Method for analyzing a 3-d image

Abstract

This method for analyzing a 3-D image comprises the following steps: i) obtaining at least one 3-D image (2, 4, 6), ii) converting (10) the at least one 3-D image (2, 4, 6) into a 2-D summary image (8) through a projection operation comprising successive convolution operations performed along a depth direction of the 3-D image, and iii) classifying the 2-D summary image (8) by using at least one 2-D neural network (12).

Description

Method for analyzing a 3-D image

[0001] The invention relates to 3-D image processing. More precisely, the invention relates to a method for analyzing and classifying a 3-D image.

[0002] Diabetic retinopathy, a complication of diabetes, is a major and growing cause of vision impairment and blindness. It is expected that around 600 million people throughout the world will have diabetes by 2040, a third of whom will have diabetic retinopathy. One major problem in the management of diabetic retinopathy is its reliance on an older imaging technique, namely color fundus photography. Various classifications based on color fundus photography were proposed over the years, but unfortunately, decisions based on these classifications have poor predictive power. This makes the management of diabetic retinopathy challenging: clinicians often err on the side of caution and treat all those patients to mitigate the risk of complications. In the past decades, a significant number of studies have relied on color fundus photography images for the automatic assessment of diabetic retinopathy. The application of machine learning techniques, particularly deep learning, to these images has shown promising results in the detection and categorization of diabetic retinopathy. While these advancements are noteworthy, such techniques will always suffer from the poor predictive power of color fundus photography.

[0003] Fortunately, new imaging modalities are emerging that may improve predictions. Optical coherence tomography (OCT) is a non-invasive imaging technique that uses interferometric information of partially coherent light to create cross-sectional (2-D B-scans) and three-dimensional (C-scans) structural images of biological tissues. Within optical scattering media, it can penetrate a few millimeters in depth, with micrometer resolution, and is therefore particularly well-suited to image the retina. OCT Angiography (OCTA) is a motion-sensitive extension of OCT enabled by fast OCT acquisitions: it was shown to contrast the retinal vasculature and can provide quantitative blood flow information. An OCTA acquisition can be summarized by two volumes: a structure volume, obtained by averaging consecutive 3-D scans, and a flow volume, describing the amplitude of local intensity variations across those consecutive 3-D scans. To analyze the blood flow in specific vascular plexuses, clinicians generally inspect en-face, or frontal, maximal intensity projections of the flow volume in the corresponding retinal or choroidal layers. In such 2-D projections, each 1-D A-scan is replaced with the maximal intensity value (throughout the entire A-scan or within the considered layers only). Recent OCTA devices enable ultra-widefield acquisitions of the retina (90°). In summary, OCTA can capture ultra-widefield volumetric structural and functional (flow) images of the retina: it is, therefore, a promising technique to diagnose various ocular pathologies. In particular, diabetic retinopathy can clearly benefit from OCTA, as the structure volume allows objective and quantitative assessment of diabetic macular edema, and flow maximal intensity projections allow quantification of retinal vascular plexuses, non-perfusion and vessel density as well as the identification of damage.

[0004] Computer-aided diabetic retinopathy diagnosis using OCTA is an emerging field of research: it is motivated by the above promises (i.e., useful biomarkers) but also by the challenge of integrating large amounts of data (i.e., 3-D ultra-widefield structural and flow images).

[0005] Through a radiomics approach, various methods were investigated to directly assess diabetic retinopathy severity from OCTA images. Some authors classified 2-D en-face maximal intensity projections images with 2-D convolutional neural networks. Other authors classified 3-D images with 3-D convolutional neural networks.

[0006] Theoretically, the radiomics approach and the 2-D classification approach are suboptimal, in the sense that relevant features useful for classification may have been lost during the preprocessing and feature extraction steps. However, the 3-D classification approach also has some limitations. First, compared to their 3-D counterparts, 2-D neural architectures have better pre-trained weights and have fewer parameters to optimize, thus requiring fewer training samples. Given the limited OCTA data sets available, this aspect is critical. Second, end-to-end 3-D classification lacks the interpretability power of the radiomics approach and, to a lesser extent, of the end-to-end 2-D classification approach.

[0007] In other words, both the radiomics / 2-D approach and the 3-D approach come with drawbacks hindering their efficiency with diabetic retinopathy diagnosis. The former bases the classification operation on data which is incomplete due to the very nature of the 2-D projection of the 3-D image which comes with a non-negligible loss of information. The latter imposes to classify a 3-D image, and because of the higher quantity of data compared to a 2-D image, training neural networks is much more complex to implement and require much more processing resources and time. In addition, a 3-D image is less convenient for a medical doctor than a 2-D image in case they wish to consult the image to have an opinion and, possibly, challenge the classification which is performed.

[0008] In the view of above, there exists a need for a 3-D image classification method, which can be used for diagnosing diabetic retinopathy and other applications, which is more reliant, less resource-intensive and easier to train with neural networks compared to the ones of the prior art.

[0009] To this end, it is provided according to the invention a method for analyzing a 3-D image, comprising the following steps:

[0010] i) obtaining at least one 3-D image,

[0011] ii) converting the at least one 3-D image into a 2-D summary image through a projection operation comprising successive convolution operations performed along a depth direction of the 3-D image, and

[0012] iii) classifying the 2-D summary image by using at least one 2-D neural network.

[0013] To alleviate the above-mentioned limitations, it is thus proposed an end-to-end 3-D image classification approach relying on 2-D views as intermediate steps, the 2-D view extraction process being trainable. This guarantees that 2-D neural architectures can be used at the end of the classification pipeline, while relevant problem-specific features can be extracted at the beginning of the pipeline.

[0014] More specifically, the convolution operations allow to conserve most of the information contained in the at least one 3-D image, ensuring the method keeps a high level of reliance. The classification being performed on the basis of a 2-D image, it is understood that the classification is much less resource-intensive that the approach of the prior art involving the classification of a 3-D image, and that it is easier to train the neural networks on this basis.

[0015] Advantageously, the method further comprises a step of providing the 2-D summary image for displaying it.

[0016] This allows a medical doctor to challenge the classification performed by the method and provides more control to the medical doctor on the diagnosis to make based on the classification performed by the method.

[0017] Advantageously, step i) consists in obtaining a first 3-D image of a retina which is a structure volume showing retinal layers of the retina and obtaining a second 3-D image of the retina which is a flow volume showing blood vessels of the retina, the first and second 3-D images being preferably obtained through optical coherence tomography angiography.

[0018] The use of several 3-D images enriches the data available for performing the classification, thus improving the reliance of the classification.

[0019] Advantageously, step iii) involves a group of 2-D neural networks, the classifying operation being performed by a subgroup of 2-D neural networks chosen from the group of 2-D neural networks.

[0020] This corresponds to a “model dropout” mechanism which allows to maximize the interpretability of en-face projections. Projections are processed by an ensemble of 2-D image classifiers, and, during training, classifiers in the ensemble are dropped at random. The extracted 2-D features thus become more classifier-independent, i.e., more general, and more meaningful to the human eye.

[0021] Advantageously, the method further comprises a step, occurring after step ii), consisting of generating altered summary images by applying affine transformations to the 2-D summary image.

[0022] This allows a data augmentation which improves the training of the neural networks classifiers.

[0023] Advantageously, the method further comprises a step iv) of extracting at least one, preferably several, 2-D transverse section image of the 3-D image which are perpendicular to the 2-D summary image, the at least one 2-D transverse section image preferably being provided for displaying it.

[0024] The extraction of at least one transverse section image allows a medical doctor to have additional information on the retina, which may facilitate and improve their interpretation of the state of the retina.

[0025] Preferably, the extracted at least one 2-D transverse section image is classified by using at least one 2-D neural network.

[0026] This further facilitates and improves the medical doctor interpretation of the state of the retina, which can render a diagnostic more reliant. Moreover, the transverse section image corresponds to additional data to be used by the neural network classifiers, which improves its training.

[0027] Preferably, the at least one 2-D transverse section image is selected by selecting a pixel of the 2-D summary image and identifying a transverse section the 3D image of the retina corresponding to said pixel.

[0028] It is thus ensured that the at least one transverse section image is selected at a location of the retina which is relevant for observation by a medical doctor.

[0029] Preferably, the method further comprises a step, occurring after step iv), consisting of generating altered transverse section images by applying affine transformations to the at least one 2-D transverse section image.

[0030] This allows an additional data augmentation which also improves the training of the neural network classifiers.

[0031] It is also provided according to the invention a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method as presented above, as well as a computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the method as presented above.Brief description of the figures

[0032] Other features and advantages would appear by reading the following description, given as an illustrative and non-restrictive example and with the annexed drawing in which:

[0033] -is a schematical view of the implementation of a method for analyzing a 3-D image according to an embodiment of the invention.Detailed description

[0034] represents a flowchart illustrating the implementation of a method for analyzing a three-dimensional (3-D) image according to an embodiment of the invention, here applied to the diagnosis of diabetic retinopathy.

[0035] I. Overview and notations

[0036] Letydenote the depth axis along which the partial coherent light penetrates tissues of a retina of a patient’s eye (A-scan). Letxdenote a fast-scanning axis: a B-scan is thus indexed byxandy. Letzdenote a slow scanning axis: a volume (C-scan) is thus indexed byx,y, andzand en-face projections byxandz. LetX×Y×Zdenote the size of the C-scans in voxels. Finally, a multi-channel volume (e.g., with a flow and a structure channel) is indexed byc,x,y, andz.

[0037] Given a multi-channel OCTA acquisitionI, which preprocessing will be described is section II, andNacquisition-level labels, the goal is to predict whether or not experts would assign then-th label to acquisition I,n= 1..N. In the experiments, the goal is to assess diabetic retinopathy (DR) severity in the patient’s eye, according to the 5-level International Clinical Diabetic Retinopathy (ICDR) scale: no DR (level 0), mild non-proliferative DR (level 1), moderate DR (level 2), severe DR (level 3), proliferative DR (level 4); DR severity assessment is formulated as anN-label classification problem (N= 4): is DR severityd(I) greater than or equal to leveln. Letp(I) = {pn(I) =p(d(I) ≥n) ∈ [0; 1],n= 1..N} denote the probabilistic predictions and letλn(I) ∈ {0, 1},n= 1..N, denote the ground truth labels.

[0038] As illustrated in, the preprocessed 3-D acquisitionIis converted to a 2-D summary imageΠ(I), defined as a parametric en-face projection ofI(see details in section III).Π(I) is defined as a color (3-channel) image for two reasons: interpretability, as it can be displayed in a viewer or inserted in a report for human inspection, and compatibility with off-the-shelf 2-D neural architectures with the ImageNet software pre-trained weights.

[0039] Next,Π(I) is classified by a first ensemble C1of 2-D off-the-shelf image classifiers, as described in section IV. A first estimationp(1)(I) of the probabilistic predictionp(I) is given by C1◦Π(I). Then, based on attributions derived fromp(1)(I), the most relevant B-scans S (I) are selected, as described in VI. For interpretability purposes, the number of selected B-scans is limited toN, i.e., one per classification output. The motivations are that a small number of B-scans is compatible with human inspection in a viewer or a report, and each selected B-scan is associated with a severity cutoff and can therefore be used to document the course of action associated with that cutoff (treatment, follow-up, etc.).

[0040] Finally, the selected B-scans S (I) are classified by a second ensemble C2of 2-D off-the-shelf image classifiers: a second estimationp(2)(I) of the probabilistic prediction is given by C2◦ S (I). It is combined with p(1)(I) to obtain the final probabilistic prediction p(I), as described in section VII.

[0041] II. Preprocessing

[0042] An Optical Coherence Tomography Angiography (OCTA) acquisition is stored as two volumes: a structure volume 2, where the retinal layers and various retinal anomalies (e.g., fluid) are visible, among other structures (e.g., the choroid, below the retina, and the vitreous core, above it), and a flow volume 4, where the blood vessels of the retina and the choroid are particularly highlighted.

[0043] Additionally, OCTA acquisitions are usually associated with a 2-D en-face localizerl, aligned with the OCTA data (size:X×Zpixels), to track eye motion. The PLEX Elite 9000 (Carl Zeiss Meditec Inc. Dublin, California, USA) device, for instance, is associated with a line scanning ophthalmoscope subsystem for that purpose. OCTA acquisitions are usually also associated with automatically-segmented surfaces delineating the vitreoretinal interface, namely the inner limiting membrane, and the chorioretinal interface, below the retinal pigment epithelium. Letssupandsinfdenote those two surfaces, respectively. They are stored as matrices ofX×Zpixels:s(x,z) represents the depth of surface s in the (x,z) A-scan of volumes S or F.

[0044] An OCTA acquisition is preprocessed as follows. First, a line-scanning ophthalmoscope volume 6 (LSO volume) is created by duplicating the line-scanning ophthalmoscope localizer along the y-axis: L(x, y, z) = l(x, z), ∀x, y, z. Second, a mask volumeMofX×Y×Zvoxels is created:M(x,y,z) = 1 ifsinf(x,z) ≤y≤ssup(x,z), 0 otherwise, ∀x, y, z. The flow, structure, and LSO volumes 2, 4, 6 are multiplied byM, element-wise, to mask the choroid and vitreous core out. LetI′denote the 3-channel volume:

[0045] I′= [F⊙M,S⊙M,L⊙M] . (1)

[0046] Third, the retinal region is flattened by shifting all voxels ofI′along they-axis, so that the ILM surfacesinfis set to a small constant depthy=Y0, 0 <Y0≤Y. LetI′′denote the resulting volume. This flattening process ensures that all the relevant information is concentrated at the top ofI′′. Fourth,I′′is cropped: all voxels with a depthy>Y1are discarded,Y0≤Y≤Y1;Idenotes the cropped version ofI′′. ParameterY0is set to a non-zero value to limit the loss of useful information during random data augmentation (see section VII). ParameterY1is chosen to ensure the retinal region is never occluded.

[0047] III.3-D to 2-D projection

[0048] The preprocessed 3-D acquisitionIis then converted to a 2-D summary image 8,Π(I), through a parametric 3-D to 2-D en-face projection process 10,Π. According to the prior art, U-Net-like architectures were proposed forΠ, where the encoder part contains 3-D operations and the decoder part contains 2-D operations. U-Net-like architectures have smaller and smaller activation maps as one goes deeper into the encoder part, and their size increases as one goes deeper into the decoder part, to finally reach the size of the input image. The goal of this contraction is to increase the receptive field of deep encoder filters, to better take the context into account without increasing their size and, therefore, the number of network parameters. The drawback of this contraction is that small details are lost in the process. To recover those details, skip-connections are therefore introduced between encoder and decoder layers. However, this trick assumes that the ground truth signal contains small details. In particular, it requires a dense supervision signal. For a classification task, the only supervision signals available for trainingΠare the class labels.

[0049] According to the invention, it is ensured that the details are never lost throughout the 3-D to 2-D projection process 10. In particular, it is guaranteed that the activation maps all have the same size in the en-face plane (X×Zpixels). Only the depth of these activation maps decreases as one goes deeper inΠ, to reach a final depth of 1 voxel (i.e., a 2-D image), through successive convolution operations then a final projection. To further prevent the loss of details in the en-face plane, the receptive field of the filters is limited to one pixel in that plane. The network is divided into basic blocks containing a pooling operator, two convolutional layers, a batch normalization operator, an optional skip-connection, a ReLU activation.

[0050] It is to be noted that the pooling operator precedes the convolutional layers in order to limit network complexity. Since no contraction in the en-face plane is performed, this is critical. An average pooling operator is used in the first block; otherwise, half of the voxels would never be used. However, a max pooling operator is used in the following blocks to add more nonlinearity. Following common practice, the number of convolutional filters increases as one goes deeper into the network. LetΦdenote the number of filters per layer in the first block. The number of filters per layer in thei-th block is set to 2i−1Φ. Each of the blocks reduces the depth by a factor of 4 (2, due to pooling, multiplied by 2, due to the stride in the first convolution layer). After three blocks, a global mean operator along the depth axis, is performed to eliminate the depth dimension. Finally, a dense layer with sigmoid activation is applied to obtain a 2-D image with the desired number of channels, namely 3 channels (see section I). The sigmoid activation facilitates conversion to a bitmap image for visualization.

[0051] IV.Classification of the 3-D to 2-D Projection

[0052] Now that a 2-D color imageΠ(I) is obtained, any image classifier 12 (C1), can be used to predict DR severity: a convolutional neural network, a transformer, an ensemble of convolutional neural networks and / or transformers, etc. For interpretation purposes,Π(I) is preferred to be as independent from the classifier as possible. The rationale is as follows: if the projection is useful for any classifier, then it can be expected to be informative for human experts as well. Various solutions can be considered: following federated learning, multiple {Π(j), C1(j)} couples can be trained in parallel, and the weights of theΠ(j)instances can be aggregated at regular intervals, or following continual learning, multiple classifiers C1(j)can be trained sequentially, initializing training with the weights obtained forΠwith the previous C1(j−1)classifier.

[0053] However, such approaches imply longer training or require more resources. Instead, it is proposed to train one ensemble of classifiers, but with one trick that is called model dropout: for each mini-batch, a random subset of the classifiers is used for prediction. Like the other solutions mentioned above, this ensures that the 3-D to 2-D projectionΠdoes not specialize for one specific classifier, or for one static ensemble of classifiers. Letγk, k = 1..K, denote the classifiers of the ensemble. It is assumed that these classifiers have no final activation function (i.e., they return logits). The ensemble prediction is given by:

[0054] C1◦ Π(I) = σ( ) (2)

[0055] subject to: δk∈ {0, 1}, k = 1..K , 1 ≤ ≤ K

[0056] whereσdenotes the sigmoid function. The number of possible classifier combinations is given by 2K− 1. This process is equivalent to training 2K− 1 classifiers in random order, which, is expected to improve the generality of Π. Model dropout is only used during training: the full ensemble is used during inference.

[0057] V.Data augmentation

[0058] Data augmentation is typically performed by randomly transforming preprocessed images before feeding them to the neural network. For 2-D image classifiers, random transformations traditionally imply random affine transformations (random rotation, translation, and scaling) and random horizontal / vertical flips. However, the input preprocessed images are heavy 3-D volumes. Applying such random transformations to the 3-D volume takes a lot of time. Instead, it is proposed to apply them after the 3-D to 2-D projection: applied to 2-D data, they are much faster. Besides, applying random spatial transformations prior to the projection is not useful since the proposed projection operatorΠdoes not take the context into account. Inserting random transformations inside the neural architecture is made possible by differentiable implementations of these transformations.

[0059] Since these random transformations can be inserted inside the neural network, it is possible to generate one transformed version ofΠ(I) for each classifierγkin the ensemble. This leads to a new definition for C1 ◦Π:

[0060] C1◦ Π(I) = σ( ) (3)

[0061] subject to: δk∈ {0, 1}, k = 1..K , 1 ≤ ≤ K

[0062] whereTdenotes the transformation operator andεkthe random transformation parameters drawn forγk. As a way to generalize test-time data augmentation, random transformations are applied during both training and inference.

[0063] VI.Relevant B-scan Selection

[0064] A first estimationp(1)(I) = C1◦Π(I) of the probabilistic predictionp(I), based on the en-face 3-D to 2-D projectionΠ, is now available. It is proposed to investigate further those B-scans ofIwhich contribute the most top(1)(I). The idea is to find additional evidence to increase or decrease the confidence in this first estimation. To detect the B-scans that contribute the most top(1)(I), which correspond to relevant transverse sections images 14, it is proposed to use known attribution methods. Note that attributions are computed for one particular output predictionpn(1)(I), i.e., for one DR severity cutoff. This is in line with the goal to collect additional evidence for each prediction: one B-scan will be selected per prediction. As for the inputs, either the 3-D preprocessed acquisitionIand accumulate voxel-wise attributions in thexy-plane or the 2-D projectionΠ(I) and accumulate pixel-wise attribution along thex-axis (the fast-scanning axis) may be used. The second option was here chosen for faster computations. LetαI(x,z,c,n) denote the attribution of pixel (x,z), in thec-th channel, for then-th prediction. A normalized attributionαI(z,n) is defined for thez-th B-scan, with respect to then-th prediction:

[0065] αI(z, n) = (4)

[0066] LetBn(I) denote then-th selected B-scan. For inference, the B-scans maximizingαI(z,n),n= 1..N, are selected. However, for data augmentation purposes and to favor exploration, a random B-scan selection process is preferred during training: theBn(I) is randomly drawn from the multinomial probability distribution defined byαI(z,n):

[0067] Bn(I) = argmaxzαI(z, n) for inference , (5)

[0068] Bn(I) ∼ MZ(1; αI(1, n), ..., αI(Z, n)) for training . (6)

[0069] VII.Final classification

[0070] Like classifier C1, the second classifier 16, C2, also requires data augmentation. Besides the random selection process described above, it is proposed to apply the same random transformationTas for classifier C1. More generally, C2is defined very similarly to C1: an ensemble of classifiersγ′k,k= 1..K, with random transformations (parameters:ε′k,n,k= 1..K,n= 1..N) and model dropout (parametersδ′k,k= 1..K). Because their input images are of a different nature, no parameter sharing was set up between C1and C2.

[0071] By design, then-th selected B-scanBn(I) is meant to correct the confidence in then-th prediction. Therefore, only then-th predictionγ′k,n(Bn(I)) of classifierγ′ for B-scanBn(I) are considered. This leads to the following expression for the predictionsp(2)(I) of C2:

[0072] pn(2)(I) = σ( ) , n = 1..N (7)

[0073] subject to: δ’k∈ {0, 1}, k = 1..K , 1 ≤ ≤ K

[0074] The second classifier C2is supposed to increase or decrease the confidence in the predictions of the first classifier C1. Therefore, the logits from both classifiers are combined linearly to obtain the final probabilistic prediction:

[0075] p(I) = σ ( σ-1(p(1)(I)) + σ−1(p(2)(I)) ) , (8)

[0076] whereσ−1is the logit function.

[0077] The multi-label classifier thus defined is trained to minimize the binary cross-entropyLbetween network predictionspn(I) and ground truth labelsλn(I),n= 1..N:

[0078] L = - (9)

[0079] It has been hypothesized that B-scan selection is most relevant when the first classifier C1is already well trained. Therefore, two training scenarios are investigated: firstly, a two-step training where C1is trained alone until convergence, then its parameters are frozen and C2is trained until convergence, and, secondly, a one-step training where C1and C2are trained jointly until convergence.

[0080] The here-above embodiments are illustrative and not restrictive embodiments. Obviously, many modifications and variations of the present invention are possible in the light of the above teachings without deviating from its inventive concept, through diverse applications. It has therefore to be understood that the invention may be practiced otherwise that as specifically described.Numerical references

[0081] 2: structure volume4: flow volume6: LSO volume8: summary image10: projection process12: first image classifier14: transverse section image16: second image classifier18: display process

Claims

Method for analyzing a 3-D image, comprising the following steps:i) obtaining at least one 3-D image (2, 4, 6),ii) converting (10) the at least one 3-D image (2, 4, 6) into a 2-D summary image (8) through a projection operation comprising successive convolution operations performed along a depth direction of the 3-D image, andiii) classifying the 2-D summary image (8) by using at least one 2-D neural network (12).Method according to the preceding claim, further comprising a step of providing the 2-D summary image for displaying (18) it.Method according to any of the preceding claims, wherein step i) consists in obtaining a first 3-D image of a retina which is a structure volume (2) showing retinal layers of the retina and obtaining a second 3-D image of the retina which is a flow volume (4) showing blood vessels of the retina, the first and second 3-D images being preferably obtained through optical coherence tomography angiography.Method according to any of the preceding claims, wherein step iii) involves a group of 2-D neural networks (12), the classifying operation being performed by a subgroup of 2-D neural networks chosen from the group of 2-D neural networks (12).Method according to any of the preceding claims, further comprising a step, occurring after step ii), consisting of generating altered summary images by applying affine transformations to the 2-D summary image (8).Method according to any of the preceding claims, further comprising a step iv) of extracting at least one, preferably several, 2-D transverse section image (14) of the 3-D image which are perpendicular to the 2-D summary image, the at least one 2-D transverse section image (14) preferably being provided for displaying (18) it.Method according to the preceding claim, wherein the extracted at least one 2-D transverse section image (14) is classified by using at least one 2-D neural network (16).Method according to claim 6 or 7, wherein the at least one 2-D transverse section image (14) is selected by selecting a line of the 2-D summary image (8) and identifying a transverse section the 3D image of the retina corresponding to saidline.Method according to any of claims 6 to 8, further comprising a step, occurring after step iv), consisting of generating altered transverse section images by applying affine transformations to the at least one 2-D transverse section image (14).Computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method of any of claims 1 to 9.Computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the method of claim 1 to 9.

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