Single-channel music separation method based on U-shaped network

Abstract

The invention discloses a single-channel music separation method based on a U-shaped network, which is used for separating human voice from accompaniment. According to the method, a U-shaped network model comprising an encoder, a connection layer, a bottleneck layer and a decoder is constructed, feature extraction is performed on input through a plurality of continuous encoding units, and then the input enters the bottleneck layer formed by a multi-scale feature extraction module, a dual-path module and a multi-scale feature extraction module. And a connection layer formed by the time-frequency enhancement module and the fusion module is used for connecting the coding unit and the bottleneck layer or the coding unit and the decoding unit, and inputting into the next decoding unit. And finally, the decoder outputs the predicted human voice mask and accompaniment mask. A time-frequency enhancement module is introduced into a jump connection layer, and input music signal features on each frequency box are weighted in a time dimension, so that a network model pays attention to more important time points, and the time sequence modeling capability is improved. And meanwhile, a multi-scale feature extraction module is introduced into a bottleneck layer, so that the music signal feature extraction capability of the model is enhanced.

Description

Technical Field

[0001] The present invention belongs to the technical field of audio processing, relates to sound signal separation, and particularly relates to a single-channel music separation method based on a U-shaped network. Background Art

[0002] Music separation is widely used in many fields such as music creation and music education. It aims to extract a specific sound source from a mixed music signal. Due to many factors such as the mixing method of the sound source, signal quality, instrument diversity, and algorithm limitations, music separation is much more complicated than simple speech separation, especially single-channel music separation, which can only rely on the frequency and time information of the audio. Compared with multi-channel separation, it loses more information.

[0003] The music separation process typically requires a combination of multiple techniques, including signal processing theory, machine learning, and deep learning. Early music separation methods primarily relied on signal processing and statistical techniques, extracting specific musical components by establishing reasonable mathematical models and filters. However, these methods have limited effectiveness. In recent years, neural networks have achieved significant breakthroughs in the field of music separation, but they still have limitations. The characteristic information of the music signal is easily lost during the sampling process, and the effective features are difficult to fully recover during the decoding stage. In particular, some frequency-domain models need to be improved in their ability to capture both the overall and detailed characteristics of the music signal's spectrum. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this paper proposes a single-channel music separation method based on a U-shaped network. By introducing a time-frequency enhancement module (TFEM) into the skip connection layer of the U-shaped network, the method weights the characteristics of each frequency band of the input music signal in the temporal dimension, allowing the network model to focus on more important time points and improving its temporal modeling capabilities. Furthermore, by introducing a multi-scale feature extraction module (MSFEM) into the bottleneck layer, the method significantly enhances the model's ability to capture music signal features and improves the quality of the separated audio signal.

[0005] A single-channel music separation method based on a U-shaped network comprises the following steps: Step 1: Preprocess the mixed music signal to extract the amplitude and phase features of the mixed music signal.

[0006] Step 1.1: Sample and digitize the original mixed music signal, converting it from a continuous analog signal into a discrete signal that can be manipulated by a computer. At the same time, downsampling is performed on the discrete signal to improve computational efficiency and reduce data redundancy.

[0007] Step 1.2: Preprocess the discrete signal Cut along the time dimension and then perform short-time Fourier transform to obtain the complex spectrum characteristics of the mixed music signal : in, is a window function, is the timeframe index, is the sample index of the mixed music signal, is the frequency unit index, is the length of each frame of the signal. Represents a discrete signal Spectral information in the time and frequency dimensions. From the complex spectrum features The real and imaginary parts of the amplitude feature are extracted and phase characteristics : in, Is a function used to find the radian value corresponding to a complex number.

[0008] Step 1.3: Amplitude characteristics of a complete song segment Perform time series frame processing as input features .

[0009] Step 2: Construct a U-shaped network model, including encoder, connection layer, bottleneck layer and decoder. Input features are encoded through multiple consecutive encoding units. The feature extraction is performed and then input into the bottleneck layer composed of the multi-scale feature extraction module, the dual path module and the multi-scale feature extraction module. The connection layer composed of the time-frequency enhancement module and the fusion module is used to connect the encoding unit with the bottleneck layer or the encoding unit with the decoding unit, and input into the next decoding unit. Finally, the decoder outputs the predicted mask mask ,in represents the batch size, =2 indicates the number of channels, represents the frequency dimension, Represents the time dimension. The features on the two channels represent the vocal mask predicted by the model. With accompaniment mask , specifically: Step 2.1: Construct an encoder to transform the input amplitude features Convert to a compact, high-dimensional feature representation for subsequent feature extraction, decoding, and separation.

[0010] The encoder consists of three sparse downsampling blocks connected in series. In each sparse downsampling block, the input features are first segmented into low-frequency, mid-frequency, and high-frequency bands along the frequency dimension. Based on the characteristics of dense low-frequency information and sparse high-frequency information, information compression is performed in the three branches. The higher the frequency, the greater the compression ratio. The compressed features are passed through the GELU activation function and stacked convolution modules to capture detailed features in different frequency bands. Finally, the features of different frequency bands are spliced along the frequency dimension. A convolution layer is set after each sparse downsampling block.

[0011] Step 2.2: Construct a time-frequency enhancement module to enhance the features of important time steps. This module calculates the weights of each time dimension at different frequency units through operations such as global averaging, one-dimensional convolution, and sigmoid activation. These weights are then used to strengthen the features. The spectrum of a music signal often contains numerous horizontal stripes, which typically represent sustained phonemes, formants, and background noise. These stripes significantly impact the effectiveness of the model separation. The time-frequency enhancement module optimizes the use of temporal information, assigning higher weights to formants and sustained phonemes, thereby enhancing their characteristic information.

[0012] Step 2.3: Construct a fusion module to combine the output features of the time-frequency enhancement module with the features from the decoding stage. To enhance feature representation, the features are amplified along the channel dimension. Two-dimensional convolution is then applied to the amplified features to extract local features. Finally, the fusion module outputs features processed by a gated linear unit (GLU), which serves as the decoder input.

[0013] Step 2.4: Construct a multi-scale feature extraction module to extract multi-scale feature information in the bottleneck layer of the U-shaped network, alleviating the problem of information loss caused by excessive dimensionality reduction of feature information in the bottleneck layer. The input features first undergo layer normalization, followed by parallel local attention blocks and cross-region attention blocks, allowing the model to take into account both fine features and global change trends. Subsequently, a SE block dynamically adjusts the channel weights and uses residual connections to fuse with the input features. The fused features serve as the input for subsequent residual connections and layer normalization operations. Finally, the features output by the layer normalization operation pass through a multi-core parallel convolution module consisting of batch normalization, dilated convolution, and RELU activation function. The output results are superimposed with the previously fused features as the final output of the module.

[0014] Step 2.5: Construct a dual-path module to model the global information of the latent representation compressed by the encoder. This involves stacking multiple dual-path RNN modules, primarily for sequence modeling and capturing long-term feature dependencies. To mitigate performance limitations due to diminishing marginal utility, a feature conversion module is introduced between the dual-path RNN modules to project features into a new space.

[0015] Step 2.6: Construct a decoder, which upsamples the high-dimensional abstract features through three serially connected sparse upsampling blocks, so that the features are gradually restored to the amplitude features of the human voice and accompaniment required for the network task.

[0016] Step 3: Mask the Vocals With accompaniment mask and input features respectively Perform element-by-element dot product and get the predicted size of 512 Amplitude characteristics of 64's vocals and accompaniment 、 : where represents the element-wise product, is the amplitude feature of the predicted human voice, is the amplitude feature of the predicted accompaniment.

[0017] The amplitude features of the predicted series of human voices and accompaniment are spliced along the time dimension at an overlap rate of 50% to obtain the amplitude features of the complete human voice. and the amplitude characteristics of the complete accompaniment If the remaining part of the song segment is less than the specified length, it will be calculated from the end forward.

[0018] Step 4: Compare the predicted amplitude characteristics of the complete vocals and accompaniment 、 Phase characteristics of separate and mixed music signals Combined with the short-time Fourier inverse transform, it is converted into a time domain human voice signal and time domain accompaniment signal .

[0019] in, is the inverse short-time Fourier transform.

[0020] Step 5: Train the above model. Select a single-channel song clip and input it into the trained network model to generate the separated time-domain vocal signal and time-domain accompaniment signal.

[0021] The present invention has the following beneficial effects: The multi-scale feature extraction module introduced in the bottleneck layer enhances the model's ability to extract local and global features of music signals. At the same time, the time-frequency enhancement module introduced in the skip connection layer also improves the network's temporal modeling ability, effectively alleviating the problem of decreased music signal reconstruction quality caused by blurred or even missing spectral textures. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a data processing flow chart of the present invention; Figure 2 Schematic diagram of a single-channel music separation method based on a U-shaped network proposed in the present invention; Figure 3 It is a schematic diagram of a single sparse downsampling block of the U-type network; Figure 4 is a schematic diagram of the time-frequency enhancement module; Figure 5 It is a schematic diagram of the fusion module of the U-shaped network; Figure 6 It is a schematic diagram of the multi-scale feature extraction module; Figure 7 It is a schematic diagram of the multi-core convolution module; Figure 8 It is a schematic diagram of the dual-path module of the U-shaped network; Figure 9 Schematic diagram of a single sparse upsampling layer of a U-shaped network. DETAILED DESCRIPTION

[0023] In order to make the purpose and technical solution of the present invention more clear, the present invention is further explained below with reference to the accompanying drawings.

[0024] like Figure 1 As shown, a single-channel music separation method based on a U-shaped network specifically includes the following steps: Step 1: Preprocess the mixed music signal to extract its amplitude and phase features. The amplitude features will serve as input data for the U-shaped network model, while the phase features will be combined with the predicted amplitude features output by the model to reconstruct the separated music signal.

[0025] Step 1.1: Split the audio file into segments ranging from 5 to 13 seconds and downsample to 8000 Hz to reduce computational complexity. Simultaneously, convert the two-channel audio segments to single-channel audio segments by taking a weighted average of the left and right channels.

[0026] Step 1.2: Process the audio clip Perform the short-time Fourier transform operation, set the window type to Hamming window, the frame length to 1024, and the frame shift to 256, and obtain the corresponding complex spectrum characteristics , and then the complex spectrum characteristics Take the absolute value and calculate the radian of the complex matrix to extract the amplitude feature and phase characteristics .

[0027] Step 1.3: Amplitude features of each audio clip along the time dimension Split and set the window size to 512 64, using a sliding window strategy with a 50% overlap rate, that is, adjacent frames overlap 32 sampling points in the time dimension as input features .

[0028] Step 2: Build Figure 2 The U-shaped network model shown, for input features Output predicted vocal mask With accompaniment mask .

[0029] Step 2.1: Construct an encoder to transform the input amplitude features Convert to a compact, high-dimensional feature representation for subsequent feature extraction, decoding, and separation.

[0030] The encoder consists of three sparse downsampling blocks connected in series. Figure 3 As shown in the figure, in each sparse downsampling block, the input features are first divided into low-frequency band, medium-frequency band and high-frequency band at a ratio of 20%, 30% and 50% along the frequency dimension, and then input into three branches for processing. For the low-frequency band, a two-dimensional convolution with a step size of 1 is first used to compress the information, and then it passes through the GELU activation function and 3 consecutive convolution modules. For the medium-frequency band, a two-dimensional convolution with a step size of 4 is first used to compress the information, and then it passes through the GELU activation function and 2 consecutive convolution modules. For the high-frequency band, a two-dimensional convolution with a step size of 16 is first used to compress the information, and then it passes through the GELU activation function and 1 convolution module. This enables the model to capture more complex detail features. Finally, the features of different frequency bands are spliced along the frequency dimension to obtain the features. ,in represents the batch size, Indicates the number of channels, represents the frequency dimension, Represents the time dimension. Then perform a convolution operation with a kernel size of 3, a step size of 1, and a padding of 1 to obtain the output of the sparse downsampling block. , , represents the index of the sparse downsampling block.

[0031] Step 2.2: Build Figure 4 The time-frequency enhancement module shown is used to enhance the features from the encoder The features of important time steps in the image are optimized to optimize the utilization of time information and give higher weights to formants and sustained phonemes.

[0032] The time-frequency enhancement module is used for the feature First, the mean is calculated along the time dimension on each frequency unit, and then a one-dimensional convolution with a convolution kernel of 3, a step size of 1, and a padding of 1 is performed. Finally, the weight on the time dimension is obtained through the sigmoid activation function. : in, Indicates reshape, represents average pooling, represents one-dimensional convolution, Represents the sigmoid activation function. Then use the weight Pair Features Weighted, the output features of the time-frequency enhancement module are obtained : Here, represents element-wise multiplication.

[0033] Step 2.3: Construct a fusion module to combine the features output by the time-frequency enhancement module It is superimposed and fused with the output features of the decoding module. Figure 5 As shown, the fusion module first integrates the features output by the time-frequency enhancement module The output features of the decoding module are added, and then amplified along the channel dimension. Local features are extracted through a two-dimensional convolution with a convolution kernel of 3, a stride of 1, and a padding of 1. Finally, the network passes through a gated linear unit (GLU) to selectively transmit or suppress information and obtain the output result. , as the input of the next decoding module.

[0034] Step 2.4: Construct a multi-scale feature extraction module to extract multi-scale feature information from the output features of the encoder and the output of the dual-path module, thereby alleviating the information loss problem caused by excessive dimensionality reduction of feature information in the bottleneck layer of the U-shaped network model.

[0035] like Figure 6 As shown, taking the first multi-scale feature extraction module as an example, for the input feature First, it undergoes layer normalization operation, and then performs local attention calculation and cross-region attention calculation respectively. Among them, the local attention block uses the multi-head self-attention mechanism to interact with the local area of the feature in the time and frequency dimensions, thereby capturing longer-distance dependencies.

[0036] in, Representation layer normalization, 、 、 and represents the linear transformation matrix, represents the normalized exponential function, Indicates the number of heads to be split. 、 and Split into h heads along the channel dimension, is the output of the th head, Indicates splicing along the channel.

[0037] The difference between the cross-region attention block and the local attention block is that it uses adaptive pooling to reduce the dimensionality of the query matrix and the key matrix, performs long-distance feature interaction in the frequency dimension, improves the information fusion capability across the frequency dimension, and enables the model to take into account both fine features and global change trends.

[0038] The remaining calculation process is the same as the above local attention calculation process, and the final cross-region attention block output feature .in, 、 represents the linear transformation matrix, represents adaptive pooling, Represents the frequency dimension.

[0039] After the local attention and cross-region attention are added together, a SE block dynamically adjusts the channel weights and weights the input features, allowing the model to better focus on important features: in, represents the squeeze-excitation operation, Represents the output of the cross-region attention block.

[0040] Weighted features The output of the multi-scale feature extraction module is added to the result of the layer normalization operation and the multi-core parallel convolution module. The multi-core parallel convolution module first extracts features from the input through three parallel multi-core convolution modules, then concatenates them along the channel dimension, and then sequentially passes through batch normalization, ReLU activation function, and 2D convolution. Finally, a residual connection is performed with the input that has passed the 2D convolution and batch normalization operation.

[0041] in, represents batch normalization, represents a two-dimensional convolution, Representation layer normalization, Represents the mapping function of the multi-core convolution module, represents the ReLU activation function, Indicates splicing along the channel.

[0042] like Figure 7 As shown, The multi-core convolution module includes two sets of parallel asymmetric dilated convolutions, batch normalization operations, ReLU activation functions and two-dimensional dilated convolutions. The convolution kernel size of each set of parallel asymmetric dilated convolutions is 3 1 and 1 3. The expansion factor of the first group is , the expansion factor of the second group is Each set of asymmetric dilated convolutions is connected in series with batch normalization and ReLU activation function respectively. The module is finally connected with convolution kernel size 3. 3. The expansion factor is The output of the two-dimensional convolution is the same as that of the convolution kernel with a size of 1 1. The output of the residual connection composed of the two-dimensional convolution with a dilation factor of 1 and the batch normalization operation is added as the output of the multi-core convolution module.

[0043] in, represents a nonlinear activation function, represents batch normalization, represents a two-dimensional convolution, represents the convolution kernel size, Represents the expansion factor.

[0044] Step 2.5: Build Figure 8 The dual-path module shown above extracts the output features of the first multi-scale feature extraction module. To model global information, four stacked dual-path RNN modules are used to model sequences and capture long-term dependency information of features. The dual-path RNN module is constructed in the frequency dimension through group normalization, LSTM modules and fully connected layers. To model, the output of the fully connected layer is fused with the input through the jump connection, and the output is . Perform the same modeling operation on the time dimension as on the time dimension, and the output is .

[0045] In order to alleviate the performance limitation caused by diminishing marginal utility, a feature conversion module is introduced after each dual-path RNN module to perform time-frequency domain conversion and project the output features of the dual-path RNN module into a new space. The first and third feature conversion modules perform fast Fourier transform, and the second and fourth feature conversion modules perform inverse fast Fourier transform. Finally, the dual-path module output is .

[0046] Step 2.6: Build a decoder to fusion module output Upsampling is performed to gradually restore the amplitude features of the human voice and accompaniment required for the network task. The decoder includes three sparse upsampling blocks connected in series.

[0047] like Figure 9 As shown in the figure, the sparse upsampling block first divides the input features into low-frequency band, medium-frequency band and high-frequency band at a ratio of 20%, 30% and 50% along the frequency dimension, and deconvolves the low-frequency, medium-frequency and high-frequency band features with a convolution kernel of size 3 and a stride of 1, a convolution kernel of size 2 and a stride of 2, and a convolution kernel of size 4 and a stride of 4, respectively. The deconvolution operations are then performed on the low-frequency, medium-frequency and high-frequency band features, and then spliced along the frequency dimension. The output is The third sparse upsampling block outputs the predicted mask , the features on the two channels represent the vocal mask predicted by the model With accompaniment mask .

[0048] Step 3: Mask the human voice output by the U-network model With accompaniment mask Respectively with the input features of the model Perform element-by-element dot product and get the size of the network model prediction to be 512 The amplitude characteristics of the human voice and accompaniment of 64. The amplitude characteristics of the human voice and accompaniment predicted in sequence are spliced along the time dimension with an overlap rate of 50% to obtain the amplitude characteristics of the complete human voice. and the amplitude characteristics of the complete accompaniment If the remaining part is less than the specified length, it will be padded from the end forward.

[0049] Step 4: Compare the amplitude characteristics of the predicted complete vocals and accompaniment with the phase characteristics of the mixed music signal Combined with the short-time Fourier inverse transform, it is converted into the time domain human voice signal predicted by the model and time domain accompaniment signal .

[0050] Step 5: Use the MIR-1K dataset for model training. The MIR-1K dataset includes 1,000 music clips cut from 110 songs. Label the pure accompaniment and vocals in the left and right channels of the music clips. Mix the left and right audio channels at 0 dB to create a single-channel mixed music signal sample. A training set of 175 mixed music signal samples featuring male singer Abjones and female singer Amy was selected to train the U-shaped network model constructed in Step 2. The remaining 825 mixed music signal samples served as the test set. These were input into the trained network model to generate separated time-domain vocal and time-domain accompaniment signals.

[0051] In order to verify the effectiveness of this method, the performance of this method and the classic method on the test set was tested, and the global normalized signal-to-noise ratio (Global Normalized Signal-to-Distortion Ratio, GNSDR), global signal-to-interference ratio (Global Signal-to-Interference Ratio, GSIR) and global signal-to-artifact ratio (Global Signal-to-Artifact Ratio, GSAR) were used as evaluation indicators to judge the accompaniment and vocal separation performance of the model. The results are shown in Table 1 and Table 2 respectively: Table 1 Table 2 As can be seen from Tables 1 and 2, the proposed method achieved the best scores in all the above evaluation indicators, indicating that the proposed method performed well in the single-channel music separation task, proving the effectiveness of the proposed method.

Claims

1. A single-channel music separation method based on a U-shaped network, characterized by: The specific steps include: Step 1: Preprocess the mixed music signal and extract the amplitude characteristics of the mixed music signal and phase characteristics ; And the amplitude characteristics of the complete music signal Perform time series frame processing as input features ; Step 2: Construct a U-shaped network model, including encoder, connection layer, bottleneck layer and decoder; input features through multiple consecutive encoding units Feature extraction is performed and then input into the bottleneck layer composed of the multi-scale feature extraction module, the dual path module and the multi-scale feature extraction module; the connection layer composed of the time-frequency enhancement module and the fusion module is used to connect the coding unit with the bottleneck layer or the coding unit with the decoding unit, and input into the next decoding unit; finally, the decoder outputs the predicted mask mask , including vocal masking With accompaniment mask ; The multi-scale feature extraction module first performs layer normalization on the input features, then dynamically adjusts the channel weights through parallel local attention blocks and cross-region attention blocks, and fuses them with the input features using residual connections. The fused features serve as the input for subsequent residual connections and layer normalization operations respectively. Finally, the features output by the layer normalization operation pass through a multi-core parallel convolution module consisting of batch normalization, dilated convolution, and RELU activation function. The output results are superimposed with the previously fused features as the final output of the module. The time-frequency enhancement module calculates the weights of each time dimension on different frequency units through operations such as global mean, one-dimensional convolution and sigmoid activation function, and strengthens the features through each weight; Step 3: Mask the Vocals With accompaniment mask and input features respectively Perform element-by-element dot product to obtain the predicted amplitude feature 、 , further splicing along the time dimension to obtain the amplitude characteristics of the human voice in the complete music signal and the amplitude characteristics of the accompaniment ; Step 4: Compare the amplitude characteristics of the vocals and accompaniment 、 Phase characteristics of separate and mixed music signals Combined with the short-time Fourier inverse transform, it is converted into a time domain human voice signal and time domain accompaniment signal ; Step 5: Train the U-shaped network model; select a single-channel song clip and input it into the trained network model to generate separated time-domain vocal signals and time-domain accompaniment signals.

2. The single-channel music separation method based on a U-shaped network as claimed in claim 1, characterized in that: The encoder includes three sparse downsampling blocks connected in series. In each sparse downsampling block, the input features are first divided into low-frequency band, medium-frequency band and high-frequency band along the frequency dimension, and then information is compressed in the three branches. The higher the frequency, the greater the compression ratio. The compressed features are passed through the GELU activation function and stacked convolution modules to capture the detailed features in different frequency bands. Finally, the features of different frequency bands are spliced along the frequency dimension. A convolution layer is set after each sparse downsampling block.

3. The single-channel music separation method based on a U-shaped network as claimed in claim 2, characterized in that: In each sparse downsampling block, the input features are first split into low-frequency, mid-frequency, and high-frequency bands along the frequency dimension with a ratio of 20%, 30%, and 50%.

4. The single-channel music separation method based on a U-shaped network as claimed in claim 1, characterized in that: The fusion module first adds the output features of the time-frequency enhancement module to the features of the decoding stage, then amplifies them along the channel dimension, extracts local features through two-dimensional convolution, and finally inputs them into the next decoding module after processing by the gated linear unit.

5. The single-channel music separation method based on a U-shaped network as claimed in claim 1, characterized in that: The dual-path module uses four stacked dual-path RNN modules to extract the output features of the first multi-scale feature extraction module. Perform global information modeling and introduce a feature conversion module after each dual-path RNN module to perform time-frequency domain conversion and project the output features of the dual-path RNN module into a new space; The dual-path RNN module models the input in the frequency dimension through group normalization, LSTM modules and fully connected layers, and the output of the fully connected layer is fused with the input through skip connections.

6. The single-channel music separation method based on a U-shaped network as claimed in claim 5, characterized in that: The first and third feature conversion modules perform fast Fourier transform, and the second and fourth feature conversion modules perform inverse fast Fourier transform.

7. The single-channel music separation method based on a U-shaped network as claimed in claim 1, characterized in that: The local attention block uses a multi-head self-attention mechanism to perform information interaction on the local area of the feature in the time and frequency dimensions; the cross-region attention block uses adaptive pooling to reduce the dimension of the query matrix and the key matrix, and performs long-distance feature interaction in the frequency dimension.

8. The single-channel music separation method based on a U-shaped network as claimed in claim 1, characterized in that: The multi-core parallel convolution module first extracts features from the input through three parallel multi-core convolution modules, then concatenates them along the channel dimension, and then sequentially passes through batch normalization operation, ReLU activation function and two-dimensional convolution, and finally performs residual connection with the input that has passed the two-dimensional convolution and batch normalization operation; The multi-core convolution module includes two sets of parallel asymmetric dilated convolutions, batch normalization operations, ReLU activation functions and two-dimensional dilated convolutions. The convolution kernel size of each set of parallel asymmetric dilated convolutions is 3 1 and 1 3. The expansion factor of the first group is , the expansion factor of the second group is .

9. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method according to any one of claims 1 to 9.

Images