DE102020211995A1 - Determination of the image parts in the latent space of the image classifier that are relevant for the decision of an image classifier - Google Patents

Abstract

Method (100) for measuring the parts (2a) of an input image (2) on which an image classifier (1) bases its decision on the assignment (14a) of this input image (2) to one or more classes of a predetermined classification, with the steps: • a trained image classifier (1) is provided (110), which is designed to generate intermediate products (11a-13a) from the input image (2) using one or more convolution layers (11-13). and using one or more classifier layers (14) to map such an intermediate product (11a-13a) to the assignment (14a) to the class or classes;• an input image (2) is provided (120);• from the input -image (2), at least one intermediate product (11a-13a) and an assignment (14a) to one or more classes are generated (130) with the image classifier (1);• at least one intermediate product (11a-13a) is divided into spatially contiguous areas (31-35) decomposed (140), the jewei ls meet a predetermined relevance criterion (3) and are separated from one another by areas that do not meet this relevance criterion (3);• these contiguous areas (31-35) are evaluated as independent components of the intermediate product (11a-13a), and it dependencies (41-45) of the decision of the image classifier (1) are determined (150) from these components (31-35); • from these dependencies (41-45) the searched for decision-relevant parts (2a) of the input image (2 ) determined (160).

Description

The present invention relates to the control of the behavior of trainable image classifiers that can be used, for example, for the quality control of mass-produced products or also for the at least partially automated driving of vehicles.

State of the art

In the series production of products, it is usually necessary to continuously check the quality of the production. The aim is to identify quality problems as quickly as possible in order to be able to remedy the cause as soon as possible and not lose too many units of the respective product as scrap.

Optical inspection of a product's geometry and/or surface is fast and non-destructive. the WO 2018/197 074 A1 discloses an inspection apparatus in which an object can be exposed to a plurality of lighting situations, images of the object being recorded with a camera in each of these lighting situations. The topography of the object is evaluated from these images.

Images of the product can also be directly assigned to one of several classes of a given classification using an image classifier based on artificial neural networks. On this basis, the product can be assigned to one of several specified quality classes. In the simplest case, this classification is binary ("OK"/"not OK").

When driving vehicles in an at least partially automated manner, image classifiers that can be trained are also used in order to evaluate traffic situations or at least to examine their content of objects.

Disclosure of Invention

Within the scope of the invention, a method was developed for measuring the parts of an input image on which an image classifier bases its decision on the assignment of this input image to one or more classes of a specified classification. In many applications, knowledge of these parts is important for assessing whether the image classifier reacts quickly and correctly in all situations, so that downstream systems react appropriately to the respective situation.

For example, it is desirable for an image classifier for traffic situations to recognize a pedestrian not only when the pedestrian is fully visible, but as soon as the head, legs or other features that clearly identify the pedestrian as such are visible will. If such an image classifier controls a warning system, a driver assistance system or a system for at least partially automated driving, dangerous situations in which, for example, a pedestrian steps onto the road between parked vehicles, can be defused earlier.

For example, in the quality control of mass-produced products, it is important that certain defects and damage always lead to the product being classified as "not OK = NOK". The defect or damage is not offset by the fact that other areas of the image may be particularly "beautiful".

A trained image classifier is provided for the method, which is designed to generate intermediate products from the input image using one or more convolution layers and to map such an intermediate product to the assignment to the class or classes using one or more classifier layers.

For example, the convolution layers of the image classifier may include filter kernels. The convolution layers then produce feature maps as intermediate products, each of which indicates activation values of the features recognized by a filter kernel. The classifier layer can include a fully crosslinked layer, for example.

An input image is provided, the decision-relevant part of which is to be determined. The image classifier maps this input image to a mapping to one or more classes. This assignment, and here in particular a class that is particularly preferred within the scope of this assignment (for example that class with a highest classification score), can be understood as a decision by the image classifier. On the way to this decision, the aforementioned intermediate products are also created automatically. One or more of these intermediate products are evaluated in order to determine the parts of the input bulge that are relevant for the decision of the image classifier.

For this purpose, starting from a predetermined relevance criterion, at least one intermediate product is broken down into spatially connected areas that each meet this relevance criterion and are separated from one another by areas that do not meet the relevance criterion. These contiguous areas are called mutually independent components of the intermediate are evaluated.

• • inwieweit sich die Entscheidung des Bildklassifikators ändern würde, wenn eine oder mehrere Komponenten nicht im Zwischenprodukt enthalten wären, bzw.
• • inwieweit das Vorhandensein einer oder mehrerer Komponenten im Zwischenprodukt hinreichend für die Entscheidung des Bildklassifikators ist, unabhängig vom restlichen Inhalt des Zwischenprodukts.

Dependencies of the decision of the image classifier on these components are now determined. This means in particular, for example, any form of measurement or other quantification,

• • to what extent the decision of the image classifier would change if one or more components were not included in the intermediate product, or
• • To what extent the presence of one or more components in the intermediate is sufficient for the decision of the image classifier, independent of the rest of the content of the intermediate.

From the dependencies determined in this way, the searched for decision-relevant parts of the input image are determined. Here, in particular, a spatial correspondence between the intermediate product and the input image can be used. The intermediate product usually has a significantly reduced dimensionality compared to the input image. However, for example, a particular corner of the input image still contributes the most to its corresponding corner.

It was recognized that the decomposition of the intermediate product into components drastically reduces the computational effort for many investigations into which parts of the input image are relevant to the decision. In the components of the intermediate that were determined to be independently, several numerical values of the intermediate that relate to individual characteristics are summarized. Instead of a very large number of features, only a significantly smaller number of components need to be examined for relevance to the decision. In particular, the number of combinations to be examined is significantly lower.

Furthermore, the subdivision of the intermediate product into features determined by the choice of filter kernels does not necessarily correspond to the meaningful subdivision according to the semantic meaning of parts of the input image. Therefore, an examination of the decision-making relevance based on the recognized independent components is much better motivated.

In a particularly advantageous embodiment, the relevance criterion includes numerical values in the intermediate product being above a predetermined threshold value. A two-dimensional feature map can then be viewed as a "mountain range" from which more or less is visible depending on the "water level" determined by the threshold value. In particular, several "high-rise" areas may be connected to one another by somewhat "lower-lying" areas. The "water level" then decides whether the "deeper" areas are still visible and thus form a coherent component of the intermediate product together with the "high-rising" areas, or whether the "lower-lying" areas "sink" and each of the "high-rise" areas form a separate component of the intermediate.

In particular, the threshold value can be optimized in a self-consistent manner, for example. For this purpose, the parts of the input image that are actually relevant to the decision and that are determined within the framework of the method can be compared with specified target parts that are supposed to be nominally relevant to the decision of the image classifier. The specified threshold value for determining the independent components can then be optimized with the aim that the actually decision-relevant parts that are then determined come into better agreement with the nominal decision-relevant parts.

However, the search for the appropriate threshold value can also start, for example, at a predetermined high threshold value, and the threshold value can be successively reduced until, for example, a combination of components is found that is essential and/or sufficient for the decision of the image classifier.

The relevance criterion, such as a threshold value, can be selected differently for different feature maps, for example. However, it is also possible, for example, to add up or average activation values from a number of feature maps, and this sum or the average value can then be evaluated using the relevance criterion. The latter alternative combines the information from all feature maps into a set of independent components of the intermediate product, so that the total number of these independent components, which is decisive for the computational effort of a further analysis, is further reduced.

In a particularly advantageous embodiment, determining the dependencies includes determining a smallest combination of components whose deactivation in the intermediate product cancels and/or changes the decision of the image classifier. For example, if the omission of a particular scratch in an image of a product causes the product to go from a "not OK = NOK" class to an "OK" class in optical quality control, then the Krat Zer relevant for the decision about the class assignment. However, a significant change in the decision can already be present, for example, when a classification score of the image classifier is minimized in relation to the previously preferred class.

However, this is only one side of the coin. It is also important to know whether this scratch alone already leads to a classification as NOK or whether, for example, a combination of scratches extending from one edge of the product to the other leads to classification as NOK . For example, the risk of a metallic fatigue fracture can only be significantly increased compared to the risk of a completely defect-free product if there is a continuous combination of scratches.

Therefore, in a further advantageous embodiment, determining the dependencies includes determining a smallest compilation of whose presence in the intermediate product is sufficient for the decision of the image classifier. In particular, this can mean, for example, that the decision of the image classifier remains unchanged even if all components except the components in the composition are deactivated.

In these investigations, a component in the intermediate can be deactivated, for example, by setting all the values of the intermediate that are assigned to the component to zero. However, activation values of exactly zero rarely occur in reality. The activation values of components that are not currently relevant will typically be very small, but will remain different from zero. Therefore, in a further particularly advantageous embodiment, a component in the intermediate product is deactivated by being assigned activation values in the intermediate product, which the image classifier assigns to this component when an input image of a different class is fed to it.

For example, an image classifier for the quality control of products can classify images of the products into the three classes "OK", "NOK" and "no decision possible". When examining whether a particular component is relevant for the classification into the class "OK" or "NOK", the activation values for this particular component can be set to those activation values that the image classifier provides for the same component if it has a Image of the class "no decision possible" is added.

In a further particularly advantageous embodiment, the importance of individual components is evaluated using a predefined degree of importance. Components can then be pre-selected for dependency determination based on this assessment. In this way, the number of components to be examined, and in particular the number of combinations of components to be examined, can be reduced even further.

For example, the importance of an individual component can be determined using an expected value for a classification score supplied by the image classifier via a large number of intermediate products, each of which contains this component. For example, if there are N individual components, a binary mask of N bits can be constructed that indicates for each component whether it is activated or not. Many such binary masks can then be drawn from a random distribution, with the bit relating to the currently examined component being set to 1 in all of these masks. An intermediate product can then be formed from each of these masks, and the image classifier can supply a classification score for each of these intermediate products. An expected value emerges from the many classification scores determined in this way.

This does not rule out that, given a comparatively small number N of individual components, a brute-force search for the intermediate product with the best classification score is also practicable. The components can also be filtered in advance. For example, all components whose number of pixels is below a predetermined threshold value can remain unconsidered. In this way, the search can be significantly simplified and the process accelerated accordingly.

In a particularly advantageous embodiment, an image of a mass-produced product is selected as the input image. The classes of the classification then represent a quality assessment of the product, such as "OK", "not OK = NOK", "no decision possible" or any gradations in between. In this context, explanations for why the image classifier assigns an input image to the class "NOK" are particularly important. Such explanations not only improve the image classifier itself, but also provide insight into the possible root cause of the quality issue that was set in the manufacturing process. If, for example, a large number of small localized defects in the product were decisive for the classification as "NOK" and these defects in turn were associated with certain physical conditions during the manufacture of the correlated to the product (such as high temperature or high pressure), efforts can be made to correct these conditions so that a greater proportion of manufactured product specimens will be classified as “OK” in the future.

In the case of a product made up of various individual parts or assemblies, it can also be recognized, for example, that the characteristics that are decisive for classification as "NOK" are all localized on an individual part or in an assembly. This is an indication that the part of the manufacturing process in which this part or assembly is created may be defective. It is therefore possible to “surgically” intervene in a complex sequence of production steps in order to specifically rectify problems without making other aspects too bad.

The determined parts of the input image, on which the image classifier bases its decision, can be compared, for example, with a part of the input image that was determined as relevant for the quality assessment of the product based on an observation of the same product with a different imaging modality. A quality assessment for the image classifier can then be determined from the result of this comparison. For example, hyperparameters of the image classifier can be optimized with the aim of optimizing this quality assessment.

In a further particularly advantageous embodiment, an image of a traffic situation taken from a vehicle is selected as the input image. The classes of the classification then represent assessments of the traffic situation, on the basis of which the future behavior of the vehicle is planned. Especially in this field of application, the image classifier and a downstream warning system, driver assistance system or system for at least partially automated driving can often only be trusted if the decisions of the image classifier can be explained. The method can provide precisely these explanations.

The determined parts of the input image, on which the image classifier bases its decision, can be compared, for example, with a part of the input image that is known to be relevant for the assessment of the traffic situation. A quality assessment for the image classifier can then be determined from the result of this comparison. Analogous to the application example of the quality control of products manufactured in series, hyper parameters of the image classifier can then be optimized with the aim that the quality of the image classifier is then better evaluated.

In particular, the method can be fully or partially computer-implemented. The invention therefore also relates to a computer program with machine-readable instructions which, when executed on one or more computers, cause the computer or computers to carry out the method described. In this sense, control devices for vehicles and embedded systems for technical devices that are also able to execute machine-readable instructions are also to be regarded as computers.

The invention also relates to a machine-readable data carrier and/or a download product with the computer program. A downloadable product is a digital product that can be transmitted over a data network, i.e. can be downloaded by a user of the data network and that can be offered for sale in an online shop for immediate download, for example.

Furthermore, a computer can be equipped with the computer program, with the machine-readable data carrier or with the downloadable product.

Further measures improving the invention are presented in more detail below together with the description of the preferred exemplary embodiments of the invention with the aid of figures.

character list

• 1 Ausführungsbeispiel des Verfahrens 100 zur Messung der für einen Bildklassifikator 1 entscheidungsrelevanten Anteile 2a eines Eingabe-Bildes 2;
• 2 Beispielhafte Anwendung des Verfahrens 100 bei der Analyse einer Verkehrssituation 50;
• 3 Beispielhafte Anwendung des Verfahrens 100 bei der Analyse eines bei der optischen Qualitätskontrolle aufgenommenen Bildes 60.

It shows:

• 1 Exemplary embodiment of the method 100 for measuring the parts 2a of an input image 2 that are relevant for an image classifier 1;
• 2 Exemplary application of the method 100 in the analysis of a traffic situation 50;
• 3 Exemplary application of the method 100 in the analysis of an image 60 recorded during optical quality control.

1 10 is a schematic flow chart of an embodiment of the method 100.

In step 110 a trained image classifier 1 is provided. In step 120 an input image 2 is provided. In step 130, one or more convolution layers 11-13 in the image classifier 1 generate intermediate products 11a-13a, and at least one classifier layer 14 of the image classifier 1 generates an assignment 14a to one or more classes from this.

At least one of the intermediate products 11a-13a is broken down in step 140 into spatially connected areas 31-35, which each meet a predetermined relevance criterion (3) and are separated from one another by areas that do not meet this relevance criterion 3. These contiguous areas 31-35 form mutually independent components of the intermediate product 11a-13a examined and are therefore only called components in the following. In step 150, dependencies 41-45 of the decision of the image classifier 1 on these components 31-35 are determined. From these dependencies 41-45, the parts 2a of the input image 2 that are relevant to the decision are determined.

According to block 141, different relevance criteria 3 can be selected, for example, for different feature maps in the intermediate products 11a-13a, which can originate from different filter cores in the convolution layers 11-13. Alternatively, according to block 142, for example, activation values of multiple feature maps can be summed up, and this sum can be evaluated using relevance criterion 3.

According to block 144, the relevance criterion 3 can in particular include, for example, that numerical values in the intermediate product 11a-13a are above a predefined threshold value 3a. In particular, according to block 144a, for example, portions 2a of the input image 2 that are actually relevant to the decision can be compared with specified target portions 2# that are supposed to be nominally relevant to the decision. The threshold value 3a can then be optimized according to block 144b with the aim that the actually decision-relevant components 2a then determined come into better agreement with the nominal decision-relevant components 2#.

According to block 151, the determination of the dependencies 41-43 can include, for example, determining a smallest combination of components 31-35 whose deactivation in the intermediate product 11a-13a cancels and/or changes the decision of the image classifier 1. A mere reduction in a classification score is not necessarily a significant change in the decision. If, on the other hand, a classification score for a class is reduced to almost zero and/or another class now comes to the fore as a result of the reduction in the classification score for the previously preferred class, one can certainly speak of an annulment or change of the decision .

Alternatively or also in combination with this, determining the dependencies 41-43 according to block 152 can include, for example, determining a smallest combination of components 31-35 whose presence in the intermediate product 11a-13a is sufficient for the decision of the image classifier 1.

A component 31-35 can be deactivated in the intermediate product 11a-13a according to block 153, for example, by assigning activation values to it in the intermediate product 11a-13a, which the image classifier 1 assigns to this component 31-35 when it receives an input image 2 from another class is supplied.

Before dependencies 41-43 of the decision of the image classifier 1 of components 31-35 are examined in detail, individual components 31-35 can first be evaluated according to block 154 with a predetermined degree of importance. According to block 155, components 31-35 can then be preselected on the basis of this evaluation for determining the dependencies 41-45.

According to block 154a, the evaluation of the importance of an individual component 31-35 can be determined, for example, using an expected value for a classification score supplied by the image classifier 1 via a large number of intermediate products 11a-13a, each of which contains this component 31-35.

According to block 105, the input image 2 can in particular be an image of a mass-produced product, for example. The classes of the classification then represent a quality rating of the product. The parts 2a of the input image 2 determined in step 160, on which the image classifier 1 bases its decision, can be compared in step 170 with a part 2b of the input image 2, which is based on an observation of the same product with a different imaging modality than relevant for the quality assessment of the product.

Alternatively, according to block 106, the input image 2 can be, for example, an image taken from a vehicle. The classes of the classification then represent assessments of the traffic situation, on the basis of which the future behavior of the vehicle is planned. The parts 2a of the input image 2 determined in step 160, on which the image classifier 1 bases its decision, can be compared in step 180 with a part 2b of the input image 2, which is known from any source to be relevant for the assessment of the traffic situation is.

A quality evaluation 1a of the image classifier 1 can be determined in step 190 from the results 170a or 180a determined in the comparisons 170 or 180 .

2 shows an exemplary application of the method 100 in the analysis of an input image 2 showing a traffic situation 50 . The traffic situation 50 contains a parked vehicle 51, a pedestrian 52 and a smartphone 53 in front of a road 54 as a background. The pedestrian 52 is just about to step out from behind the vehicle 51 and does not pay attention to the moving traffic because he is using the smartphone 53 in his hand and deep in a phone call.

If the processing of this input image 2 by the image classifier 1 is analyzed using the method 100 described above, for example the 2 indicated five components 31-35 come to light, which for the sake of clarity have already been transferred from the space of the intermediate products 11a-13a back into the space of the input images 2. Therefore, the components 31-35 also partly adjoin one another in this representation, while they are spaced apart from one another in the space of the intermediate products 11a-13a.

Component 31 contains the head of pedestrian 52. Component 32 contains part of the torso of pedestrian 52. Component 33 contains the arm and hand of pedestrian 52. Component 34 contains the smartphone 53. Component 35 contains the parked vehicle 51.

The method 100 can now be used to check, for example, whether the pedestrian 52 is still recognized as such when he has lowered his arm and is not holding the smartphone 53 to his ear. In this case neither the arm nor the smartphone 53 are visible. Paradoxically, if the image classifier 1 has seen a large number of training images with people phoning and has practically learned the smartphone as an additional body part of a person, a pedestrian 52 who behaves correctly in traffic and does not make a phone call when crossing a street could be recognized too late and run over will.

Conversely, it can be checked, for example, whether the image classifier 1 also deduces the presence of a pedestrian 52 from the presence of a smartphone 53 and reports its detection. A vehicle controlled by the image classifier 1 could then be prompted to brake hard, for example by a smartphone 53 lost on the road 54, which can trigger a rear-end collision.

3 shows a further exemplary application of the method 100 in the analysis of an image 60 recorded during the optical quality control of a screw nut 61 as input image 2. In FIG 3 Example 61 shown, the nut 61 has two cracks 62 and 63. Accordingly, for example, three components 31-33 can emerge from the analysis.

Component 31 contains the first crack 62. Component 32 contains the second crack 63. Component 33 contains the undamaged remainder of the nut 61. Analogous to 2 the components 31-33 are transferred here again to the space of the input images 2.

As part of quality control, for example, it may be desirable for a nut 61 that is completely undamaged to be classified as A-goods and a nut 61 with only one crack 62 or 63 as price-reduced but still salable B-goods. In the 3 The nut 61 shown as an example with two cracks 62 and 63, which together with the central hole of the nut 61 divide the nut 61 into two parts, should be classified as rejects, since there is a high risk that the nut 61 will break through completely under mechanical stress.

With the method 100 it is possible to analyze whether the image classifier 1 shows this desired behavior solely on the basis of the input image 2 and the image classifier 1 .

QUOTES INCLUDED IN DESCRIPTION

This list of documents cited by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent Literature Cited

• WO 2018/197074 A1 [0003]

Claims (18)

Method (100) for measuring the parts (2a) of an input image (2) on which an image classifier (1) bases its decision on the assignment (14a) of this input image (2) to one or more classes of a predetermined classification, with the steps: • a trained image classifier (1) is provided (110), which is designed to generate intermediate products (11a-13a) from the input image (2) using one or more convolution layers (11-13) and using a or a plurality of classifier layers (14) to map such an intermediate product (11a-13a) to the assignment (14a) to the class or classes; • an input image (2) is provided (120); • at least one intermediate product (11a-13a) and an assignment (14a) to one or more classes are generated (130) from the input image (2) using the image classifier (1); • at least one intermediate product (11a-13a) is broken down (140) into spatially contiguous areas (31-35), which each meet a predetermined relevance criterion (3) and are separated from one another by areas that do not meet this relevance criterion (3); • these contiguous areas (31-35) are evaluated as mutually independent components of the intermediate product (11a-13a), and dependencies (41-45) of the decision of the image classifier (1) on these components (31-35) are determined (150 ); • From these dependencies (41-45), the parts (2a) of the input image (2) relevant to the decision are determined (160). Method (100) according to claim 1 , wherein the intermediate product (11a-13a) comprises one or more feature maps each indicating activation values of the features recognized by a filter core. Method (100) according to claim 2 , different relevance criteria (3) being selected (141) for different feature maps. Method (100) according to claim 2 , whereby activation values of several feature cards are summed or averaged (142) and this sum or the mean value is evaluated (143) with the relevance criterion (3). Method (100) according to any one of Claims 1 until 4 , wherein determining the dependencies (41-45) includes determining (151) a smallest set of components (31-35) whose deactivation in the intermediate product (11a-13a) cancels and/or changes the decision of the image classifier (1). . Method (100) according to any one of Claims 1 until 5 , wherein determining the dependencies (41-45) includes determining (152) a smallest combination of components (31-35) whose presence in the intermediate product (11a-13a) is sufficient for the decision of the image classifier (1). Method (100) according to any one of Claims 5 until 6 , wherein a component (31-35) in the intermediate product (11a-13a) is deactivated by assigning (153) activation values to it in the intermediate product (11a-13a), which the image classifier (1) assigns to this component (31-35), when fed an input image (2) of another class. Method (100) according to any one of Claims 1 until 7 , wherein the importance of individual components (31-35) is evaluated with a predetermined degree of importance (154) and wherein components (31-35) are preselected (155) on the basis of this evaluation for determining the dependencies (41-45). Method (100) according to claim 8 , the importance of an individual component (31-35) being determined using an expected value for a classification score supplied by the image classifier (1) via a large number of intermediate products (11a-13a), each of which contains this component (31-35). (154a). Method (100) according to any one of Claims 1 until 9 , wherein an image of a mass-produced product is selected (105) as the input image (2) and the classes of the classification represent a quality assessment of the product. Method (100) according to claim 10 , The determined parts (2a) of the input image (2), on which the image classifier (1) bases its decision, being compared (170) with a part (2b) of the input image (2) which is based on an observation of the same product with a different imaging modality was determined as relevant for the quality assessment of the product, and from the result (170a) of this comparison (170) a quality assessment (1a) for the image classifier (1) is determined (190). Method (100) according to any one of Claims 1 until 9 wherein an image of a traffic situation taken from a vehicle is selected as input image (2) (106) and wherein the classes of the classification represent ratings of the traffic situation on the basis of which the future behavior of the vehicle is planned. Method (100) according to claim 12 , where the determined parts (2a) of the input image (2), on which the image classifier (1) bases its decision, is compared (180) with a portion (2b) of the input image (2) which is known to be relevant for the assessment of the traffic situation, and from the result (180a) this Comparison, a quality rating (1a) for the image classifier (1) is determined (190). Method (100) according to any one of Claims 1 until 13 , wherein the relevance criterion (3) includes (144) that numerical values in the intermediate product (11a-13a) are above a predetermined threshold value (3a). Method (100) according to Claim 14 , wherein • the ascertained components (2a) that are actually relevant to the decision are compared (144a) with specified target components (2#), which are supposed to be nominally relevant to the decision for the image classifier (1); • the threshold value (3a) is optimized (144b) with the aim that the actually decision-relevant components (2a) determined then come better into line with the nominal decision-relevant components (2#). Computer program containing machine-readable instructions which, when executed on one or more computers, cause the computer or computers to perform the method (100) according to any one of Claims 1 until 15 to execute. Machine-readable data carrier with the computer program Claim 16 . Computer equipped with the computer program according to Claim 16 , and/or with the machine-readable data carrier Claim 17 .

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