmoid activation function. The convolutional layer has 2 input channels and 1 output channel. The output is the attention weight coefficient of the spatial attention subnetwork, which has 1 channel. The spatial resolution is the same as the input feature map. Figure 1 The attention weight coefficients are multiplied element-wise with the corresponding multi-scale height feature maps to obtain a weighted multi-scale height feature map. In the weighted feature map, the features corresponding to high-frequency noise in the specular reflection region are suppressed, while the features corresponding to abnormal coin surface texture regions are enhanced.

[0088] The multiplied multi-scale height feature map is input into the decoder, and deconvolution is performed to restore it to the same resolution as the height map matrix, outputting local texture anomaly features. The decoder contains four levels of deconvolution blocks. Each level of deconvolution block contains one deconvolution layer with a kernel size of 2×2 and a stride of 2, and two convolutional layers with a kernel size of 3×3, a stride of 1, and padding of 1. Each level of deconvolution block is followed by a batch normalization layer and a ReLU activation function. The output of the deconvolution layer of each level of the decoder is concatenated with the output of the corresponding level of the encoder's convolutional block in the channel dimension, and used as the input of the convolutional layer of that level of deconvolution block to achieve skip connections. The input to the first-level deconvolution block is the weighted feature map output from the fourth-level convolution block. The output has 128 channels and a feature map size of H / 4 × W / 4. The second-level deconvolution block has 64 output channels and a feature map size of H / 2 × W / 2. The third-level deconvolution block has 32 output channels and a feature map size of H × W. The fourth-level deconvolution block has 128 output channels and a feature map size of H × W, with the same resolution as the input heightmap matrix. Global average pooling and global max pooling are performed on the feature map output from the fourth-level deconvolution block. The two pooled vectors are concatenated to obtain a local texture anomaly feature with a dimension of 256.

[0089] This embodiment constructs a gridded node set through downsampling, builds a topology graph with the cosine of the angle between the normal vectors as the edge weights, and achieves multi-scale extraction of global geometric features of the coin surface through message passing and aggregation updates of multi-layer graph convolutional layers. Combined with a spatial attention sub-network, the multi-scale height feature map is weighted to filter out high-frequency noise in the specular reflection area and enhance the features of local texture abnormal areas, providing more discriminative feature data for subsequent feature fusion and classification.

[0090] refer to Figure 5 and 6 In another preferred embodiment, the weight calculation and feature fusion process of the cross-modal adaptive feature fusion layer, as well as the feature processing and authenticity identification output process of the fully connected classification layer, are refined. A cross-modal adaptive feature fusion layer is constructed. Based on the gradient magnitude of local regions in the normal vector matrix, the fusion weight matrix of global geometric features and local texture anomaly features is dynamically calculated, and the global geometric features and local texture anomaly features are weighted and concatenated. The normal vector matrix is ​​divided into multiple non-overlapping local window regions, each with a size of M×M pixels, where M is 8. Adjacent local window regions have no overlap or gaps. The normal vector matrix has a size of H×W×3, therefore, it is divided into... For each local window region, if the edge region of the normal vector matrix is ​​less than M×M pixels, it is padded with zero to M×M pixels to ensure that all local window regions have the same size.

[0091] Calculate the difference between the normal vector in the horizontal and vertical directions within each local window region. Take the square root of the sum of the squares of these differences as the gradient magnitude of the local window region. For all pixels within each local window region, calculate the first-order difference of the X-axis component of the normal vector in the horizontal direction and the first-order difference of the Y-axis component in the vertical direction. Average the first-order differences in the horizontal direction for all pixels within the local window region to obtain the average horizontal difference value for that local window region. The average vertical difference value of the local window region is obtained by averaging the first-order differences of all pixels in the vertical direction. The gradient magnitude of the local window region is calculated based on the average difference between the horizontal and vertical directions. The gradient magnitudes of all local window regions are then subjected to minimum-maximum normalization to map the range of gradient magnitudes to the [0,1] interval, thereby eliminating the influence of magnitude differences between different batches of data.

[0092] The gradient magnitudes of all local window regions are concatenated according to their spatial positions in the normal vector matrix to generate a gradient feature map. The spatial size of the gradient feature map is [value missing]. The gradient feature map is input into a weight prediction subnetwork containing two convolutional kernels, and the output channel number is the same as that of the global geometric feature map. The first convolutional kernel of the weight prediction subnetwork has a kernel size of 3×3, a stride of 1, padding of 1, an input channel of 1, and an output channel number of 64. The output of the first convolutional kernel is processed by the ReLU activation function to generate the first feature map, and the spatial resolution of the first feature map is the same as that of the gradient feature map. The first feature map is input into the second convolutional kernel of the weight prediction subnetwork. The second convolutional kernel has a kernel size of 1×1, a stride of 1, padding of 0, an input channel number of 64, and an output channel number that is the same as that of the global geometric feature map. Here, the global geometric feature map has 256 channels, so the output channel number of the second convolutional kernel is 256, generating the initial weight matrix. The spatial size of the initial weight matrix is ​​the same as that of the gradient feature map, and the number of channels is 256.

[0093] The initial weight matrix is ​​normalized for each channel dimension, and the normalized matrix is ​​used as the fusion weight matrix. The initial weight matrix is ​​then subjected to Softmax normalization along the channel dimensions, as shown in the following formula:

[0094] in, To fuse the weights of the spatial location (x, y) and the weight coefficient corresponding to the c-th channel in the weight matrix, Let be the value corresponding to the c-th channel at spatial position (x, y) in the initial weight matrix, where C is the number of channels in the initial weight matrix. After Softmax normalization, the sum of the weight coefficients of all channels at each spatial position in the fused weight matrix is ​​1, with a value range of [0, 1].

[0095] The correspondence between the gradient magnitude of the local window region and the fusion weight coefficient in this embodiment is shown in the table below:

[0096] The table shows the correspondence between the gradient magnitude of the local window region and the fusion weight coefficient of the two types of features. The larger the gradient magnitude, the higher the weight coefficient of the global geometric shape feature. The smaller the gradient magnitude, the higher the weight coefficient of the local texture anomaly feature. This realizes adaptive feature fusion based on local geometric shape changes and improves the robustness of features to the manufacturing tolerance and circulation wear of genuine coins.

[0097] The global geometric features and local texture anomaly features are weighted and concatenated. Both the global geometric features and local texture anomaly features have 256 channels and a spatial size of 1×1. The fusion weight matrix is ​​subjected to global average pooling to obtain a fusion weight vector of dimension 256. The fusion weight vector is multiplied channel-by-channel with the global geometric features to obtain the weighted global geometric features. The result of subtracting the fusion weight vector from 1 is multiplied channel-by-channel with the local texture anomaly features to obtain the weighted local texture features. The weighted global geometric features and the weighted local texture features are concatenated along the channel dimension to obtain a concatenated feature vector of dimension 512.

[0098] The concatenated feature vector is input into a fully connected classification layer, which outputs the authentication result of the gold and silver coins to be authenticated. The concatenated feature vector is then sequentially input into a flattening layer, a random deactivation layer, and two sequentially connected fully connected layers. The flattening layer flattens the 512-dimensional feature vector into a one-dimensional vector of length 512. The random deactivation layer zeros out the feature dimensions output by the flattening layer according to a preset discard probability of 0.5. During the model training phase, the random deactivation layer randomly selects 50% of the feature dimensions for zeroing to avoid overfitting. During the model inference phase, the zeroing operation is disabled in the random deactivation layer, and all feature dimensions participate in the calculation.

[0099] The first fully connected layer has an input dimension of 512 and an output dimension of 128. The output of the first fully connected layer undergoes batch normalization and ReLU activation to generate an intermediate feature vector of dimension 128. The second fully connected layer has an input dimension of 128 and two output nodes, corresponding to the genuine coin category and the counterfeit coin category, respectively. The output of the second fully connected layer undergoes Softmax activation, mapping the output values ​​of the two output nodes to probability values ​​within the interval [0,1]. The sum of the two probability values ​​is 1. The category corresponding to the maximum probability value is selected as the authentication result for the gold or silver coin to be authenticated. When the probability value of the first output node is greater than the probability value of the second output node, the authentication result is genuine; when the probability value of the second output node is greater than the probability value of the first output node, the authentication result is counterfeit.

[0100] This embodiment calculates the gradient magnitude of the normal vector by dividing a local window region. Based on the gradient magnitude, an adaptive fusion weight matrix is ​​generated through a weight prediction sub-network, realizing the dynamic weighted fusion of global geometric features and local texture anomaly features. Combined with feature processing and probability mapping of the fully connected classification layer, the authenticity of the gold and silver coins to be identified is output, reducing the misjudgment rate of genuine coins in the same batch due to manufacturing tolerances and improving the robustness of the identification model to gold and silver coins under different circulation wear conditions.

Claims

1. A deep learning-based method for authenticating gold and silver coins against counterfeits, characterized in that: include: A multi-frame image sequence of the gold and silver coins to be identified was acquired under a multi-angle ring light source array, and the normal vector matrix and height map matrix of the surface of the gold and silver coins to be identified were calculated by photometric stereo method. The normal vector matrix is ​​input into the graph convolution feature extraction branch, and a topological graph is constructed with the surface pixels of the gold and silver coins to be identified as nodes and spatial adjacency relationships as edges to extract global geometric features. The height map matrix is ​​input into the spatial attention feature extraction branch to filter out high-frequency noise in the specular reflection area and extract local texture anomaly features. A cross-modal adaptive feature fusion layer is constructed. The fusion weight matrix of the global geometric features and the local texture anomaly features is dynamically calculated based on the gradient magnitude of the local region in the normal vector matrix. The global geometric features and the local texture anomaly features are then weighted and concatenated. The concatenated feature vector is input into a fully connected classification layer, which outputs the authentication result of the gold and silver coins to be authenticated.

2. The deep learning-based anti-counterfeiting authentication method for gold and silver coins according to claim 1, characterized in that, The process of acquiring a multi-frame image sequence of the gold and silver coin to be identified under a multi-angle ring light source array and calculating the normal vector matrix and height map matrix of the surface of the gold and silver coin to be identified using the photometric stereo method includes: the multi-angle ring light source array containing a preset number of point light sources evenly distributed on the circumference, controlling the preset number of point light sources to be lit sequentially, and acquiring a single-frame grayscale image of the gold and silver coin to be identified under the illumination of each point light source. The single-frame grayscale image corresponding to the preset number of point light sources is masked and cropped to retain the effective pixel area containing the main pattern of the gold and silver coins to be identified. Based on the gray values, light source direction vector, and camera viewing vector within the effective pixel area, the surface reflection equation is solved to generate the normal vector matrix; The height map matrix is ​​generated by performing an integral transformation on the normal vector matrix.

3. The deep learning-based anti-counterfeiting authentication method for gold and silver coins according to claim 1, characterized in that, The step of inputting the normal vector matrix into the graph convolution feature extraction branch, constructing a topology graph with the surface pixels of the gold and silver coins to be identified as nodes and spatial adjacency relationships as edges, and extracting global geometric features includes: performing downsampling processing on the normal vector matrix to obtain a gridded node set, and using the node coordinates in the gridded node set as the node attributes of the topology graph; Calculate the cosine of the angle between the normal vectors of any two adjacent nodes in the gridded node set, and use the cosine of the angle between the normal vectors as the edge weight of the connecting edge in the topology graph; The topology graph is input into the graph convolution feature extraction branch, which consists of multiple graph convolution layers. The graph convolution layers perform message passing and aggregation updates on the node attributes and edge weights, and output the global geometric features that include the coin surface curvature change features and the embossing depth change features.

4. The deep learning-based anti-counterfeiting authentication method for gold and silver coins according to claim 1, characterized in that, The step of inputting the height map matrix into the spatial attention feature extraction branch to filter out high-frequency noise in the specular reflection area and extract local texture anomaly features includes: inputting the height map matrix into a U-shaped network structure composed of an encoder and a decoder, wherein the encoder extracts multi-scale height feature maps through multi-level convolution operations; The multi-scale height feature map is input into the spatial attention sub-network, the attention weight coefficient of each spatial location in the multi-scale height feature map is calculated, and the attention weight coefficient is multiplied element-wise with the multi-scale height feature map. The multiplied multi-scale height feature map is input into the decoder, and deconvolution is performed to restore it to the same resolution as the height map matrix, outputting the local texture anomaly features.

5. The deep learning-based anti-counterfeiting authentication method for gold and silver coins according to claim 1, characterized in that, The construction of the cross-modal adaptive feature fusion layer, which dynamically calculates the fusion weight matrix of the global geometric features and the local texture anomaly features based on the gradient magnitude of the local regions in the normal vector matrix, includes: dividing the normal vector matrix into multiple non-overlapping local window regions, calculating the difference between the normal vectors in the horizontal and vertical directions in each local window region, and taking the square root of the sum of the squares of the differences in the horizontal and vertical directions as the gradient magnitude of the local window region; The gradient magnitudes of all the local window regions are concatenated to form a gradient feature map. The gradient feature map is then input into a weight prediction subnetwork containing two convolutional kernels, and the fusion weight matrix with the same number of channels as the global geometric feature channels is output.

6. The deep learning-based anti-counterfeiting authentication method for gold and silver coins according to claim 1, characterized in that, The step of inputting the spliced ​​feature vector into a fully connected classification layer and outputting the authenticity identification result of the gold and silver coins to be identified includes: inputting the spliced ​​feature vector into a flattening layer, a random deactivation layer and two fully connected layers in sequence, and the random deactivation layer sets the feature dimension output by the flattening layer to zero according to a preset discard probability. The second fully connected layer has two output nodes, and the output values ​​of the two output nodes are mapped to probability values ​​within a range using an activation function. The category corresponding to the maximum value among the probability values ​​is selected as the authenticity authentication result of the gold and silver coins to be authenticated.

7. The deep learning-based anti-counterfeiting authentication method for gold and silver coins according to claim 2, characterized in that, The step of solving the surface reflection equation based on the gray values, light source direction vector, and camera line-of-sight vector within the effective pixel area to generate the normal vector matrix includes: constructing the surface reflection equation using a Lambertian diffuse reflection model and transforming the surface reflection equation into a linear overdetermined system of equations. By introducing the surface roughness parameter and metal reflectivity parameter of the gold and silver coins to be identified as regularization constraints, the linear overdetermined equations are transformed into a constrained optimization problem. The constrained optimization problem is solved iteratively using the alternating direction multiplier method to obtain the three-dimensional normal vector coordinates corresponding to each pixel on the surface of the gold and silver coin to be identified. The three-dimensional normal vector coordinates are then arranged according to the pixel rows and columns on the surface of the gold and silver coin to be identified to generate the normal vector matrix.

8. The deep learning-based anti-counterfeiting authentication method for gold and silver coins according to claim 3, characterized in that, The step of performing message passing and aggregation updates on the node attributes and edge weights through the graph convolutional layer includes: in each graph convolutional layer, for each central node in the topology graph, obtaining all first-order neighboring nodes of the central node; The node attributes of the central node are concatenated with the node attributes of each of the first-order neighboring nodes, and the concatenated vector is multiplied by the edge weights connecting the central node to each of the first-order neighboring nodes to generate an edge feature message. All the edge feature messages are summed and aggregated, and the aggregation result is input into a non-linear activation function. The activated result is then updated to reflect the node attributes of the center node in the current graph convolutional layer.

9. The deep learning-based anti-counterfeiting authentication method for gold and silver coins according to claim 4, characterized in that, The step of inputting the multi-scale height feature map into the spatial attention sub-network and calculating the attention weight coefficient of each spatial location in the multi-scale height feature map includes: performing max pooling and average pooling operations on the multi-scale height feature map along the channel dimension to generate max pooling feature maps and average pooling feature maps. The max pooling feature map and the average pooling feature map are concatenated along the channel dimension. The concatenation result is input into a concatenated network containing a convolutional layer with a kernel size of a preset size and an activation function. The attention weight coefficients of the spatial attention subnetwork are output, and the number of channels of the attention weight coefficients is set to 1.

10. The deep learning-based anti-counterfeiting authentication method for gold and silver coins according to claim 5, characterized in that, The step of inputting the gradient feature map into a weight prediction subnetwork containing two convolutional kernels and outputting a fusion weight matrix with the same number of channels as the global geometric feature channels includes: inputting the gradient feature map into the first convolutional kernel of the weight prediction subnetwork, wherein the kernel size and stride of the first convolutional kernel are set according to the spatial resolution of the gradient feature map, and outputting the first feature map; The first layer feature map is input into the second layer convolutional kernel of the weight prediction sub-network. The kernel size of the second layer convolutional kernel is set to a preset value, and the output is an initial weight matrix with the same number of channels as the global geometric feature channels. Each channel dimension in the initial weight matrix is ​​normalized, and the normalized matrix is ​​used as the fusion weight matrix.

Images