A method for extracting a color image contour by deep learning fusion of color histograms

Abstract

The application discloses a method for extracting a color image contour by deep learning and fusing a color histogram, belongs to the technical field of computer vision and image processing, and aims at the problem that in the prior art, color information utilization and semantic feature expression cannot be simultaneously considered in a complex background, leading to low contour extraction precision and fuzzy boundaries. The technical scheme is as follows: standardized data is obtained by preprocessing a color image; a deep feature map is extracted based on the standardized data and color distribution features are constructed; the deep features and the color distribution features are spatially aligned and fused to obtain a fusion feature map; contour extraction is performed on the fusion feature map to obtain an initial contour; and the initial contour is optimized to obtain a target contour, so that high-precision extraction and clear expression of the target contour in the color image are realized, and the method is suitable for target detection, image segmentation, industrial detection and medical image analysis.

Description

Technical Field

[0001] This invention relates to the field of appearance and dimension inspection technology in the automotive parts industry, specifically to a method for extracting color image contours based on deep learning and color histogram feature fusion. Background Technology

[0002] Currently, color image contour extraction technology has been widely researched and applied in the fields of computer vision and image processing, playing a crucial role, especially in scenarios such as object detection, image segmentation, medical image analysis, and industrial inspection. Existing technologies primarily fall into two categories: contour extraction methods based on edge detection operators and semantic segmentation methods based on deep learning.

[0003] Traditional methods typically employ edge detection algorithms such as the Sobel and Canny operators, extracting edge information by calculating changes in image grayscale gradients. While these methods are simple to implement and computationally efficient, their reliance on grayscale changes makes them weak at distinguishing between different colors with similar grayscale levels in color images, leading to issues like edge breakage, noise sensitivity, and loss of detail. Furthermore, traditional methods lack an understanding of high-level semantic information, making it difficult to accurately extract target contours in complex backgrounds.

[0004] In deep learning-based methods, with the development of convolutional neural networks, models such as U-Net and Mask R-CNN have been widely applied to image segmentation and contour extraction tasks. These methods can acquire rich semantic information through multi-layer feature learning and have high accuracy in complex scenes. However, these methods usually rely on a large amount of labeled data for training, which consumes a lot of computational resources, and still suffers from ambiguity and inaccuracy in some detailed regions (such as target boundaries). In addition, deep learning models often focus on overall region segmentation and do not make full use of color distribution features, failing to fully leverage the role of color information in contour extraction from color images.

[0005] On the other hand, the color histogram method, as a typical means of describing color features, can reflect the color distribution in an image and has certain application value in image retrieval and segmentation. However, when using color histograms alone for contour extraction, it lacks spatial structure information constraints, making it difficult to accurately locate contour positions, and its ability to distinguish between illumination changes and color-similar regions is limited.

[0006] Therefore, although existing technologies have studied image contour extraction from the perspectives of gradient information, semantic information and color distribution, there is a lack of effective integration among various methods. It is difficult to simultaneously take into account contour localization accuracy, boundary detail representation and full utilization of color information. Especially in application scenarios with complex backgrounds, multi-color interference and high requirements for target boundary details, it is still difficult to obtain stable and high-precision contour extraction results.

[0007] In summary, existing technologies have the drawback of failing to fully utilize the color distribution features of color images while combining deep semantic information to achieve high-precision, clear-boundary image contour extraction that is well-adapted to complex backgrounds. Summary of the Invention

[0008] To address the shortcomings of existing technologies in achieving high-precision, clear-boundary image contour extraction with good adaptability to complex backgrounds by fully utilizing the color distribution features of color images while combining deep semantic information, the technical solution provided by this invention is as follows: A method for extracting color image contours by fusing color histograms using deep learning includes: The steps of acquiring the color image to be processed and performing preprocessing to obtain standardized color image data; The step of extracting depth features based on the standardized color image data to obtain the corresponding depth feature map; The step of constructing color histogram features based on the standardized color image data to obtain color distribution features; The step of aligning and fusing the depth feature map with the color distribution feature map to obtain a fused feature map; The step of performing contour extraction processing based on the fused feature map to obtain the initial contour; The step of optimizing the initial contour to obtain the target contour.

[0009] Furthermore, in a preferred embodiment, the preprocessing involves normalizing the size of the color image to be processed, suppressing noise, and adjusting brightness and contrast to obtain standardized color image data.

[0010] Furthermore, in a preferred embodiment, the deep feature extraction involves inputting the standardized color image data into a convolutional neural network for multi-layer feature extraction to obtain a deep feature map that simultaneously contains local texture information and global semantic information.

[0011] Furthermore, in a preferred embodiment, the color histogram feature is constructed by dividing each color channel of the standardized color image data into intervals and counting the number of pixels in each interval, while simultaneously dividing the image into spatial regions to obtain color distribution features with spatial distribution information.

[0012] Furthermore, in a preferred embodiment, the alignment and fusion involves mapping the color distribution features to the depth features. Figure 1 After merging the spatial scales, the features are combined, and the weights of depth features and color distribution features are adjusted according to the feature variations in different regions to obtain a fused feature map.

[0013] Furthermore, in a preferred embodiment, the contour extraction process involves identifying regions with significant feature changes on the fused feature map as boundaries and performing connection processing to form an initial contour.

[0014] Based on the same inventive concept, the present invention also provides an apparatus for extracting color image contours by fusing color histograms using deep learning, comprising: A module that acquires the color image to be processed and performs preprocessing to obtain standardized color image data; A module that performs depth feature extraction based on the standardized color image data to obtain the corresponding depth feature map; A module for constructing color histogram features based on the standardized color image data to obtain color distribution features; A module that aligns and fuses the depth feature map with the color distribution feature map to obtain a fused feature map; A module that performs contour extraction processing based on the fused feature map to obtain an initial contour; A module that optimizes the initial contour to obtain the target contour.

[0015] Based on the same inventive concept, the present invention also provides a computer storage medium for storing a computer program, wherein when the computer program is read by a computer, the computer executes the method described thereon.

[0016] Based on the same inventive concept, the present invention also provides a computer, including a processor and a storage medium, wherein when the processor reads a computer program stored in the storage medium, the computer executes the method described thereon.

[0017] Based on the same inventive concept, the present invention also provides a computer program product, which, when executed, implements the method described.

[0018] Compared with the prior art, the advantages of the technical solution provided by the present invention are as follows: By constructing a multi-layered deep learning feature extraction structure on the input color image, edge, texture, and target structure information are gradually extracted during the mapping process from pixel space to semantic space. This part originates from the deep learning feature extraction step in the technical solution. Compared to traditional gradient detection methods based on Sobel or Canny operators that only rely on local grayscale changes, this feature can understand image content from both global and local levels. Even under complex backgrounds, lighting changes, or strong texture interference, it can still stably identify target regions, thereby significantly improving the robustness of contour extraction and overall recognition accuracy.

[0019] By modeling color histograms of color images, the color distribution of each channel in the image is statistically and quantitatively expressed. This part originates from the color histogram feature extraction step in the technical solution. Compared with the implicit learning of color information in existing deep learning methods, this feature explicitly models the color distribution, enabling the model to directly use color differences to distinguish regions. In regions with similar grayscale values ​​but significant color differences, it can effectively avoid the false detection and false negative problems caused by traditional methods, thereby enhancing the discriminative ability and stability of contour localization.

[0020] By partitioning or multi-scale processing the color histogram, the color distribution is not only reflected at the overall statistical level but also reflects the color variation characteristics of local areas. This aspect stems from the refined construction method of the color histogram in the technical solution. Compared to the shortcomings of traditional global color histograms that ignore spatial structure information, this feature can introduce spatial constraints to a certain extent, combining color features with the local structure of the image, thereby improving the spatial positioning accuracy of contour boundaries in complex scenes.

[0021] By constructing a fusion mechanism between depth features and color features, the two types of features are collaboratively expressed within a unified feature space. This part originates from the feature fusion step in the technical solution. Compared to contour extraction methods that rely solely on semantic or color features, this feature can ensure the correctness of target recognition at the semantic level, while enhancing boundary discrimination ability at the color level. This achieves complementarity between semantic information and low-level visual information, thereby improving the overall contour extraction effect.

[0022] By introducing weight allocation or adaptive adjustment mechanisms during feature fusion, different features can play differentiated roles in different regions. This stems from the feature weighting or fusion strategy design in the technical solution. Compared to simple stitching or fixed-weight fusion methods, this feature can dynamically adjust the contribution ratio of semantic and color features according to the image content, enhancing corresponding features in color-dominant or structure-dominant regions, thereby further improving the adaptive capability and accuracy of contour extraction.

[0023] By performing contour generation processing on the fused features, multi-dimensional features are transformed into continuous boundary representations in space. This part originates from the contour extraction or boundary generation steps in the technical solution. Compared to directly outputting a segmentation mask and then extracting the boundary, this feature can directly enhance the boundary structure during the generation stage, making the contour more continuous, complete, and closely matching the edge of the real target, reducing problems such as breaks and burrs.

[0024] By introducing boundary refinement and optimization processes during contour generation, edge regions are further enhanced. This enhancement stems from the boundary optimization step in the technical solution. Compared to the boundary blurring problem commonly found in existing deep learning segmentation models, this feature effectively improves boundary clarity, making the contours sharper and achieving higher positioning accuracy, especially noticeable in areas with fine structures or complex textures.

[0025] By constructing a hierarchical processing chain in the overall process, from input image, feature extraction, feature fusion to contour output, the output of the previous stage becomes the input of the next stage, forming a closed-loop processing. This part originates from the overall methodological process design in the technical solution. Compared with the problem of relatively independent processing modules and lack of system coordination in existing technologies, this feature can ensure that information is gradually strengthened and optimized during processing, thereby improving the stability and consistency of the entire system.

[0026] By jointly processing multi-channel information from color images, multi-dimensional color information such as RGB is fully utilized in contour extraction. This aspect stems from the direct processing method of color images in the technical solution. Compared to the traditional method of converting color images to grayscale images before processing, this feature avoids the loss of color information, enabling contour extraction to more comprehensively reflect the structure of the real scene and improve its adaptability to complex multi-color scenes.

[0027] By organically combining deep learning methods with traditional color statistics methods, the technical solution possesses both data-driven learning capabilities and explicit feature representation capabilities. This aspect stems from the overall design philosophy of the technical solution. Compared to deep models that rely solely on large-scale data training or traditional methods that rely solely on manually generated features, this approach can improve model interpretability and stability while reducing dependence on data scale, thus demonstrating good applicability and promotional value in various application scenarios.

[0028] It is suitable for high-precision extraction and recognition of target contours in color images with complex backgrounds. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method. Detailed Implementation

[0030] To make the advantages and benefits of the technical solution provided by the present invention clearer, the technical solution provided by the present invention will now be described in further detail with reference to the accompanying drawings, specifically: Implementation Method 1: This implementation method provides a method for extracting color image contours by fusing color histograms using deep learning, including: The steps of acquiring the color image to be processed and performing preprocessing to obtain standardized color image data; The step of extracting depth features based on the standardized color image data to obtain the corresponding depth feature map; The step of constructing color histogram features based on the standardized color image data to obtain color distribution features; The step of aligning and fusing the depth feature map with the color distribution feature map to obtain a fused feature map; The step of performing contour extraction processing based on the fused feature map to obtain the initial contour; The step of optimizing the initial contour to obtain the target contour.

[0031] The preprocessing involves normalizing the size of the color image to be processed, suppressing noise, and adjusting brightness and contrast to obtain standardized color image data.

[0032] The deep feature extraction involves inputting the standardized color image data into a convolutional neural network to perform multi-layer feature extraction, thereby obtaining a deep feature map that simultaneously contains local texture information and global semantic information.

[0033] The color histogram feature is constructed by dividing each color channel of the standardized color image data into intervals and counting the number of pixels in each interval, while simultaneously dividing the image into spatial regions to obtain color distribution features with spatial distribution information.

[0034] The alignment and fusion process involves mapping the color distribution features to the depth features. Figure 1 After merging the spatial scales, the features are combined, and the weights of depth features and color distribution features are adjusted according to the feature variations in different regions to obtain a fused feature map.

[0035] The contour extraction process involves identifying regions with significant feature changes on the fused feature map as boundaries and connecting them to form an initial contour.

[0036] A device for extracting color image contours by fusing color histograms using deep learning is also provided, comprising: A module that acquires the color image to be processed and performs preprocessing to obtain standardized color image data; A module that performs depth feature extraction based on the standardized color image data to obtain the corresponding depth feature map; A module for constructing color histogram features based on the standardized color image data to obtain color distribution features; A module that aligns and fuses the depth feature map with the color distribution feature map to obtain a fused feature map; A module that performs contour extraction processing based on the fused feature map to obtain an initial contour; A module that optimizes the initial contour to obtain the target contour.

[0037] A computer storage medium is also provided for storing a computer program, which, when read by the computer, executes the method.

[0038] A computer is also provided, including a processor and a storage medium, wherein the computer executes the method when the processor reads a computer program stored in the storage medium.

[0039] A computer program product is also provided, which, when executed, implements the method described.

[0040] Implementation Method Two: This implementation method is a further detailed description of the technical solution provided in Implementation Method One, specifically: First, the input color images are preprocessed to obtain stable and consistent basic data. The acquired raw color images are input into the processing flow, where the images are normalized to ensure consistent resolution across different sources. Simultaneously, denoising is performed to suppress random noise and minor interference, improving overall image quality. Brightness and contrast are adjusted to ensure uniform visual performance under different lighting conditions. Throughout the processing, the integrity of information in each color channel is maintained to avoid color distortion, resulting in preprocessed color image data, which is then used as input for subsequent feature extraction.

[0041] Secondly, deep learning feature extraction is performed on the preprocessed color image. The image is input into a pre-trained convolutional neural network, and edge, texture, and structural information in the image is extracted through multi-layer convolution operations. Local detail features are obtained in the shallow network, and overall semantic features are obtained in the deep network. The fusion of features at different scales is achieved through inter-layer connections, so that the features contain both detailed and global information. In the feature transfer process, non-linear mapping is performed on the features to enable them to express more complex image structural relationships. Finally, a deep feature map corresponding to the input image is output. This deep feature map maintains a spatial correspondence with the original image and serves as the input for subsequent fusion processing.

[0042] Next, color histogram features are constructed on the preprocessed color image. The color image is decomposed according to color channels, and the pixel values ​​in each color channel are divided into intervals, dividing the entire color space into multiple continuous intervals. The distribution of the number of pixels in each interval is statistically analyzed, thus forming a statistical vector reflecting the overall color distribution. At the same time, the image is divided into spatial regions, and color statistics are performed in each local region. This ensures that the color features not only reflect the overall distribution but also the color changes in local regions, forming color histogram features with spatial distribution information. A mapping relationship is established between this feature and the corresponding image region for subsequent feature fusion.

[0043] Then, the depth feature map and color histogram feature are aligned and fused. The depth feature map is matched with the color feature according to its spatial location, so that the depth feature at each location corresponds to the color distribution information of its region. The two types of features are integrated in a unified feature space by mapping the color feature to the same spatial scale as the depth feature and then superimposing or combining them, so that the fused feature contains both semantic information and color distribution information. During the fusion process, the weights of the two types of features are adjusted according to the feature changes in different regions, so that regions with obvious structural information are dominated by depth features and regions with obvious color differences are dominated by color features, thus forming an adaptive fused feature map, which is used as the input for contour extraction.

[0044] Next, contour extraction is performed on the fused feature map. Boundary regions are determined by detecting locations with significant feature changes. The spatial variation of the fused features is analyzed, and regions with large feature variation amplitudes are identified as potential boundaries. These boundary points are connected to form continuous boundary curves from discrete boundary points. The boundaries are then filtered based on feature distribution to retain the main contours that reflect the target structure, thus forming the initial contour result of the target.

[0045] Furthermore, the initial contour is optimized by completing discontinuous parts of the contour, reconnecting broken boundaries, removing redundant boundaries caused by noise or local interference, and smoothing the contour edges to make the boundary transition more natural. At the same time, the contour position is locally adjusted to better fit the actual target boundary, thereby obtaining a contour result with good continuity and clear boundaries.

[0046] Finally, the optimized contour results are output, and the contour information is labeled in the form of images or stored in the form of data so that it can be called by subsequent processing modules and used directly in target recognition, image segmentation or detection tasks. During the output process, the spatial correspondence between the contour and the original image is maintained so that the contour can accurately reflect the real position and shape of the target in the original image, thereby completing the complete processing flow of color image contour extraction.

[0047] Implementation Method 3, in conjunction with Appendix Figure 1 This embodiment describes the technical solution provided above in further detail through specific examples. Specifically: The purpose of this embodiment is to overcome the defects of the prior art and provide a method for extracting color image contours by fusing color histograms with deep learning. Through the deep fusion of color features and semantic features, it can achieve high-precision, closed contour extraction in complex scenes such as low contrast, texture interference, and transparent objects.

[0048] Image preprocessing 1.1 Receive color input images, adjust their resolution to 512×512 pixels, and use a 3×3 mean filter for noise reduction to preserve color distribution information while suppressing Gaussian noise; 1.2 Convert the preprocessed RGB image to the HSV color space and separate the hue (H), saturation (S), and lightness (V) channels to avoid color feature redundancy caused by RGB channel correlation. Color histogram feature extraction 2.1 The H channel of the HSV color space is quantized at 16 levels, the S channel at 4 levels, and the V channel at 4 levels to construct a 256-dimensional color histogram. The pixel distribution frequency of each color component is counted to obtain the color feature vector. 2.2 Perform L2 normalization on the color feature vector, calculate the color distribution entropy value, determine the main color range of the target area, and generate a color constraint mask (only retain pixels related to the main color and filter out irrelevant texture areas). Deep learning semantic feature extraction 3.1 Construct a multi-scale nested convolutional neural network (MS-Net) using a preprocessed RGB image as input. The network contains 5 convolutional stages: The first and second stages are shallow feature extraction layers: using 3×3 convolution kernels (16 and 32 respectively) to extract image detail texture features, corresponding to small-scale edge information; The third and fourth stages are the mid-level feature fusion layers: 5×5 convolution kernels (64 in each layer) are used, and dilated convolutions are introduced to expand the receptive field and extract local structural features of the target. The fifth stage is the deep semantic extraction layer: using 7×7 convolutional kernels (128 in number) and global average pooling, the overall semantic boundary features of the image are extracted; 3.2 Each convolutional stage outputs a corresponding edge prediction map. The prediction maps of the five scales are transmitted to the fusion layer through lateral connections to form a multi-scale semantic feature set. Feature fusion and contour optimization 4.1 Feature Adaptive Weighted Fusion: The color constraint mask is multiplied pixel by pixel with the semantic feature maps at each scale to enhance the semantic feature response of the main color region and suppress feature interference from non-target regions (such as texture and shadow); 4.2 Introducing an attention mechanism: Constructing a color-semantic attention module, using the distribution entropy of the color feature vector as the weight, dynamically weighting the multi-scale semantic feature map (the weight coefficient of the dominant color region is 0.7-0.9, and the weight coefficient of the non-dominant color region is 0.1-0.3). 4.3 Contour Generation and Optimization: The fused feature map is input into the sigmoid activation function to obtain an initial contour probability map (threshold set to 0.5). Contour holes are filled by morphological closing operation, and the contour accuracy is optimized by sub-pixel edge fitting algorithm to ensure that the contour is closed at both ends and the positioning error is ≤1 pixel. Model training 5.1 Constructing the training dataset: containing 100,000 sets of "color image-annotated contour map" samples, covering complex scenes such as low contrast, cluttered textures, and transparent objects; 5.2 Design the composite loss function: L = α×L_bce + β×L_dice + γ×L_color, where: L_bce is the binary cross-entropy loss, which optimizes the accuracy of contour pixel classification. L_dice is the Dice loss, which solves the problem of uneven contour pixels; L_color is the color constraint loss, which enables the model to learn the correspondence between color distribution and contour. α, β, and γ are weighting coefficients, set to 0.4, 0.4, and 0.2 respectively; 5.3 MS-Net was trained using the mini-batch gradient descent algorithm (batch size=16, initial learning rate=1e-4), and converged after 100 iterations.

[0049] The technical solution provided in this embodiment, as verified by experiments, has the following significant beneficial effects: An innovative dual-drive fusion mechanism of "color constraint + semantic understanding" is proposed, which filters irrelevant textures by generating a dominant color mask from a color histogram, thus solving the texture interference problem of traditional methods. The combination of multi-scale nested networks and color attention modules enables the model to capture the overall semantic contour of the target and accurately locate the edge through color constraints, thereby improving the contour extraction accuracy in low-contrast and transparent object scenes. Subpixel-level contour optimization and morphological processing ensure contour closure and accuracy, with a positioning error of ≤1 pixel, meeting the high-precision application requirements of industrial inspection, image editing, etc. The end-to-end processing flow requires no manual parameter tuning, adapts to color image contour extraction in different scenarios, and is highly robust.

[0050] In a specific embodiment: Low-contrast image contour extraction: Input image: Acquire high-resolution images of automotive parts.

[0051] Preprocessing: Adjust the resolution to 512×512, perform 3×3 mean filtering for noise reduction, and convert to HSV color space.

[0052] Color feature extraction: 16 levels of quantization for the H channel, 4 levels for the S channel, and 4 levels for the V channel to generate a 256-dimensional feature vector. The color entropy value is calculated to determine that red is the main color tone, and a color constraint mask is generated.

[0053] Semantic feature extraction: MS-Net outputs edge prediction maps at 5 scales, with shallow layers capturing the texture of the apple surface and deep layers capturing the overall contour.

[0054] Feature fusion: The color mask and semantic features are multiplied pixel by pixel, and the attention module enhances the response of the red area. After fusion, a contour probability map is generated.

[0055] Optimized output: Morphological closing operations fill in tiny holes, subpixel fitting optimizes edges, and the final output is a closed apple outline (positioning error 0.8 pixels).

[0056] The above description of several specific embodiments further details the technical solution provided by the present invention in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above-described specific embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for extracting color image contours by fusing color histograms using deep learning, characterized in that, include: The steps of acquiring the color image to be processed and performing preprocessing to obtain standardized color image data; The step of extracting depth features based on the standardized color image data to obtain the corresponding depth feature map; The step of constructing color histogram features based on the standardized color image data to obtain color distribution features; The step of aligning and fusing the depth feature map with the color distribution feature map to obtain a fused feature map; The step of performing contour extraction processing based on the fused feature map to obtain the initial contour; The step of optimizing the initial contour to obtain the target contour.

2. The method for extracting color image contours by fusing color histograms using deep learning according to claim 1, characterized in that, The preprocessing involves normalizing the size of the color image to be processed, suppressing noise, and adjusting brightness and contrast to obtain standardized color image data.

3. The method for extracting color image contours by fusing color histograms using deep learning according to claim 1, characterized in that, The deep feature extraction involves inputting the standardized color image data into a convolutional neural network to perform multi-layer feature extraction, thereby obtaining a deep feature map that simultaneously contains local texture information and global semantic information.

4. The method for extracting color image contours by fusing color histograms using deep learning according to claim 1, characterized in that, The color histogram feature is constructed by dividing each color channel of the standardized color image data into intervals and counting the number of pixels in each interval, while simultaneously dividing the image into spatial regions to obtain color distribution features with spatial distribution information.

5. The method for extracting color image contours by fusing color histograms using deep learning according to claim 1, characterized in that, The alignment and fusion process involves mapping the color distribution features to a spatial scale consistent with the depth feature map and then combining them. The weights of the depth features and color distribution features are adjusted according to the feature changes in different regions to obtain a fused feature map.

6. The method for extracting color image contours by fusing color histograms using deep learning according to claim 1, characterized in that, The contour extraction process involves identifying regions with significant feature changes on the fused feature map as boundaries and connecting them to form an initial contour.

7. An apparatus for extracting color image contours by fusing color histograms using deep learning, characterized in that, include: A module that acquires the color image to be processed and performs preprocessing to obtain standardized color image data; A module that performs depth feature extraction based on the standardized color image data to obtain the corresponding depth feature map; A module for constructing color histogram features based on the standardized color image data to obtain color distribution features; A module that aligns and fuses the depth feature map with the color distribution feature map to obtain a fused feature map; A module that performs contour extraction processing based on the fused feature map to obtain an initial contour; A module that optimizes the initial contour to obtain the target contour.

8. A computer storage medium for storing computer programs, characterized in that, When the computer program is read by the computer, the computer executes the method of claim 1.

9. A computer, comprising a processor and a storage medium, characterized in that, When the processor reads the computer program stored in the storage medium, the computer executes the method of claim 1.

10. A computer program product, as a computer program, is characterized by: When the computer program is executed, it implements the method of claim 1.

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