An intelligent monitoring method and system for injection molding of automobile parts

Abstract

The present invention belongs to the field of image processing technology, and specifically relates to an intelligent monitoring method and system for injection molding of automotive parts. The method comprises: obtaining an injection-molded image of the automotive part to be tested and calculating a gradient field of the injection-molded image; performing a hierarchical topological analysis on the gradient field to generate topological features that characterize the structural characteristics of local regions in the image; generating an enhanced feature descriptor based on the topological features; and classifying regions in the injection-molded image using a preset classifier based on the enhanced feature descriptor to identify surface defects in the regions. By deeply analyzing the subtle topological structure of the gradient field, the present invention can sensitively capture the unique visual features of injection-molded defects in automotive parts, thereby significantly improving the accuracy of identifying surface defects in automotive parts.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of image processing. More particularly, the present application relates to an intelligent monitoring method and system for injection molding of automobile parts. BACKGROUND

[0002] Injection molding is the core process for producing automobile plastic parts. However, during injection molding, due to the complex interaction of mold design, injection parameter setting or raw material characteristics, parts are prone to produce a kind of hidden surface defect called sink mark at certain positions (such as the back of the reinforcing rib) when cooling and shrinking. From the physical form, sink mark appears as a smooth, gradual depression on the surface of the part, and its depth may only be microns. This defect does not produce obvious edges or color differences in vision, thus posing a great challenge to traditional machine vision detection methods.

[0003] At present, a commonly used technical solution is to use a feature descriptor based on a histogram of gradient direction, and combine a support vector machine and other classifiers for defect recognition. The invention patent with publication number CN106952258A gives a bottle mouth defect detection method based on a histogram of gradient direction, which includes: dividing the sample picture into multiple windows, counting the histogram of gradient direction in the window to obtain a feature vector, and using a support vector machine to form a classifier; then, the feature vector of each detection window is calculated by the histogram of gradient direction, and the classifier formed in advance is combined to determine whether the current bottle mouth is a defective bottle mouth.

[0004] However, the physical characteristics of sink mark defects are smooth depressions on the surface, and their visual features projected in two-dimensional images are continuous and gradual changes in gradient direction. For example, in a sink mark area, the gradient direction may smoothly transition from 45 degrees to 55 degrees. However, the coarse-grained angle quantization mechanism used by the existing histogram of gradient technique will classify all these continuous changes in small angles that should reflect differences into the same statistical interval, thus completely losing some key information. This may result in the feature vectors generated by the areas containing sink marks and normal areas being highly similar, making the classifier unable to learn the effective distinguishing boundary, and ultimately resulting in low detection sensitivity, serious missed detection, and inability to meet the pursuit of high quality in the automobile industry. SUMMARY

[0005] To solve the above technical problems of low recognition rate and serious missed detection of machine vision detection algorithms for surface defects in the injection molding process of automobile parts, especially for smooth and gradual sink mark defects, the present application provides solutions in the following aspects.

[0006] In a first aspect, the present application provides an intelligent monitoring method for injection molding of an automobile part, comprising: acquiring an injection molding image of the automobile part to be tested, and calculating a gradient field of the injection molding image; performing hierarchical topological analysis on the gradient field to generate topological features representing structure characteristics of a local region of the image; generating an enhanced feature descriptor based on the topological features; and classifying regions in the injection molding image based on the enhanced feature descriptor using a preset classifier to identify surface defects of the regions, thereby achieving intelligent monitoring of the injection molding quality of the automobile part.

[0007] The present application characterizes the essential difference between surface defects and normal surfaces by performing hierarchical topological analysis on the gradient field from multiple dimensions such as consistency of gradient direction, bending shape of principal direction field, and topological singularity. This method is no longer limited to simple gradient statistics, but can analyze the structure information of the gradient field, thereby sensitively identifying the weak gradient changes caused by shrink marks and other defects.

[0008] Preferably, the hierarchical topological analysis of the gradient field to generate topological features representing structure characteristics of a local region of the image comprises: calculating a structure tensor based on the gradient field in a local region of the injection molding image, and determining a direction consistency index representing the uniformity of gradient direction in the local region according to the eigenvalues of the structure tensor; selecting a structure ordered region based on the direction consistency index, and determining a principal direction field in the structure ordered region; calculating the Laplacian value of the principal direction field to obtain a gradient field curvature index representing the bending degree of the principal direction field; calculating the divergence of the principal direction field to obtain a flow field divergence index representing the convergence or divergence degree of the principal direction field; and taking the direction consistency index, gradient field curvature index, and flow field divergence index as the topological features.

[0009] The present application can gradually filter out irrelevant background and noise interference by analyzing a four-layer analysis framework from consistency to principal direction field to curvature to divergence. Random texture interference is effectively excluded, flat edges are distinguished from defect areas, and surface defects are accurately separated from complex backgrounds.

[0010] Preferably, the direction consistency index satisfies the expression: wherein is the gradient direction consistency index, and are the maximum eigenvalue and minimum eigenvalue of the structure tensor, respectively, is a preset positive number for preventing the denominator of the relationship from being zero.

[0011] Preferably, the gradient field curvature index satisfies the expression: wherein a gradient field curvature indicator of a pixel with coordinates is the main direction field, is a partial derivative.

[0012] Preferably, the flow field divergence indicator satisfies the expression: wherein, is a flow field divergence indicator of a pixel with coordinates .

[0013] Preferably, further comprising: normalizing the gradient field curvature indicator and the flow field divergence indicator; performing weighted summation on the normalized gradient field curvature indicator and the flow field divergence indicator; calculating an average value of gradient amplitudes of all pixels in the local region as a local average gradient amplitude; multiplying the result of the weighted summation, the direction consistency indicator and the local average gradient amplitude to generate a topological saliency indicator.

[0014] Preferably, the topological saliency indicator satisfies the expression: wherein, is a topological saliency indicator, and are absolute values of the normalized gradient field curvature indicator and the flow field divergence indicator respectively, and are preset weights, is a local average gradient amplitude.

[0015] Preferably, the generating an enhanced feature descriptor based on the topological feature comprises: calculating a standard gradient direction histogram feature vector in a local region of the injection molding image; concatenating a topological feature vector composed of the topological feature and the topological saliency indicator with the gradient direction histogram feature vector to form the enhanced feature descriptor.

[0016] The present application fuses the topological feature and the traditional gradient direction histogram feature to form an enhanced feature descriptor with richer information dimension and more comprehensive description capability. The descriptor not only retains the description capability of traditional algorithms on clear contours, but also can more effectively separate normal curved surfaces and surface defects in the feature space, so that the classifier can learn more accurate decision boundaries.

[0017] Preferably, the preset classifier is a support vector machine classifier.

[0018] ​In a second aspect, the present application provides an intelligent monitoring system for injection molding of automobile parts, comprising a processor and a memory, the memory storing computer program instructions which, when executed by the processor, implement the above-mentioned intelligent monitoring method for injection molding of automobile parts.

[0019] By adopting the above technical solution, the above-mentioned intelligent monitoring method for injection molding of automobile parts is generated into a computer program and stored in the memory to be loaded and executed by the processor, so that a terminal device is made according to the memory and the processor, and use is facilitated.

[0020] The present application can identify all structured regions in the image through direction consistency analysis, effectively filter out unstructured texture noise, and then further lock the regions that simultaneously satisfy the morphological bending and topological singular double characteristics through the collaborative analysis of the gradient field curvature and the flow field divergence in these ordered regions, so as to separate surface defects such as shrink marks from normal surfaces with ordinary design curvature.

[0021] Further, the novel topological features are fused with traditional gradient direction histogram features to construct an enhanced feature descriptor with high sensitivity and discrimination to surface defects. The recognition sensitivity is obviously improved, and the discrimination and recognition accuracy of the features are greatly enhanced, while the false alarm caused by normal highlights, curvature, etc. is effectively suppressed. BRIEF DESCRIPTION OF DRAWINGS

[0022] The above and other objects, features and advantages of the exemplary embodiments of the present application will be more apparent from the following detailed description taken in conjunction with the accompanying drawings, in which several embodiments of the present application are shown by way of example, and wherein like reference numerals refer to like elements throughout. In the drawings:

[0023] Figure 1 is a flowchart schematically showing an intelligent monitoring method for injection molding of automobile parts in the present application;

[0024] Figure 2 is a physical diagram schematically showing injection molding of the automobile part to be tested;

[0025] Figure 3 is a schematic diagram of an original gray-scale image of a shrink mark defect;

[0026] Figure 4 is a schematic diagram showing calculation of gradient amplitude;

[0027] Figure 5 is a visualized image showing calculation of the direction consistency index;

[0028] Figure 6 is a visualization image illustratively showing a computed gradient field curvature indicator;

[0029] Figure 7 is a visualization image illustratively showing a computed flow field divergence indicator;

[0030] Figure 8 is a topology feature image illustratively showing a fusion of the gradient field curvature and flow field divergence indicators;

[0031] Figure 9 is a visualization image illustratively showing a topology saliency indicator. DETAILED DESCRIPTION

[0032] The technical solutions in the embodiments of the present application will be apparently and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by a person skilled in the art without creative labor fall within the protection scope of the present application.

[0033] The specific embodiments of the present application will be described in detail below with reference to the drawings.

[0034] The embodiments of the present application disclose an intelligent monitoring method for injection molding of automobile parts, referring to Figure 1 , comprising steps S1-S4:

[0035] S1, acquiring an injection molding image of a to-be-tested automobile part, and calculating a gradient field of the injection molding image.

[0036] Specifically, a high-resolution industrial camera is deployed on an automobile part injection molding production line, and the position and angle of the camera are fixed relative to the position of the to-be-tested part. At the same time, a single and fixed non-direct light source is used to acquire the injection molding image of the to-be-tested automobile part, so that a clear, stable and information-rich reflection can be formed on the surface of the part, thereby ensuring that the shrink mark defect is presented in a consistent optical form.

[0037] In an optional embodiment, as shown in Figure 2 , is a physical diagram illustratively showing injection molding of a to-be-tested automobile part. To further improve the reliability of the acquired image, the acquired color image can be converted into a gray-scale image, and then the gray-scale image is subjected to gamma correction to linearize the image brightness, thereby ensuring that the gray-scale value of the pixel is in a linear relationship with the scene illumination intensity. As shown in Figure 3 , is a schematic diagram of an original gray-scale image showing a shrink mark defect.

[0038] In the optional embodiment, a Gaussian filter is applied to the linearized grayscale image for smoothing to suppress the interference of sensor noise on the gradient calculation. Exemplarily, the size of the Gaussian kernel can be .

[0039] In the optional embodiment, a 3x3 Sobel operator can be used to calculate the first-order partial derivatives of the image in the horizontal (x) and vertical (y) directions, respectively, to obtain the gradient components of the pixel with coordinates and . Thus, the gradient amplitude and the gradient direction of each pixel point can be calculated. In the present application, the gradient amplitudes and the gradient directions obtained are taken together as the gradient field of the injection molded image. As shown in Figure 4 , it is a schematic diagram illustrating the calculation of the gradient amplitude.

[0040] In this way, through the standardized image acquisition and preprocessing means, high-quality gradient field data can be provided for subsequent topological analysis, ensuring the accuracy and reliability of the final recognition result.

[0041] S2, performing layered topological analysis on the gradient field to generate topological features representing the structural characteristics of the local region of the image.

[0042] In an optional embodiment, in order to extract topological features with strong directionality to surface defects from the fine structure of the gradient field, the basic unit of analysis can be set as a local block of 16x16 pixels.

[0043] Specifically, first, in each 16x16 local block, a structure tensor is constructed:

[0044]

[0045] wherein W represents the local block being analyzed, and then two eigenvalues and of the 2x2 matrix are calculated, and from which the gradient direction consistency index can be calculated:

[0046]

[0047] wherein is the direction consistency index representing the uniformity of the gradient direction in the local block region, and the value range is [0, 1]; , is the maximum and minimum eigenvalues of the structure tensor ; ​Is a very small positive number used to prevent the denominator from being 0, such as .

[0048] Specifically, when the gradient direction in the region is highly consistent (such as a straight line), ,at this time When the gradient direction in the region is completely random and isotropic (such as ideal noise), ,at this time For a shrinkage area, the reflection distortion caused by it is orderly. Typically high values, similar to a normal smooth surface.

[0049] Furthermore, the maximum eigenvalue can be calculated The corresponding eigenvector, whose direction is the main gradient direction of the block , all local blocks Together they form the main direction field. If the indicator is higher than a specific threshold, for example, the specific threshold is 0.6, then the corresponding local block can be considered as a structured area and is the key area for subsequent analysis; while the local block below the specific threshold can be considered as unstructured and can be directly excluded, thereby improving the processing efficiency of the subsequent process.

[0050] like Figure 5 As shown, it is a visualization image schematically showing the calculated directional consistency index. It can be seen that most areas including the background and defects are highlighted, indicating that they are all structurally ordered.

[0051] In an optional embodiment, after identifying the structurally ordered region, it is necessary to further distinguish between straight structures and curved structures, because a normal cylindrical part surface will also form ordered, straight reflective stripes, while sink marks will cause it to bend.

[0052] Specifically, whether a pixel belongs to a smooth defect area depends not only on the gradient of the point, but also on the overall shape of the gradient direction field in its neighborhood. For a flat or regularly curved surface, its gradient direction field is smooth and linear, and its second-order derivative approaches zero. However, in a shrinkage area, its gradient direction field will show a concave or convex shape, resulting in a significantly non-zero second-order derivative value. Therefore, the gradient of the main direction can be calculated. The Laplace value of is used to obtain the gradient field curvature index used to characterize the degree of curvature of the main direction field:

[0053]

[0054] in, The gradient field curvature characterizes the degree of curvature of the main direction field; is the main gradient direction obtained through structural tensor analysis.

[0055] It is worth noting that the second-order partial derivative in the discrete image can be approximated by further differentiating the first-order difference image. Figure 6 As shown, it is a schematic visualization image showing the calculated gradient field curvature index. It can be seen that Figure 6 A ring-shaped highlighted area corresponding to the defect edge is shown, proving that the gradient field curvature metric successfully identified the curved feature.

[0056] Furthermore, on a flat or regular cylindrical surface, the main gradient direction is constant or changes linearly, and its second-order derivative is zero, so is 0; however, in a shrinkage area, its concave shape will inevitably lead to nonlinear bending of the main direction field, resulting in a significant non-zero value.

[0057] In this way, by calculating the gradient field curvature index, it is possible to further screen out regions with curved morphology from all structurally ordered regions.

[0058] In an optional embodiment, after further screening out curved regions from the structurally ordered regions, since the part's inherent rounded corners can also produce curvature, sink marks can cause the gradient flow field to converge or diverge. Therefore, further analysis can be performed using Divergence, a specialized tool that describes this phenomenon.

[0059] Specifically, the main direction field Considered as a two-dimensional vector field , and calculate the divergence of its gradient flow field as the flow field divergence index characterizing the degree of convergence or divergence of the main direction field :

[0060]

[0061] Specifically, for a designed fillet, although its main direction field is curved ( non-zero), but usually nearly parallel streamlines with divergence For a sink mark with a concave center, the gradient streamlines converge toward the center, resulting in a significant negative divergence ( ), and vice versa, its absolute value | ∣ will be significantly non-zero. Figure 7 , which schematically illustrates a visualization image of the calculated flow field divergence index.

[0062] In this way, by calculating the flow field divergence index, the structural center with converging or diverging topological characteristics can be accurately identified, which is the main feature that distinguishes sink marks from other curved structures.

[0063] In this optional embodiment, the directional consistency index, the gradient field curvature index and the flow field divergence index are used as topological features. Specifically, for an area to be highly suspected of being a surface defect, it must simultaneously meet the following conditions: High), structural bending ( High), and the curvature presents a converging or diverging shape ( |High). Therefore, in this application, these conditions are combined to construct a topological significance index .

[0064] Specifically, an area only needs or If a key topological dimension shows a strong enough response, it should be considered as a potential defect. Through linear weighted summation, the contributions of the two can be comprehensively considered. Even if one feature is slightly weak, the other strong feature can still ensure that the defect is effectively detected. At the same time, in order to eliminate and To avoid the influence of different numerical ranges of two indicators, they are linearly normalized to the interval [0,1] independently before fusion. Figure 8 As shown in FIG, this application schematically illustrates a topological feature image after the gradient field curvature and flow field divergence index are fused. In this application, the normalized index is n( )and , then the topological significance index for:

[0065]

[0066] in, is the topological significance index, and are the absolute values ​​of the normalized gradient field curvature index and flow field divergence index, and is the preset weight, is the non-negative local average gradient magnitude.

[0067] It is worth noting that it is possible to give more specificity to the center point positioning Slightly higher weight, exemplary, , to highlight the defect center. The term as an energy weight can effectively suppress the pseudo features of low-gradient noise areas, while suppressing the weights of high-gradient strong edges to prevent their excessive influence, allowing the algorithm to focus more on the topological structure itself.

[0068] Specifically, when an area is a flat dark area, For zero, this zero weight will be multiplied to the topological feature of the region, so that its final topological saliency index also becomes zero, thus effectively suppressing the noise false features from the no-information region.

[0069] Only when a region has valid gradient changes, It will be a positive number, allowing its topological features to contribute to the final result, The greater, the more energy information the region has, the higher the reliability of the topological analysis result, and the greater the weight obtained. For smaller values, It is approximately linear growth, and for very large values, The growth becomes very slow.

[0070] For example, suppose in a certain analysis block, after calculation and normalization, we get (structure order), (significant bending), (strong convergence), and local average gradient amplitude , Then ; Then This is a very high saliency score, indicating that the region is very likely to be a surface defect. As Figure 9 shown, it is a visual image of the topological saliency index, which can be seen that the defect region presents a very concentrated, bright highlight patch, while other regions are effectively suppressed.

[0071] In this way, by constructing and calculating the topological saliency index, the topological information and energy information in multiple dimensions can be effectively fused to generate a representation index with high signal-to-noise ratio and discrimination for surface defects, providing a solid foundation for the final classification and discrimination.

[0072] S3, generating an enhanced feature descriptor based on the topological features.

[0073] In an optional embodiment, in the local region of the injection molding image, a standard gradient direction histogram feature vector is calculated; the topological feature vector composed of the topological features and the topological saliency index is concatenated with the gradient direction histogram feature vector to form an enhanced feature descriptor.

[0074] Specifically, a standard gradient direction histogram (Histogram of Oriented Gradients, HOG) feature vector According to the conventional method, in each 16x16 block, the block is divided into four 8x8 units, and a gradient direction histogram of nine bins is calculated for each unit (when constructing the gradient direction histogram, the angle range of 0-180 degrees is divided into nine 20-degree intervals), and finally a 36-dimensional HOG feature vector is formed in series.

[0075] Then a topological feature vector is constructed In each 16x16 block, the four indicators calculated are combined to form a 4-dimensional topological feature vector: .

[0076] Finally, the topological feature vector and the gradient direction histogram feature vector are concatenated to form a 40-dimensional enhanced feature descriptor .

[0077] In this way, by fusing the topological features and the HOG features, a new enhanced feature descriptor is created, which can not only describe the macro shape contour, but also represent the micro surface curvature change, greatly improving the description ability of the surface defects of the automobile parts.

[0078] S4, based on the enhanced feature descriptor, a preset classifier is used to classify the regions in the injection molding image to identify the surface defects of the regions, thereby realizing intelligent monitoring of the injection molding quality of the automobile parts.

[0079] In an optional embodiment, a large number of injection molding image samples of automobile parts can be prepared, and the surface defect regions (positive samples) and various typical defect-free regions (negative samples) can be accurately labeled by professional quality inspectors. The 40-dimensional enhanced feature descriptor is extracted for each labeled region. A binary support vector machine (SVM) classifier is trained using these labeled feature vectors to learn the decision boundary for distinguishing between defective and non-defective regions.

[0080] Further, for a new injection molding image of an automobile part to be tested, a sliding window method is used to move a 16x16 window over the image block by block, and the enhanced feature descriptor is extracted at each window position and sent to the trained SVM for discrimination to obtain a defect probability value, thereby generating a defect saliency map. By thresholding and non-maximum suppression of the saliency map, all surface defects can be accurately located and segmented.

[0081] In this way, by training the classifier using the enhanced feature descriptor, automatic, high-precision online identification and positioning of surface defects of automobile parts on the production line can be achieved, effectively solving the missed detection problem of the conventional method.

[0082] The embodiment of the present application further discloses an intelligent monitoring system for injection molding of automobile parts, comprising a processor and a memory, and the memory stores computer program instructions, which realize the intelligent monitoring method for injection molding of automobile parts according to the present application when executed by the processor.

[0083] The system further comprises other components such as communication bus and communication interface which are well known to those skilled in the art, and their settings and functions are known in the art, thus not described here.

[0084] In the description of the present specification, the meaning of "a plurality of", "several" is at least two, for example, two, three or more, etc., unless otherwise explicitly specifically limited.

[0085] Although the present specification has shown and described several embodiments of the present application, it will be apparent to those skilled in the art that many modifications, changes and substitutions can be made to the embodiments described herein without departing from the spirit and scope of the present application. It should be understood that various alternatives to the embodiments of the present application described herein can be employed in practicing the present application.

Claims

1. An intelligent monitoring method for injection molding of automobile parts, characterized in that: include: Acquire an injection molding image of the automobile part to be tested, and calculate the gradient field of the injection molding image; Performing a hierarchical topological analysis on the gradient field to generate a topological feature that characterizes the structural characteristics of a local area of ​​the image; performing a hierarchical topological analysis on the gradient field to generate a topological feature that characterizes the structural characteristics of a local area of ​​the image includes: calculating a structural tensor based on the gradient field in the local area of ​​the injection molding image, and determining a directional consistency index for characterizing the degree of uniformity of the gradient direction in the local area according to the eigenvalue of the structural tensor; screening a structurally ordered region based on the directional consistency index, and determining a main direction field in the structurally ordered region; calculating the Laplace value of the main direction field to obtain a gradient field curvature index for characterizing the degree of curvature of the main direction field; calculating the divergence of the main direction field to obtain a flow field divergence index for characterizing the degree of convergence or divergence of the main direction field; using the directional consistency index, the gradient field curvature index, and the flow field divergence index as the topological feature; generating an enhanced feature descriptor based on the topological features; Based on the enhanced feature descriptor, a preset classifier is used to classify the regions in the injection molding image to identify surface defects in the regions, thereby realizing intelligent monitoring of the injection molding quality of the automobile parts.

2. The intelligent monitoring method for automobile parts injection molding according to claim 1, characterized in that: The directional consistency index satisfies the expression: in is the gradient direction consistency indicator, and are the maximum eigenvalue and minimum eigenvalue of the structure tensor, respectively. A preset positive number used to prevent the denominator of the relationship from being zero.

3. The intelligent monitoring method for automobile parts injection molding according to claim 1, characterized in that: The gradient field curvature index satisfies the expression: in The coordinates are The gradient field curvature index of the pixel, is the main direction field, is the partial derivative.

4. The intelligent monitoring method for automobile parts injection molding according to claim 1, characterized in that: The flow field divergence index satisfies the expression: in, The coordinates are The flow field divergence index of the pixel.

5. The intelligent monitoring method for automobile parts injection molding according to claim 1, characterized in that: Also includes: Normalizing the gradient field curvature index and the flow field divergence index; Perform weighted summation on the normalized gradient field curvature index and flow field divergence index; Calculating the average value of the gradient amplitudes of all pixels in the local area as the local average gradient amplitude; The weighted summation result is multiplied by the directional consistency index and the local average gradient magnitude to generate a topological significance index.

6. The intelligent monitoring method for automobile parts injection molding according to claim 5, characterized in that: The topological significance index satisfies the expression: in, is the topological significance index, and are the absolute values ​​of the normalized gradient field curvature index and flow field divergence index, and is the preset weight, is the non-negative local average gradient magnitude, is the gradient direction consistency indicator.

7. The intelligent monitoring method for automobile parts injection molding according to claim 5, characterized in that: The generating of an enhanced feature descriptor based on the topological feature comprises: Calculating a standard gradient direction histogram feature vector in a local area of ​​the injection molding image; A topological feature vector composed of the topological feature and the topological significance index is connected in series with the gradient direction histogram feature vector to form the enhanced feature descriptor.

8. The intelligent monitoring method for automobile parts injection molding according to claim 1, characterized in that: The preset classifier is a support vector machine classifier.

9. An intelligent monitoring system for injection molding of automobile parts, characterized in that: include: A processor and a memory, wherein the memory stores computer program instructions, and when the computer program instructions are executed by the processor, an intelligent monitoring method for injection molding of automobile parts according to any one of claims 1 to 8 is implemented.

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