Image Classification Method Based on Super-Resolution Image Reconstruction and Class Consistency Constraint

Abstract

The present invention discloses an image classification method based on super-resolution image reconstruction and class consistency constraint. The implementation steps are as follows: obtaining a training sample set and a test sample set; constructing an image classification network model based on super-resolution reconstruction and class consistency; performing iterative training on the image classification network model; and obtaining the classification result of the low-resolution image. The present invention uses the short-circuit connection between the super-resolution reconstruction network modules to improve the quality of the low-resolution image, enrich the detailed information of the image, and improve the classification accuracy of the network. By constraining the class probabilities between the networks to be consistent, the discriminability of the features extracted by the low-resolution feature extraction network is increased, and the image classification accuracy is further improved. It can be used for low-resolution image classification.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, and relates to an image classification method, an image classification method based on super-resolution image reconstruction and class consistency constraint, which can be used in fields such as image classification. Background Art

[0002] In different scenarios, due to the influence of the shooting position of the camera device, there is a problem of "near objects appear large and far objects appear small" in the scene images captured by the camera. At the same time, affected by environmental changes and compression algorithms during image transmission, the obtained images have different resolutions. Low-resolution images will cause loss of image feature information, and the classification accuracy of image classification algorithms is severely affected. In order to classify low-resolution images more accurately, it is necessary to improve the image resolution and reduce the influence brought by different resolutions. With the development of deep learning and image processing technologies, when processing different low-resolution images, generally, the image is first subjected to super-resolution reconstruction, and then the reconstructed super-resolution image is classified.

[0003] Zhejiang Sci-Tech University disclosed a method for classifying blurred images based on super-resolution reconstruction in its patent document "A Method for Classifying Blurred Images Based on Super-Resolution Reconstruction" (Application No.: 202110713780.4, Publication No.: CN113344110A). The method includes the following steps: (1) Specify class labels for the original high-resolution images, and then perform Gaussian smoothing on the original high-resolution images and then downsample them to obtain low-resolution images with labels; (2) Construct a fusion model, including a super-resolution reconstruction model and a classification model connected in series. The super-resolution reconstruction model includes a generation model and a discriminant model connected in series; (3) Establish loss functions for the super-resolution reconstruction model and the classification model respectively, use the training set to train the fusion model established in step (2), and use the test set to test the fusion model to obtain a fusion model with online production ability. This method improves the classification accuracy to a certain extent, but its disadvantages are: in the training of the classification model in the fusion model, only low-resolution image information is used, and the distinguishability of the low-resolution image features extracted is insufficient, which further affects the further improvement of the image classification accuracy. Summary of the Invention

[0004] The object of the present invention is to overcome the defects existing in the above-mentioned prior art, and propose an image classification method based on super-resolution image reconstruction and class consistency constraint, aiming to improve the classification accuracy of images.

[0005] To achieve the above object, the technical solutions adopted by the present invention include the following steps:

[0006] (1) Obtain a training sample set and a test sample set:

[0007] (1a) Obtain a dataset D1 that includes M target categories, with each category containing K RGB images. Label the targets in each image, and then downsample each image in D1 to obtain a dataset D2 that includes MK low-resolution images, where M≥100 and K≥40;

[0008] (1b) Randomly select X images from each category in the image dataset D1. Combine the selected N = MX RGB images and their corresponding low-resolution images, as well as the category labels of each image, to form a training sample set R. At the same time, combine the remaining M(K - X) low-resolution images and the category labels of each image to form a test sample set E, where X > 0.5K;

[0009] (2) Construct an image classification network model C based on super-resolution reconstruction and category consistency:

[0010] Construct an image classification network model C that includes a first feature extraction network H1 with network parameters arranged in parallel and a low-resolution feature extraction network L with network parameters θ L . The low-resolution feature extraction network L consists of a super-resolution image reconstruction network S and a second feature extraction network H2 connected in sequence; both the first and second feature extraction networks H1 and H2 include multiple convolutional layers, multiple MBConv modules, a fully connected layer, and a SoftMax activation function layer; the super-resolution image reconstruction network S includes multiple convolutional layers, multiple RBConv residual network modules, and multiple sub-pixel convolutional layers; the loss function Z(θ L ) of the low-resolution feature extraction network L is composed of a low-resolution image cross-entropy loss function J(θ L ), a super-resolution reconstruction pixel loss function F(θ L ), and a category consistency loss function B(θ L );

[0011] (3) Iteratively train the image classification network model C;

[0012] (3a) Initialize the iteration number as t, the maximum iteration number as T, T≥100, and set t = 0;

[0013] (3b) Use the training sample set R as the input of the image classification network model C. The first feature extraction network H1 extracts features from each RGB image in R to obtain the features of each RGB image. The SoftMax activation function layer calculates the class probability of each RGB image through the features of each RGB image. At the same time, the super-resolution image reconstruction network S in the low-resolution feature extraction network L reconstructs the low-resolution image corresponding to each RGB image in R to obtain a reconstructed image. The second feature extraction network H2 extracts features from each reconstructed image output by S to obtain the features of each reconstructed image. The SoftMax activation function layer calculates the class probability of each low-resolution image through the features of each reconstructed image.

[0014] (3c) Calculate the loss value of the first feature extraction network H1 and the loss value Z(θ L ) of the low-resolution feature extraction network L, and update and Z(θ L ) respectively for θ L to obtain the image classification network model C of this iteration t ;

[0015] (3d) Determine whether t≥T holds. If so, obtain the trained image classification network model C'. Otherwise, set t = t + 1 and execute step (3b);

[0016] (4) Obtain the low-resolution image classification result:

[0017] Use the test sample set E as the input of the low-resolution feature extraction network L for forward propagation to obtain the probability of each low-resolution image belonging to each class, and use the class with the highest probability of each image as the classification result of the image.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] The image classification network model constructed by the present invention includes a first feature extraction network arranged in parallel and a low-resolution feature extraction network composed of a super-resolution image reconstruction network and a second feature extraction network connected in sequence. During the training process of the model, the first feature extraction network extracts features from each RGB image, the super-resolution image reconstruction network reconstructs each low-resolution image, and the second feature extraction network extracts features from each reconstructed image. Short-circuit connections are made between different RBConv modules in the super-resolution reconstructed image, which can effectively restore the detailed information of the image, thereby improving the classification accuracy of the network. At the same time, the category consistency loss function is used to constrain the difference between the category probability distribution of the low-resolution image and the category probability distribution of the RGB image. By learning, the low-resolution image features are fitted to the high-resolution image features, which can avoid the defect of lack of discrimination of the low-resolution image features and further improve the classification accuracy of the network. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a flowchart for the implementation of the present invention;

[0021] Figure 2 is a schematic structural diagram of the super-resolution image reconstruction network in an embodiment of the present invention;

[0022] Figure 3 is a schematic structural diagram of the RBConv residual network module in the present invention;

[0023] Figure 4 is a schematic diagram of the principle of the training process of the image classification network of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] The following further describes the present invention in detail with reference to the accompanying drawings and specific embodiments.

[0025] Refer to Figure 1 , the present invention includes the following steps:

[0026] Step 1) Obtain a training sample set and a test sample set:

[0027] (1a) Obtain a data set D1 including M target categories and each category contains K RGB images, and label the targets in each image. In order to obtain low-resolution images, then downsample each image in D1 to obtain a data set D2 including MK low-resolution images, where M≥100 and K≥40; in this example, the 101Flowers data set with 101 categories and each category contains 40 images is used, and the data set is downsampled by 4 times to obtain a low-resolution data set containing 4040 images;

[0028] (1b) Randomly select X images from each category in the image dataset D1, and form a training sample set R with the selected total of N = MX RGB images, their corresponding low-resolution images, and the category labels of each image. At the same time, form a test sample set E with the remaining M(K - X) low-resolution images and the category labels of each image, where X > 0.5K; in this example, randomly select 24 images from each category in the 101Flowers dataset, their corresponding low-resolution images, and the category labels of each image to form a training sample set of 4848 images, and at the same time form a test sample set with the remaining 1616 low-resolution images and the category labels of each image;

[0029] Step 2) Build a generative adversarial network model:

[0030] Construct an image classification network model C including a first feature extraction network H1 and a low-resolution feature extraction network L arranged in parallel with consistent category probabilities. The low-resolution feature extraction network L consists of a super-resolution image reconstruction network S and a second feature extraction network H2 connected in sequence. Among them, the first and second feature extraction networks H1 and H2 both include multiple convolutional layers, multiple MBConv modules, a fully connected layer, and a SoftMax activation function layer; the super-resolution image reconstruction network S includes multiple convolutional layers, multiple RBConv residual network modules, and multiple sub-pixel convolutional layers;

[0031] In this example, the specific structures and parameters of the first and second feature extraction networks H1 and H2 are as follows:

[0032] First convolutional layer Conv1 → 16 MBConv modules → Second convolutional layer Conv2 → Fully connected layer → SoftMax activation function layer

[0033] The MBConv module includes a sequentially connected convolutional MBConv_1 and a depthwise separable convolutional MBConv_2. The depthwise separable convolutional MBConv_2 includes a sequentially connected pointwise convolutional layer and a pointwise convolutional layer;

[0034] The convolutional kernel size of the first convolutional layer Conv1 is 3×3, the convolutional stride is 1, the number of convolutional kernels is 32, and a batch normalization BN layer is used after the convolutional layer;

[0035] In the first MBConv, the convolutional kernel size of MBConv_1 is 1×1, the convolutional stride is 1, the number of convolutional kernels is 16, the convolutional kernel size of the pointwise convolutional layer in MBConv_2 is 3×3, the convolutional stride is 1, the number of convolutional kernels is 16, the convolutional kernel size of the pointwise convolutional layer is 1×1, the convolutional stride is 1, the number of convolutional kernels is 16, and a batch normalization BN layer is used after each convolutional layer;

[0036] In the 2nd - 3rd MBConv, the convolutional kernel size of MBConv_1 is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 24. In MBConv_2, the convolutional kernel size of the depthwise convolution is 3×3, the convolutional stride is 1, and the number of convolutional kernels is 24. The convolutional kernel size of the pointwise convolution is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 24. After each convolutional layer, a batch normalization BN layer is adopted.

[0037] In the 3rd - 4th MBConv, the convolutional kernel size of MBConv_1 is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 40. In MBConv_2, the convolutional kernel size of the depthwise convolution is 5×5, the convolutional stride is 1, and the number of convolutional kernels is 40. The convolutional kernel size of the pointwise convolution is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 40. After each convolutional layer, a batch normalization BN layer is adopted.

[0038] In the 4th - 5th MBConv, the convolutional kernel size of MBConv_1 is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 40. In MBConv_2, the convolutional kernel size of the depthwise convolution is 5×5, the convolutional stride is 1, and the number of convolutional kernels is 40. The convolutional kernel size of the pointwise convolution is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 40. After each convolutional layer, a batch normalization BN layer is adopted.

[0039] In the 6th - 8th MBConv, the convolutional kernel size of MBConv_1 is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 80. In MBConv_2, the convolutional kernel size of the depthwise convolution is 3×3, the convolutional stride is 1, and the number of convolutional kernels is 80. The convolutional kernel size of the pointwise convolution is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 80. After each convolutional layer, a batch normalization BN layer is adopted.

[0040] In the 9th - 11th MBConv, the convolutional kernel size of MBConv_1 is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 112. In MBConv_2, the convolutional kernel size of the depthwise convolution is 5×5, the convolutional stride is 1, and the number of convolutional kernels is 112. The convolutional kernel size of the pointwise convolution is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 112. After each convolutional layer, a batch normalization BN layer is adopted.

[0041] In the 12th - 15th MBConv, the convolutional kernel size of MBConv_1 is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 192. In MBConv_2, the convolutional kernel size of the depthwise convolution is 5×5, the convolutional stride is 1, and the number of convolutional kernels is 192. The convolutional kernel size of the pointwise convolution is 1×1, the convolutional stride is 1, and the number of convolutional kernels is 192. After each convolutional layer, a batch normalization BN layer is adopted.

[0042] The convolution kernel size of MBConv_1 in the 16th MBConv is 1×1, the convolution stride is 1, the number of convolution kernels is 320. The convolution kernel size of the depthwise convolution in MBConv_2 is 3×3, the convolution stride is 1, the number of convolution kernels is 320, the convolution kernel size of the pointwise convolution is 1×1, the convolution stride is 1, the number of convolution kernels is 320, and a batch normalization BN layer is used after each convolution layer.

[0043] The convolution kernel size of convolution layer Conv2 is 1×1, the convolution stride is 1, the number of convolution kernels is 1280, and a batch normalization BN layer is used after the convolution layer; the number of nodes in the fully connected layer is 101.

[0044] Refer to Figure 2 In this example, the specific structure and parameters of the super-resolution image reconstruction network S are as follows:

[0045] The super-resolution image reconstruction network S includes 3 convolution layers, 12 RBConv residual network modules, and 2 sub-pixel convolution layers; its specific structure is: the first convolution layer Conv2_1 → 12 RBConv residual network modules → the second convolution layer Conv2_2 → the first sub-pixel convolution layer SubConv2_1 → the second sub-pixel convolution layer SubConv2_2 → the third convolution layer Conv2_3

[0046] In the 12 RBConv module residual networks, the outputs of the 7th, 8th, 9th, 10th, 11th, and 12th RBConv modules are short-circuited to the outputs of the 6th, 5th, 4th, 3rd, 2nd, and 1st modules respectively.

[0047] Refer to Figure 3 The RBConv residual network module includes RBConv_1 and RBConv_2 connected in sequence.

[0048] The convolution kernel size of the first convolution layer Conv2_1 is 7×7, the convolution stride is 1, the number of convolution kernels is 64, and a LeakyRelu activation function and a batch normalization BN layer are used after the convolution layer.

[0049] In the 12 RBConv residual network modules, the convolution kernel sizes of RBConv_1 and RBConv_2 are both 3×3, the strides are both 1, the number of convolution kernels is both 64, and a LeakyRelu activation function is used after the RBConv_1 convolution layer.

[0050] In the first and second sub-pixel convolution layers SubConv2_1 and SubConv2_2, the convolution kernel sizes are both 3×3, the strides are both 1, the number of convolution kernels is both 256, and a pixel shuffle PixelShuffle operation and a LeakyRelu activation function are used after the SubConv2_1 and SubConv2_2 convolution layers.

[0051] The convolution kernel size of the third convolutional layer Conv2_3 is 7×7, the stride is 1, and the number of convolution kernels is 3;

[0052] Step 3) Iteratively train the image classification network model C, where the principles of steps 3b) and 3c) are as Figure 4 shown;

[0053] Step 3a) Initialize the iteration number as t, the maximum iteration number as T, T≥100, and the network parameters of the first feature extraction network H1 are the network parameters of the low-resolution feature extraction network L are θ L , and let t = 0; in this example, T = 100;

[0054] Step 3b) Use the training sample set R as the input of the image classification network model C. Conv1 in the first feature extraction network H1 extracts the low-level features of each RGB image in R, and 16 MBConv and Conv2 extract the high-level features of each RGB image from the low-level features. The SoftMax activation function layer calculates the class probability of each RGB image through the high-level features of each RGB image; at the same time, the super-resolution image reconstruction network S in the low-resolution feature extraction network L reconstructs the low-resolution image corresponding to each RGB image in R. Conv2_1, 12 RBConv, and Conv2_2 extract the features of each low-resolution image. Among them, the output of the RBConv residual network module is obtained by summing the input and the output of RBConv_2, and the different RBConv residual network modules of the super-resolution reconstruction network are short-circuited to achieve the fusion of features between different layers, which can effectively restore the image detail information. SubConv2_1 and SubConv2_2 perform two upsamplings, and Conv2_3 obtains the reconstructed image through the upsampled features; the second feature extraction network H2 extracts the features of each reconstructed image output by S to obtain the features of each low-resolution image, and the SoftMax activation function layer calculates the class probability of each low-resolution image through the features of each low-resolution image;

[0055] The calculation formulas for the class probability of each RGB image and the class probability of each low-resolution image are respectively:

[0056]

[0057]

[0058] p nm represents the probability that the nth RGB image belongs to class m, e represents the natural constant, v nmThe m-th eigenvalue representing the feature of the n-th RGB image, q nm The probability that the n-th low-resolution image belongs to class m, u nm The m-th eigenvalue representing the feature of the n-th low-resolution image;

[0059] Step 3c) Calculate the loss value of the first feature extraction network H1 and the loss value Z(θ L ) of the low-resolution feature extraction network L, and through and Z(θ L ) respectively update θ L to obtain the image classification network model C t ;

[0060] Step 3c1) Calculate the cross-entropy loss value of the first feature extraction network H1

[0061]

[0062] where y nm represents whether the class label of the n-th RGB image is m. If so, y nm = 1, otherwise y nm = 0, and log represents the logarithmic operation with base e

[0063] Step 3c2) Calculate the loss function Z(θ L ) of the low-resolution feature extraction network L composed of the low-resolution image cross-entropy loss function J(θ L ), the super-resolution reconstruction pixel loss function F(θ L ), and the class consistency loss function B(θ L ):

[0064] Z(θ L ) = w1J(θ L ) + w2B(θ L ) + w3X(θ L )

[0065]

[0066]

[0067]

[0068] where w1, w2, and w3 represent weight coefficients respectively, u nm represents whether the class label of the n-th RGB image is m. If so, u nm = 1, otherwise u nm = 0, Sn represents the number of pixels in the n-th RGB image, I ns represents the value of the s-th pixel in the n-th RGB image, R ns represents the value of the s-th pixel in the n-th reconstructed image.

[0069] B(θ L ) constrains to minimize the difference between the class probabilities of the low-resolution image and the RGB image, so that the features of the low-resolution image fit the features of the RGB image with higher discriminability, that is, the low-resolution feature extraction network can extract more discriminable feature information.

[0070] Step 3c3) Update the network parameters of H1 through the cross-entropy loss value of the first feature extraction network H1 for the network parameters of H1 and at the same time update the network parameters θ of L through the loss value Z(θ L ) of the low-resolution feature extraction network L L to obtain the update result of θ L as θ' L :

[0071]

[0072]

[0073] where α represents the learning rate of the image classification network model C, represents the partial derivative operation.

[0074] Step 4) Obtain the low-resolution image classification result:

[0075] Perform forward propagation with the test sample set E as the input of the low-resolution feature extraction network L to obtain the probability of each low-resolution image belonging to each category, and take the category with the highest probability for each image as the classification result of the image; in this example, only low-resolution images are used to represent the situation where there are only low-resolution images in the real application scenario. Input 1616 low-resolution images into the trained low-resolution feature extraction network model L to obtain the classification result of the low-resolution images.

Claims

1. An image classification method based on super-resolution image reconstruction and class consistency constraint, characterized in that It includes the following steps: (1) Obtain a training sample set and a test sample set: (1a) Obtain a data set D1 including M target categories, with each category containing K RGB images. Annotate the targets in each image, and then downsample each image in D1 to obtain a data set D2 including MK low-resolution images, where M≥100 and K≥40; (1b) Randomly select X images from each category in the image data set D1, and form a training sample set R with the selected total of N = MX RGB images, their corresponding low-resolution images, and the category labels of each image. At the same time, form a test sample set E with the remaining M(K - X) low-resolution images and the category labels of each image, where X > 0.5K; (2) Construct an image classification network model C based on super-resolution reconstruction and category consistency: Construct an image classification network model C that includes a first feature extraction network H1 with network parameters arranged in parallel and a low-resolution feature extraction network L with network parameters θ L . The low-resolution feature extraction network L is composed of a super-resolution image reconstruction network S and a second feature extraction network H2 connected in sequence. The first and second feature extraction networks H1 and H2 both include multiple convolutional layers, multiple MBConv modules, a fully connected layer, and a SoftMax activation function layer. The super-resolution image reconstruction network S includes multiple convolutional layers, multiple RBConv residual network modules, and multiple sub-pixel convolutional layers. The loss function Z(θ L ) of the low-resolution feature extraction network L consists of a low-resolution image cross-entropy loss function J(θ L ), a super-resolution reconstruction pixel loss function F(θ L ), and a class consistency loss function B(θ L ); (3) Iteratively train the image classification network model C; (3a) Initialize the iteration number as t, the maximum iteration number as T, T≥100, and set t = 0; (3b) Use the training sample set R as the input of the image classification network model C. The first feature extraction network H1 extracts features from each RGB image in R to obtain the features of each RGB image. The SoftMax activation function layer calculates the category probability of each RGB image through the features of each RGB image; at the same time, the super-resolution image reconstruction network S in the low-resolution feature extraction network L reconstructs the low-resolution images corresponding to each RGB image in R to obtain reconstructed images. The second feature extraction network H2 extracts features from each reconstructed image output by S to obtain the features of each reconstructed image. The SoftMax activation function layer calculates the category probability of each low-resolution image through the features of each reconstructed image; (3c) Calculate the loss value of the first feature extraction network H1 and the loss value Z(θ L ) of the low-resolution feature extraction network L, and and Z(θ L ) are used to update θ L respectively, and the image classification network model C t for this iteration is obtained; (3d) Determine whether t≥T holds. If so, obtain the trained image classification network model C'; otherwise, set t = t + 1 and execute step (3b); (4) Obtain the low-resolution image classification result: Use the test sample set E as the input of the low-resolution feature extraction network L for forward propagation to obtain the probability of each low-resolution image belonging to each category, and take the category with the highest probability of each image as the classification result of the image.

2. The image classification method based on super-resolution image reconstruction and class consistency constraint according to claim 1, wherein The image classification network model C described in step (2), where: The number of convolutional layers included in the first and second feature extraction networks H1 and H2 is 2, the number of MBConv modules is 16, and the number of fully connected layers is 1; The MBConv module includes a sequentially connected convolutional MBConv_1 and a depthwise separable convolutional MBConv_2; The number of convolutional layers, RBConv residual network modules, and sub-pixel convolutional layers included in the super-resolution image reconstruction network S are 3, 12, and 2 respectively; The RBConv residual network module includes a sequentially connected convolutional RBConv_1 and a convolutional RBConv_2.

3. The image classification method based on super-resolution image reconstruction and class consistency constraint according to claim 1, wherein The SoftMax activation function layer described in step (3b) calculates the class probabilities of each RGB image through the features of each RGB image, and the SoftMax activation function layer calculates the class probabilities of each low-resolution image through the features of each reconstructed image. The calculation formulas are as follows: p nm represents the probability that the nth RGB image belongs to class m, e represents the natural constant, v nm represents the mth eigenvalue of the nth RGB image, q nm represents the probability that the nth low-resolution image belongs to class m, u nm represents the mth eigenvalue of the nth reconstructed image.

4. The image classification method based on super-resolution image reconstruction and class consistency constraint according to claim 1, wherein The loss value of the first feature extraction network H1 described in step (3c) The loss value Z(θ of the low-resolution feature extraction network L L are updated respectively for θ L The implementation steps are as follows: (3c1) Calculate the cross-entropy loss value of the first feature extraction network H1 where y nm indicates whether the class label of the nth RGB image is m. If so, y nm = 1; otherwise y nm = 0, and log represents the natural logarithm operation; (3c2) Calculate the loss value Z(θ L ) of the low-resolution feature extraction network L: Z(θ L ) = w1J(θ L ) + w2B(θ L ) + w3X(θ L ) Among them, w1, w2, and w3 respectively represent the weight coefficients, and u nm represents whether the class label of the nth low-resolution image is m. If so, u nm = 1; otherwise, u nm = 0. S n represents the number of pixels of the nth RGB image, and I ns represents the value of the s-th pixel of the nth RGB image, and R ns represents the value of the s-th pixel of the nth reconstructed image; (3c3) The cross-entropy loss value of the first feature extraction network H1 updates the network parameters of H1 and simultaneously updates the network parameters θ L of L through the loss value Z(θ L ) of the low-resolution feature extraction network L, obtaining the updated result of θ L : θ' L : where α represents the learning rate of the image classification network model C, represents the partial derivative operation.

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