Automated Logistics Packaging Inspection Based on Deep Learning and Computer Vision: A Two-Dimensional Flow Model Approach

With the rapid development of e-commerce, the demand in the logistics industry continues to grow [1, 2], which promotes the rapid development of logistics packaging automation technology [3]. As a key link in commodity distribution, the quality and efficiency of logistics packaging directly affect the operational efficiency of the supply chain and the shopping experience of consumers [4, 5]. Traditional manual inspection methods are inadequate when facing large-scale and high-frequency logistics packaging and are easily affected by human factors [6-9]. Therefore, developing an efficient and automated logistics packaging inspection technology has become an urgent and important issue. In recent years, the application of deep learning and computer vision technology in industrial inspection has shown great potential, especially in image recognition and processing, which provides a new technical path for logistics packaging automation inspection.

Relevant studies show that logistics packaging automation inspection not only helps to improve the stability of packaging quality but also reduces labor costs and improves production efficiency [10-12]. In addition, with the increase of logistics demand, the accuracy and real-time performance of logistics packaging inspection play a decisive role in the competitiveness of enterprises and the efficiency of the supply chain [13]. Therefore, using deep learning and computer vision technology for automated logistics packaging inspection not only has significant economic significance but also can further promote the intelligent and automated process of the logistics industry. Through efficient and accurate inspection technology, better product quality control can be achieved to ensure a good experience for consumers when receiving goods.

Although some progress has been made in automated inspection, the existing methods still have some obvious shortcomings and deficiencies. Most of the existing studies rely on traditional machine learning algorithms such as Support Vector Machine (SVM) [14] and Random Forest (RF) [15], which often perform poorly when dealing with complex and high-dimensional image data, and lack real-time and high-precision detection capabilities. In addition, many studies have not deeply explored how to ensure the robustness and adaptability of the detection model in complex logistics environments. There are certain limitations when the model processes images of different packaging materials and under different environments [16-19]. Therefore, the existing detection methods fail to fully utilize the advantages of deep learning technology when facing diversified and complex practical applications.

This paper aims to propose a new method for automated logistics packaging inspection based on deep learning and computer vision, and to explore its application possibility in practical scenarios by constructing an inspection framework based on a two-dimensional flow model. Firstly, the paper analyzes the basic idea of using the two-dimensional flow model for automated logistics packaging inspection and discusses the advantages of the model in complex scenarios. Secondly, the paper introduces the key modules of the model in detail, including the probabilistic distribution transformation module, the global feature extraction module, and the multi-scale feature fusion module. Through the design of these innovative modules, the paper hopes to solve the problems of accuracy and robustness in diversified packaging inspection. The research results not only help to improve the efficiency and accuracy of logistics packaging inspection technology but also provide valuable theoretical support and technical reference for the intelligent development of the logistics industry.

3.1 Probability distribution transformation module

The traditional application of normalized flow usually focuses on unsupervised anomaly detection tasks, and it may encounter accuracy issues in some tasks. Although traditional DifferNet can handle low-dimensional data distributions and perform anomaly detection, it "flattens" the output of the feature extractor, making it difficult to precisely locate anomalies. This shortcoming is particularly prominent in logistics packaging inspection, as packaging images typically contain rich local details and complex spatial relationships, which the smoothing process of normalized flow cannot effectively capture. In contrast, the two-dimensional normalized flow model offers significant advantages for automatic logistics packaging inspection. The two-dimensional normalized flow performs affine transformations on segmented input data using Real NVP’s masking technique, enabling reversible transformation of data distribution while retaining the spatial structure and local details of images. This method allows effective preservation of spatial information in images, making it more suitable for anomaly localization tasks in logistics packaging inspection. In logistics packaging inspection, factors such as the size, shape, material, and possible defects of packaging form a complex data distribution. The two-dimensional normalized flow can better retain this multi-level information through parallel transformations and efficient processes, ensuring that the detection model can accurately locate abnormal areas when facing complex and diverse packaging data. Moreover, the reversibility and efficiency of the two-dimensional normalized flow model allow it to perform real-time processing in practical applications, meeting the logistics industry's needs for efficient and rapid anomaly detection.

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Figure 2. Structure of the affine coupling layer in the reversible transformation module of the two-dimensional normalized flow model

In the scenario of automatic logistics packaging inspection, the architecture of the two-dimensional normalized flow model's reversible transformation module includes affine coupling layers, channel permutation layers, and Actnorm layers. Among them, the channel permutation layer introduces reversible 1×1 convolution to replace the traditional reverse permutation method, which is crucial for multi-level and multi-scale feature fusion in logistics packaging inspection. In packaging images, the morphology of objects, background complexity, and packaging defects often manifest as subtle spatial structural differences. The channel permutation layer initializes its weight matrix using a randomly rotated matrix, thereby reducing the demand for computational resources while optimizing feature representation based on the premise of maintaining model reversibility. For diverse packaging types and materials in logistics packaging inspection, the channel permutation layer can effectively perform spatial information transformation and feature reconstruction, thus ensuring that the model can handle complex image structures, improve the ability to capture local details, and ensure the accuracy and stability of detection. Mapping the normal feature a to the standard Gaussian distribution space O_C(c) is expressed as:

$O_C(c)=\frac{1}{\sqrt{2 \tau}} \exp \left(-\frac{c^2}{2}\right)$              (1)

The Actnorm layer plays an important role in the two-dimensional normalized flow model. As a preprocessing operation for input data, it helps improve the model's training effectiveness and stability. In automatic logistics packaging inspection tasks, packaging images usually have different brightness, contrast, and noise levels, making feature extraction from images more challenging. The Actnorm layer applies scaling and offset parameters to each channel, realizing an affine transformation of activations, thereby ensuring that each channel's subsequent processing has zero mean and unit variance. This operation not only helps to solve the bias problem between different data batches but also accelerates the convergence speed of the model and enhances the stability of the training process. For complex logistics packaging images, the Actnorm layer can balance the influence of different scales and feature channels, ensuring that the network can perform robust learning under various input conditions, thereby improving the model's performance in anomaly detection and localization tasks.

In the application scenario of automatic logistics packaging inspection, the affine coupling layer is the core module of the two-dimensional normalized flow model that implements reversible transformation. Through a series of precise operations, it can efficiently process complex packaging images while retaining spatial information and local features of the images. The specific architecture is shown in Figure 2. The following are the five specific transformation steps of the affine coupling layer and their applications in automatic logistics packaging inspection:

(1) Channel Splitting: The first step of the affine coupling layer is to split the input feature map along the channel dimension into two parts. The input feature map a is split into a_1:z and a_z+1:f, where z represents the first z channels, and f represents the remaining channels from z+1 to the total number of channels. This splitting process is critical for processing packaging images, which often contain multiple levels of features, such as background and foreground information. By splitting the channels, the affine coupling layer can independently process different feature layers, ensuring efficient modeling of both detailed and global information, which leads to more effective feature fusion in subsequent steps.

(2) Calculation of Mean and Standard Deviation: After channel splitting, the affine coupling layer calculates the mean ω and standard deviation δ of the input feature map a along the spatial dimension. By statistically analyzing the spatial distribution of the input image, the model can capture important global information. In logistics packaging inspection, variations in lighting and shadows in images may cause spatial feature differences. Calculating mean and standard deviation helps normalize image data, eliminate unnecessary effects, and improve the stability of subsequent processing. Assuming that the height and width of the feature map are represented by G and Q, and a very small constant is represented by γ, the calculation formulas are:

$\omega_u=\frac{1}{G \times Q} \sum_{g=1}^G \sum_{q=1}^Q a_{u, g, q}$            (2)

$\delta_u=\sqrt{\frac{1}{G \times Q} \sum_{g=1}^G \sum_{q=1}^A\left(a_{u, g, q}-\omega_u\right)^2+\gamma}$            (3)

(3) Learning Affine Transformation Parameters: The affine coupling layer uses a two-dimensional convolutional layer to learn the affine transformation parameters t_u and y_u, and performs affine transformation on the split a_1:z using these parameters. In this way, the affine coupling layer can adjust the features of different areas in the image, making the data distribution more in line with model requirements and optimizing its representation capability. In automatic logistics packaging inspection, local features such as package surface, labels, and defects need to undergo precise transformations to be effectively recognized. Learning affine transformation parameters helps the model better process these local details, thereby improving detection accuracy. Assuming the learnable parameters are t_u and y_u, and the normalized output a_u is represented by y_u, the calculation formula is:

$b_u=t_u \cdot \frac{a_u-\omega_u}{\delta_u}+y_u$            (4)

(4) Channel Merging: In logistics packaging detection applications, inspection of packaging images relies not only on a part of the features but also on a comprehensive understanding of all types of information in the image. After affine transformation, a_1:z and a_z+1:f are merged into a new output feature map a^, ensuring that the features after affine transformation are fully integrated with the original features, thereby retaining both local and global information of the image. The merged feature map provides a richer feature representation, helping the detection model more accurately identify and locate anomalies in packaging.

$\hat{a}=\left[b_1, b_2, \ldots, b_z, a_{z+1}, a_{z+2}, \ldots, a_f\right]$              (5)

(5) Backpropagation to Compute Gradients: Finally, the affine coupling layer performs backpropagation to compute the model gradients, thereby optimizing the model parameters. In the task of automatic logistics packaging inspection, the model aims to maximize the description capability for normal samples while minimizing the misidentification of abnormal samples. Through gradient descent algorithms, the model continuously optimizes its parameters to minimize the loss function M_H(ϕ), thereby improving model accuracy and effectiveness. In practical applications, gradient optimization not only allows the model to achieve better fitting results on the training set but also provides more robust anomaly detection capabilities when facing complex packaging images. By computing gradients through backpropagation, the model can gradually adjust parameters to ensure high efficiency and accuracy in logistics packaging detection scenarios. Assuming the output of the two-dimensional normalized flow is c_u, the Jacobian matrix between the output q and the input of the two-dimensional normalized flow is K_u, and the number of normal samples is V, the expression is:

$M_H(\varphi)=-\log O_A(a)=\left[\frac{1}{V} \sum_{u=1}^V \frac{\left\|c_u\right\|_2^2}{2}-\log \left|D E T\left(K_u\right)\right|\right]$              (6)

In the application scenario of automatic logistics packaging inspection, the two-dimensional flow model, through its bidirectional reversible characteristics, can effectively implement transformation and generation of image features. In the forward process, the model receives feature maps from the packaging image feature extractor. These feature maps may contain information such as the shape, identification, print quality, and surface texture of the packaging. The two-dimensional flow model transforms the distribution of these original feature maps into a Gaussian distribution in a two-dimensional space. This process improves the efficiency of subsequent processing by simplifying image features into a probability distribution that conforms to Gaussian distribution. The advantage of this transformation lies in its ability to eliminate noise and unnecessary complexity in packaging images, allowing the model to focus more on key information such as defects, damage, or unclear labels. In the reverse process, the two-dimensional flow model samples from the Gaussian distribution and generates corresponding packaging image features based on these samples. For automatic logistics packaging inspection, the generated features can reproduce the original packaging information in images, and even simulate possible image noise or interference by adding noise. In this process, by visualizing the generated feature tensors, it is possible to clearly observe how the model captures and highlights abnormal areas in the image. For example, when damage, deformation, or printing errors appear in packaging images, these anomalies can be clearly displayed in the feature visualization images.

3.2 Global feature extraction module

Although traditional convolutional neural networks (CNNs) perform excellently in image classification tasks, their performance is often limited when dealing with high-dimensional and complex image data, especially when the features in the image have long-distance dependencies. This limitation mainly comes from the local receptive field of CNNs. Therefore, this paper introduces ViT as the feature extraction module into the model. In logistics packaging images, defects, printing errors, or damage may be distributed in different parts of the image. ViT, through its global feature modeling capability, effectively improves the detection ability of these defects, enabling the detection model to more accurately identify various anomalies in packaging. In addition, in automated detection of logistics packaging, the diversity and complexity of image data require the model to have strong generalization ability. Compared with CNNs, the structure of ViT has more advantages in processing large-scale datasets because it integrates information globally through the self-attention mechanism, reduces the number of model parameters, and avoids the risk of overfitting.

ViT first divides the input image into multiple image patches of the same size and performs dimensionality reduction and linear transformation on these patches to generate a series of f-dimensional vectors. This patch-based processing method allows the model to capture more detailed information in local regions, while the linear transformation helps simplify the expression of image features. Each image patch is also added with position encoding information to retain its positional information in the original image, which is crucial for packaging images. For example, printing errors or defects in packaging images may appear in different locations, and position encoding ensures that the model correctly understands the spatial relationships between different parts. Finally, these processed image patches form a two-dimensional matrix, which is fed into the Transformer encoder for processing. This process can effectively capture complex features in the image and enhance the model's understanding of image content.

The multi-head self-attention mechanism of the Transformer further enhances the performance of ViT in automated detection of logistics packaging. By dividing the input two-dimensional matrix into multiple subspaces, the model can capture the interrelationships between different regions of the image in different subspaces, thereby identifying subtle differences in packaging images. In the multi-head self-attention structure, the calculation process of the query matrix, key matrix, and value matrix ensures that the model can effectively perform weighted combinations of the features of each image patch, and then extract richer and more diverse feature representations. This mechanism is very effective for complex features in packaging images, especially when there are various printing quality issues, physical damage, or unclear labels on the packaging surface. ViT can capture long-distance dependencies between different parts through multi-head self-attention, improving detection accuracy and robustness. Specifically, l attention heads are used to divide the query matrix, key matrix, and value matrix into l parts by columns to obtain W^u, J^u, and N^u, and then project them into different linear subspaces to perform multi-head self-attention transformation. Assuming that the output feature maps of all attention heads are represented by P^u, P^u is concatenated. The specific calculation formulas are as follows:

$j=f / l$              (7)

$P^u=\operatorname{softmax}\left(\frac{W^u\left(J^u\right)^S}{\sqrt{j}}\right) N^u, u \in[1, l]$              (8)

$P=\operatorname{cancat}\left(\left\{P^1, \ldots, P^u, \ldots, P^l\right\}\right)$              (9)

3.3 Multi-scale feature fusion module

In the scenario of automated detection of logistics packaging, the anomalies of packaging images often appear as subtle damages, scratches, color differences, or irregular shapes and other small-object features. These small objects occupy a relatively small proportion in the image and may exist in a more complex background or with noise. Therefore, how to effectively capture these detailed features and accurately locate them during anomaly detection is a challenging task. To improve the detection accuracy for these small-object anomalies, the two-dimensional stream model proposed in this paper adopts an optimized FPN structure for multi-scale feature fusion. This strategy can make full use of features at different levels, thereby enhancing the model's ability to recognize small-sized defects.

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Figure 3. Principle of FPN network structure

The multi-scale feature fusion mechanism of FPN has special significance in automated detection of logistics packaging. Defects in packaging images often present as low-resolution details and high-resolution background information. Although traditional deep networks can effectively capture global semantic information, they gradually lose the details of local features, resulting in low detection accuracy for small-sized defects. The structure principle is shown in Figure 3. By introducing FPN, shallow detailed information and deep global semantic information can be effectively fused to form a complementary effect. The FPN structure extracts features through convolution from the bottom to the top, and transfers the semantic information of high-level features to the bottom layer through the upsampling process. At the same time, the lateral connections are used to enhance the fusion effect of the feature maps, enabling the model to utilize the high resolution and weak semantic information of the low-level features and the low resolution and strong semantic information of the high-level features. In the detection of logistics packaging images, FPN helps the model to capture both the subtle local defects and the global packaging structure information on multi-level feature maps, thereby improving the recognition accuracy of small-object anomalies in complex environments.

Assuming that the feature matrices of different levels in the FPN structure are represented by a^x and a^y, and the fused feature matrix is represented by b. In the above process, the spatial feature fusion calculation formula is as follows:

$M a^x+a^y=b$            (10)

The mathematical expression of the additive fusion function is:

$b_{u, k, f}^{S U M}=S U M\left\{a_{u, k, f}^x, a_{u, k, f}^y\right\}$           (11)

Specifically for the two-dimensional flow model based on the ViT model, the optimized version of the FPN can further enhance the multi-scale processing capability of image features. The specific architecture is shown in Figure 4. The ViT model itself has already captured global features through its multi-head self-attention mechanism, while the FPN introduces multi-scale fusion to better combine feature maps at various levels, thereby improving the comprehensiveness and accuracy of feature extraction. In logistics packaging automated detection, defects on the package may appear in any area of the image. Therefore, extracting features at different scales and performing effective fusion are essential for improving the detection rate of small target anomalies. Through the optimized FPN structure, the model can perform fusion on feature maps at multiple scales, which not only strengthens the localization ability of small surface defects on packages, but also improves the overall performance of the model, making the automatic detection of packaging defects more accurate and efficient.

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