CN111753980A

CN111753980A - Method for transferring features of a first image to a second image

Info

Publication number: CN111753980A
Application number: CN202010220100.0A
Authority: CN
Inventors: 娄中余; D.T.阮; M.克拉尔
Original assignee: Robert Bosch GmbH
Current assignee: Robert Bosch GmbH
Priority date: 2019-03-26
Filing date: 2020-03-25
Publication date: 2020-10-09
Also published as: DE102019204118A1

Abstract

The method of transferring features of a first image to a second image comprises: generating an intermediate generator image by providing a feature image of a plurality of feature images including a feature and a pure image without the feature of a plurality of pure images without the feature to a generator network; superimposing the intermediate generator image with the feature image to construct a pseudo-image; providing the pseudo-image and the pure image to a first discriminator network; calculating a loss function for the first discriminator network at any odd training sequence; superimposing the inverted intermediate generator image with the pure image to construct a pseudo feature image; providing the pseudo feature image and the feature image to a second discriminator network; calculating a loss function for the second discriminator network at any odd training sequence; recalculating the network parameters of the first discriminator network and the second discriminator network at any odd training sequence; calculating a loss function of the generator network at any even training sequence; and recalculating the network parameters of the generator network at any even training sequences.

Description

Method for transferring features of a first image to a second image

Technical Field

The present invention relates to methods of transferring features of a first image to a second image using artificial neural networks, and methods for training these artificial neural networks.

Background

Image generation has attracted a great deal of interest due to the success of the deep generation countermeasure network (GAN). These models learn the distribution of features in the actual dataset and generate images using the trained models. While generating images from random vectors or image classes suffers from causing image blur, image-to-image generation models can generate sharp, realistic images. Different approaches to the problem of hard image generation have been proposed. Most of these models learn the distribution of the data set in the image space and sample the complete image from a trained model conditioned on the image.

The generation of images from given features has been studied using depth feature interpolation in a trained model that utilizes the given features to generate images or manipulate features in a GAN framework. A two-stage approach is applied to train the entire framework and generate images with given features. To ensure the realistic appearance of the generated image, an algorithm is used that includes two networks, a transformation network and an enhancement network. Such algorithms typically attempt to learn an implicit distribution of attributes.

For some practical applications of image classification, such as defect detection in production automation and disease detection in medical image classification, the data sets of the images are highly unbalanced. Images showing abnormalities (e.g., product images with defects, medical images with malignant tumor cells) are much fewer than images without abnormalities. Based on such data sets, training robust image classifiers becomes challenging.

Disclosure of Invention

The invention therefore relates to a method of transferring a feature image comprising the feature to a pure image using an artificial neural generator network, and to a method of training an artificial neural generator network using the feature, as described in the independent claims. The invention also relates to a computer program product and a computer-readable storage medium configured to carry out these methods.

Advantageous modifications of the invention are set forth in the dependent claims. All combinations of at least two of the features disclosed in the description, the claims and the drawings fall within the scope of the invention. To avoid repetition, features disclosed in accordance with the method should also be applicable to and claimable from the mentioned systems and devices.

The idea on which the invention is based is to avoid teaching the neural network about the distribution of features within an image, but to teach to copy only certain features from an image to another image, while keeping other areas of the image unchanged. Otherwise, since some features (e.g., scratches on a product) are rather random, the implicit distribution of these features complicates learning due to the large amount of data required.

To achieve these and other advantages and in accordance with the purpose of the present invention, as embodied and broadly described herein, there is provided a method for training an artificial neural generator network, which transfers a feature including a feature image of the feature to a pure image by repeating a training sequence of the generator network until an absolute value of a loss function of the generator network is lower than a predefined threshold.

The neural generator network may be an Artificial Neural Network (ANN), which is a computing system that is ambiguously inspired by biological neural networks that make up an animal's brain. Neural networks are not algorithms in themselves, but rather a framework in which many different machine learning algorithms work together and process complex data inputs. Such systems typically learn to perform tasks by considering examples without being programmed with any task-specific rules. The ANN is based on a collection of connected units or nodes called artificial neurons. Each connection may transmit signals from one artificial neuron to another. An artificial neuron receiving a signal may process the signal and then signal additional artificial neurons connected thereto.

In a common ANN implementation, the signal at the junction between artificial neurons is a real number, and the output of each artificial neuron is calculated by some non-linear function of the sum of its inputs. The weights of artificial neurons and edges are typically adjusted as learning progresses. The weights increase or decrease the strength of the signal at the connection. The artificial neuron may have a threshold such that the signal is only sent when the aggregate signal crosses the threshold. Typically, artificial neurons are polymeric in layers. Different layers may carry out different kinds of transformations on their inputs. The signal travels from the first layer (input layer) to the last layer (output layer), possibly after traversing the layers multiple times.

The mentioned training sequence comprises the following steps: an intermediate generator image is generated by providing a feature image including a feature in a plurality of feature images including the feature and a pure image without the feature in a plurality of pure images without the feature to a generator network.

When carrying out the training sequence of the method as described above, a plurality of feature images comprising features that should be transferred to a plurality of pure images without the features may be used as a set of training images of the generator network.

The generator network generates an intermediate generator image at an output of the generator network, the intermediate generator image being produced from an image provided at an input of the generator network. The generator network is specified by its network parameters, which are available for specific tasks of the generator network and which, together with the input images, determine the output of the generator network.

Another step of the training sequence is to overlay the intermediate generator image with the feature image comprising the feature to construct a pseudo-image. Due to the structure of the neural network framework, the intermediate generator image is a negative image of the feature. Depending on the quality of performance of the generator network, the superposition of the feature image with the intermediate generator image may result in the generated pseudo-image no longer comprising the feature.

A further step of the training sequence is to provide the pseudo-image and the pure image to the first discriminator network.

Another step is to compute the loss function of the first discriminator network at any odd training sequence.

Due to this data flow and structure, the first discriminator network has the task of predicting whether the pseudo-picture is a real picture or not.

The discriminator is usually made up of a sequence of layers. The first layer of the discriminator accepts the image and the discriminator generates values indicating the probability of the input image being true or false. For both the generator and the discriminator, typical layers are: convolutional network layers (e.g., with or without dilation, with or without depth-wise separation), deconvolution layers, pooling layers (e.g., maximum pooling, average pooling), normalization layers (e.g., batch normalization, layer normalization, partial response normalization, and instance normalization), activation functions (e.g., rectifying linear units (RELU), leakage rectifying linear units (leaked RELU), exponential linear units (elu), scaling exponential linear units (selu), sigmoid functions, or tanh functions), ResNet, or a block of ResNet.

The training sequence further involves the steps of: the previously inverted intermediate generator image is superimposed with the pure image to construct a pseudo-feature image. Since the intermediate generator image is a negative image of a feature as discussed previously, the intermediate generator image must first be inverted to add the feature to the image that was originally free of the feature by superimposing the feature with the image. This results in a pseudo-image that includes the feature and is based on a pure image.

Providing the pseudo feature images and the feature images to the second discriminator network is another step of the training sequence. Thus, as a next step, it is possible to calculate the loss function of the second discriminator network at any odd training sequence.

As a further step of the described method, the network parameters of the first and second discriminator networks are recalculated at any odd training sequence. Alternatively, the individual network parameters are subjected to such recalculation at any other sequence using the generator network.

The training sequences are counted and the step of recalculating the network parameters of the first and second discriminator networks is performed if the count is odd, otherwise no update calculation is performed. This updating of the parameters of the generator network and of the discriminator network can be done by a method called back-propagation.

Another step of the training sequence is to compute the loss function of the generator network at any even training sequence. The loss function may be a measure of the quality of the generator network to effect the desired transfer of features.

The absolute value of the loss function of the generator network determines the end of the training sequence. If the absolute value of the loss function is below a predefined threshold, the training sequence of the generator network is terminated and the generator network may be called a trained generator network.

In any even numbered training sequence of the generator network, a recalculation of the network parameters of the generator network is carried out. This means that the recalculation of the generator network and the two discriminator networks is performed alternately.

An improvement using the described method is that training the generator network in the described manner with two discriminator networks and recalculating its parameters results in a very stable training behavior of the generator network for different images and features to be transferred. No careful over-parameter tuning is required. Using only one discriminator network is less stable.

Another benefit of the disclosed method is the interpretability of the intermediate results, since the generator network generates, in addition to the required pseudo feature images, intermediate generator images that represent features to be transferred, such as defects of the product. This gives an intuitive idea about additional pseudo feature images.

According to one aspect of the invention, the calculation of the loss function of the generator takes into account the outputs of the first and second discriminators.

According to another aspect of the invention, the loss function of the generator is calculated by using the following formula:

where Lg represents the loss function of the generator network, E_x1〜p(x)Is the expectation of a true image distribution without attributes, and E_x2〜p(x+)Is a desire for a true image distribution with attributes. x1 is one sample of image space, D1(x1) is the output of the discriminator, and G is the output of the generator.

According to another aspect of the described method, the artificial neural generator network used in the described method is a convolutional encoder decoder neural network.

Additionally, a method for transferring a feature of a feature image comprising the feature to a receiving image by means of an artificial neural generator network is provided, the artificial neural generator network being trained according to the described method for training the artificial neural generator network.

A method for transferring features of a feature image to a received image by means of an artificial neural generator network is disclosed, wherein the generator network is trained according to the above method for training an artificial neural generator network.

The step of the method for transferring a feature is to provide a feature image comprising the feature and a received image without the feature (which should be the basis of a pseudo-feature image) to an input of an artificial neural generator network, wherein the generator network provides an intermediate generator image at an output of the generator network.

The next step of the method of transferring features is to superimpose the inverted intermediate generator image with the received image to transfer the features of the feature image to the received image. This results in a pseudo feature image that includes the feature and is based on the received image.

Technical applications of the method of transferring a feature from a feature image comprising the feature to another image may be used for data enhancement. If the training data set used to train the neural network is small, more training images may be generated using the described methods for improved model training. This generates a large set of true-looking images with anomalies, since the number of images without defects is not limited and the required number of images comprising features to be transferred is small. As an example value, it may be used for hundreds of images that include the desired feature. The described method does not require having a large number of defect images to learn how to apply features to images of products that are not defective. This is because it is not necessary to learn the feature distribution in the image.

For example, such a data enhancement method may support automated optical inspection. When the training data set is small, since there are only a small number of images from a small number of defects during production, this approach can be used to generate more training images for better model training. With such an improved model, for example, defect detection (e.g., for optical inspection) based on detection methods by neural networks can be improved. For example, if at least some defective product samples are available, a product image having defects such as scratches may be generated based on a product image having no defects.

Another technical application may be image analysis for medical use. Because the disclosed method generates an intermediate generator image that represents a feature, the feature may be correlated with a feature that indicates a characteristic tissue change that is modified based on the lesion. This distinction helps to divide the image into benign pixels and tumor pixels.

A further technical application of the disclosed method may be to apply the method as e.g. a mobile phone application to enable modification of an image of a person with sunglasses worn by other people and where the image of the sunglasses is available.

Additionally, a method for generating a pseudo feature image comprising a feature is described. The steps of the method are iteratively carrying out a method for transferring features of a feature image according to the above, wherein a feature image comprising the feature is selected from a first plurality of feature images and repeatedly provided to a generator network, while each selected from a second plurality of received images is uniquely provided to the generator network. The number of elements of the second plurality is higher than the number of elements of the first plurality.

If the number of original images including such features is limited, this enables the user to manually generate a plurality of images including the desired features by transferring the features of the feature images to another image.

A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method according to claims 1 to 4 is described.

A computer-readable storage medium is described comprising instructions which, when executed by a computer, cause the computer to carry out the method according to claims 1 to 4.

A system is described that includes an artificial neural network system executed by one or more computers, the artificial neural network system configured to implement the method of claims 1-4.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principle of the invention. In the drawings:

fig. 1 shows the data flow within the framework of a neural network comprising a generator and two discriminators;

FIG. 2 schematically illustrates the structure of an artificial neural generator network;

FIG. 3 schematically illustrates the structure of an artificial neural discriminator network;

FIG. 4 shows steps of a method for training a generator network; and

fig. 5 shows a data stream for transferring features of a feature image to a received image.

Detailed Description

Fig. 1 illustrates a data flow of a framework of a neural network including a generator network (G) 1, a first discriminator network (D1) 2, and a second discriminator network (D2) 3 for training an artificial neural generator-network (G) 1 to transfer features included in feature images to pure images. This framework can be used to let the generator network (G) 1 learn to transfer a feature from the feature image I + to the pure image I, which should receive the feature, for example because it does not include the feature.

The specification of the features to be transferred may depend on the particular task. For example, for facial image analysis, the feature may be "beard", "glasses", or "smile". For optical inspection during production, the feature may be a "defect".

A feature image I + (i.e. an image comprising the feature to be transferred) and a pure image I (i.e. an image without this feature) are provided at the input 1a or 1b of the generator network (G) 1. The input data of the generator network (G) 1 may be a stack of two images, and the output of the generator network (G) 1 may be an image having the same resolution as the input image.

As indicated in fig. 1, the generator output 1c may provide an intermediate generator image as its input and the result of the generator network (G) 1, and may be superimposed with the feature image I + and provided to the first discriminator network D1 at the first input 2 a. A second input 2b of the discriminator (D1) 2 is supplied with the pure image I. The discriminator (D1) 2 provides its discrimination result at its output 2 c.

It is also indicated in fig. 1 that the intermediate generator image is inverted, superimposed with the pure image I, and supplied to the first input 3a of the second discriminator network (D2) 3. A second input 3b of the second discriminator network (D2) 3 is supplied with the characteristic image I +. The discriminator (D2) 3 provides its discrimination result at its output 3 c.

The entire data stream as shown in fig. 1 results in the generation of two pseudo-images, one with features derived from two real images, and the other without, the feature image and the pure image being supplied to the generator.

Apart from the fact that this framework of neural networks involves a generator network and a discriminator framework, it is also distinguished from the generation of a countermeasure network (GAN) by the inclusion of a second discriminator D2 and provides the generator network G with two images, rather than noise in the case of a GAN network. Additionally, the intermediate generator images provided at the output 1c of the generator network G are not passed directly to the discriminators, but are added to one of the two input images before they are provided to one of the discriminators.

The architecture of the generator network may be any architecture configured to receive a stack of two images in its input stage and to provide the images in the output stage, such as an auto-encoder or any architecture for semantic segmentation. An embodiment of a generator network is discussed below with reference to fig. 2.

In fig. 2, the structure of an artificial encoder-decoder neural network is schematically shown. The architecture of such encoder-decoder neural networks is typically made up of two parts. The first part is a sequence of layers that down-samples the input grid to a lower resolution with the aim of retaining the desired information and dumping (dump) the redundant information. The second part is a sequence of layers that upsample the output of the first part and restore the desired output resolution (e.g., input resolution). Alternatively, there may be additional skip connections directly connecting certain layers in the first and second portions.

An embodiment of the generator network (G) 2 may have an architecture of an encoder-decoder network 20, which may be used to generate an output tensor representing the intermediate generator image. The encoder-decoder network 20 may be composed of a Convolutional Neural Network (CNN) encoder 23 and a CNN decoder 24. Layer 21 is an input layer 22 of the encoder-decoder network 20 and layer 22 is an output layer of the encoder-decoder network 20.

The encoder 23 of the encoder-decoder network 20 is constructed from d (e.g., d ═ 8) blocks. Each block may contain one layer or sequence of layers or even other layer blocks. One convolutional layer with a kernel number of N1 (e.g., N1= 32) and a stride of 2 may be present; a leaky RELU layer, a convolutional layer with a kernel number of N2 (e.g., N2= 64) and a stride of 2, a normalization layer (e.g., an instance specification); a leaky RELU layer, a convolutional layer with a kernel number of N3 (e.g., N3= 128) and a stride of 2, a normalization layer (e.g., an instance specification); a plurality of layer blocks, each block containing a leaked RELU layer, a convolutional layer with a kernel number of N4 (e.g., N4= 256) and a stride of 2, a normalization layer (e.g., an example specification).

The decoder 24 of the encoder-decoder network 20 is also constructed from d blocks. The decoder may include a plurality of layer blocks, each of which may include a leaked RELU layer, a deconvolution layer with a kernel number of N5 (e.g., N5= 256) and a stride of 2, a normalization layer (e.g., an instance specification); a leaky RELU layer, an deconvolution layer with a kernel number of N6 (e.g., N6= 128) and a stride of 2, a normalization layer; a leaky RELU layer, an deconvolution layer with a kernel number of N7 (e.g., N7= 128) and a stride of 2, a normalization layer; a leaky RELU layer, an deconvolution layer with a kernel number of N8 (e.g., N8= 64) and a stride of 2, a normalization layer; and a leaked RELU layer, an deconvolution layer with a core number of N9 (e.g., N9= 32) and a step size of 2, and a tanh layer. Table 1a describes these layers in more detail.

TABLE 1a Structure of Generator G
	Inputting 256x256x3 images
32 convolution 4x 4. The stride 2.
	Leaked RELU, 64 convolution 4x4, step 2. Example Specifications
The leaked RELU, 128 convolution 4x4, step 2. Example Specifications
	The leaked RELU, 256 convolves 4x4, step 2. Example Specifications
The leaked RELU, 256 convolves 4x4, step 2. Example Specifications
	The leaked RELU, 256 convolves 4x4, step 2. Example Specifications
The leaked RELU, 256 convolves 4x4, step 2. Example Specifications
	The leaked RELU, 256 convolves 4x4, step 2. Example Specifications
The leaked RELU, 256 deconvolutes 4x4, step 2. Example Specifications
	The leaked RELU, 256 deconvolutes 4x4, step 2. Example Specifications
The leaked RELU, 256 deconvolutes 4x4, step 2. Example Specifications
	The leaked RELU, 256 deconvolutes 4x4, step 2. Example Specifications
The leaked RELU, 128 deconvolutes 4x4, step 2. Example Specifications
	Leaked RELU, 64 deconvolutes by 4x4, step 2. Example Specifications
Leaked RELU, 32 deconvolution 4x4, step 2. Example Specifications
	Leaked RELU, 3 deconvolutes 4x4, step 2. tan h

Fig. 3 outlines the architecture of the discriminator D1 or D2. Layer 31 is the input layer for embodiments of discriminator D1 or D2. Each discriminator may contain a plurality of layer blocks. It may contain convolutional layers with N10 (e.g., N10= 64) cores and stride of 2, leaky RELU; convolutional layer, leaky RELU with N11 (e.g., N11= 128) kernels and stride 2; convolutional layer, leaky RELU with N12 (e.g., N12= 256) kernels and stride 2; convolutional layer, leaky RELU with N13 (e.g., N13= 512) kernels and stride 2; and a convolutional layer or an optional softmax layer. Table 1b describes these layers in more detail.

Table 1 b: structure of discriminator D1/D2
	Inputting 256x256x3 images
64 convolution 4x4, step 2, leaked RELU
	128 convolution 4x4, stride 2, instance specification, leaked RELU
256 convolution 4x4, stride 2, instance Specification, leaked RELU
	512 convolution 4x4, stride 2, instance specification, leaked RELU
Convolution 4x4, step 1.

An artificial neural generator network is trained to generate an intermediate generator image that can be overlaid with the pure image and transfer features of the feature image to the received image to construct a pseudo-feature image that includes the features. To do so, the generator needs to learn the appearance of the feature images, which means that the generator needs to learn to transfer the feature images including the features to the output intermediate generator images representing only the features. This intermediate generator image is superimposed on the image without the feature to generate a new pseudo-feature image that includes the feature.

FIG. 4 depicts the steps of training an artificial neural generator network to transfer a feature image that includes the feature to a pure image.

Each parameter of the network is set to have an initial value before training is started. There are several initialization methods such as setting the initial value of the parameter to 0, randomly selecting a value from a gaussian distribution of N (0, 1), or using a certain standard parameter initialization method (such as xavier initialization).

At step S1, an intermediate generator image is generated by the generator network if a feature image of the plurality of feature images that includes a feature and a plain image without the feature of the plurality of plain images without the feature are provided to an input of the generator network.

At step S2 of the described method, the intermediate generator image and the feature image are superimposed to construct a pseudo-image.

At step S3, the pseudo-image and the pure image are provided to a first network of discriminators.

At step S4, a loss function for the first discriminator network is calculated. The loss function of D1 is defined as:

in this equation, x2 indicates an image having an attribute, and x1 indicates an image without an attribute. This loss L1 comprises two parts. The first term is the loss of the real image without the feature. The second term is the loss of a pseudo image generated by adding the generated residual image G (x1, x 2) to x 2.

In step S5, the inverted intermediate generator image is superimposed with the pure image to construct a pseudo feature image.

At step S6, the pseudo feature image and the feature image are provided to a second network of discriminators.

At step S7, a loss function for the second discriminator network is calculated. The loss function of D2 is defined to be similar to the loss function of D1 explained above:

in method step S8, the network parameters of the first and second discriminator networks are recalculated if the number of training sequences counted for the exercised training sequences is odd.

In step S9, a loss function for the generator network is calculated. The loss function of generator G is defined as:

this loss function includes three parts. The first term is the penalty defined for D1. The second term is the loss defined by D2. The third term is L1 normalization of the generated residual map, which encourages the generated residual map to be sparse.

At step S10, if the number of training sequences is even, the network parameters of the generator network are recalculated. This means that during training, the parameters of the generator and the discriminator are updated iteratively.

In step S11, the absolute value of the loss function of the generator network is compared to a predefined threshold to decide whether to continue with step 1 or to end the training sequence.

Fig. 5 depicts a data stream for transferring a feature image comprising the feature to a received image. After training the generator network (G) 1 as described above, the generator network (G) 1 may generate a pseudo image by transferring the features of the feature image I + to another image such as a received image.

At the input 1a or 1b of the generator network (G) 1, a feature image I + (i.e. an image comprising the feature to be transferred) and a receiving image (i.e. an image to which the feature should be provided) are provided.

The input data of the generator network (G) 1 may be constructed in the same manner as the training method of the generator network described above.

As indicated in fig. 5, the generator output 1c may provide as its input an intermediate generator image and the result of the trained generator network (G) 1, and may be superimposed with the feature image I + to construct a generated pseudo-image without the feature based on the feature image.

After inverting the intermediate generator image as indicated in fig. 5, it is superimposed with the received image I to provide a generated pseudo feature image comprising the feature and based on the received image.

As is clear, the structure of the generator network (G) 1 is the same as the generator network (G) used for training and has been described in detail above.

Claims

1. A method for training an artificial neural generator network (1) by repeating a training sequence of the generator network (1) to transfer features of a feature image comprising the features to a pure image until an absolute value of a loss function of the generator network (1) is below a predefined threshold (S11), the training sequence comprising:

generating an intermediate generator image by providing a feature image of a plurality of feature images including the feature and a plain image without the feature of a plurality of plain images without the feature to a generator network (S1);

superimposing (S2) the intermediate generator image with the feature image to construct a pseudo-image;

providing the pseudo-image and the pure image to a first discriminator network (2) (S3);

calculating a loss function (S4) for the first discriminator network (2) at any odd training sequence;

superimposing (S5) the inverted intermediate generator image with the pure image to construct a pseudo feature image;

providing the pseudo feature image and the feature image to a second discriminator network (3) (S6);

calculating a loss function (S7) for the second discriminator network (3) at any odd training sequence;

recalculating the network parameters of the first discriminator network (2) and the second discriminator network (3) at any odd training sequence (S8);

calculating a loss function of the generator network (1) at any even training sequence (S9); and

the network parameters of the generator network (1) are recalculated at any even training sequence (S10).

2. The method according to claim 1, wherein the loss function (S9) of the calculation generator takes into account the output values of the first discriminator (2) and the second discriminator (3).

3. The method according to one of the preceding claims, wherein the loss function of the generator is calculated (S9) using the following formula:

。

4. the method according to one of the preceding claims, wherein the artificial neural generator network (1) is a convolutional encoder decoder neural network.

5. Method of transferring features of a feature image comprising features to a received image by means of an artificial neural generator network (1) trained according to claims 1 to 4, the method comprising:

providing the feature image and the received image to a generator network (S1), the generator network (10) providing the feature image;

the inverted feature image is superimposed with the received image (S5) to transfer the features of the feature image including the features to the received image.

6. A method for generating a pseudo feature image comprising features, the method comprising:

method for transferring features of a feature image according to claim 5, carried out iteratively, wherein

The feature image selected from the first plurality of feature images comprising said feature is repeatedly provided to the generator network (1), while each received image selected from the second plurality of received images is uniquely provided to the generator network (1), and

wherein the number of elements of the second plurality is higher than the number of elements of the first plurality.

7. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method according to claims 1 to 6.

8. A computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to implement the method of claims 1-6.