Deep learning pre-positioning method based on convolution-Transform hybrid architecture

Abstract

The invention discloses a deep learning pre-positioning method based on a convolution-Transform hybrid architecture, and belongs to the technical field of medical imaging and intelligent diagnosis and treatment equipment. According to the method, a multi-channel three-axis magnetic sensor array is used for collecting magnetic field signals of a magnetic control capsule, local features are extracted through a residual convolutional network, channel dimensions are expanded, and then coding information of sensor positions and directions is injected in a residual form, so that the perceptual ability of a model to array geometry is enhanced. And then, capturing a global dependency relationship through Transform coding in which a channel is combined with space attention, and outputting the position, the posture and the confidence coefficient of the capsule by a multi-task prediction head after global aggregation. The method can still keep millimeter-level positioning precision in complex interference and dynamic scenes, has the advantages in the aspects of anti-interference performance, real-time performance and adaptability compared with a traditional analysis modeling or optimization searching method, and provides reliable support for clinical navigation and minimally invasive treatment of the magnetic control capsule.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of medical imaging and intelligent diagnosis and treatment equipment, and particularly relates to a deep learning pre-positioning method based on a convolution-Transformer hybrid architecture, which is suitable for related scenes such as a magnetically controlled capsule robot, a magnetic source positioning and a wearable magnetic sensor array. BACKGROUND

[0002] In recent years, as an important development direction of wireless capsule endoscopy, the magnetically controlled capsule endoscope gradually becomes an important tool for screening and diagnosis of digestive diseases, because it can realize non-invasive, portable and high comfort examination in the human gastrointestinal tract. Compared with the traditional endoscope, the magnetically controlled capsule can realize a certain degree of direction and navigation in the gastrointestinal tract through the driving of the external magnetic field, thereby improving the lesion coverage rate and reducing the missed detection. However, the magnetically controlled capsule still has the problem of insufficient positioning and navigation accuracy in actual clinical application, especially under the condition of patient's free body position change or daily activities, the real-time position and attitude of the capsule are difficult to accurately estimate, which directly affects the accurate positioning of the lesion and the controllability of the clinical operation.

[0003] The existing magnetically controlled capsule positioning methods mainly include analytical modeling method, grid search method, optimization algorithm and filter-based state estimation method. Among them, the analytical modeling method depends on the magnetic dipole equation to establish the analytical relationship between the sensor and the magnetic source, but it has large calculation amount and is easily disturbed in complex environment; the grid search method can estimate the position in the global range, but the search efficiency is low and the real-time performance is insufficient; the swarm intelligence optimization method can overcome the local extremum problem, but it is sensitive to the initial value and has large calculation overhead; the filter-based algorithm such as extended Kalman filter and unscented Kalman filter can be used for dynamic tracking, but when there is strong geomagnetic interference or motion artifact, the filter convergence and stability are insufficient.

[0004] With the development of artificial intelligence, especially deep learning technology, researchers try to introduce convolutional neural network, recurrent neural network and self-attention mechanism to model the sensor observation data end to end, in order to break through the limitations of traditional model methods under nonlinear and dynamic interference conditions. CNN has advantages in local feature extraction, but lacks the ability to model global dependencies; Transformer performs outstandingly in capturing long-range dependencies, but its perception of local patterns is less efficient than convolution. How to combine the two and effectively introduce the sensor spatial pose prior to realize high-precision estimation of the position and attitude of the magnetically controlled capsule has become an important direction of current research. SUMMARY

[0005] To solve the problems of existing magnetic capsule positioning methods, such as being easily disturbed by geomagnetic and motion pseudo errors in dynamic wearable scenarios, being sensitive to initial values, and having high computational complexity, the application provides a deep learning pre-positioning method based on a convolution-Transformer hybrid architecture, which realizes high-precision and robust capsule pre-positioning through the cooperative modeling of residual convolution feature extraction and channel-space dual attention mechanisms, and the explicit encoding of sensor spatial pose. On the one hand, the method uses a convolutional neural network to extract local features and expand high-dimensional features from multi-channel magnetic field observation data, enhancing the model's ability to perceive the correlation of the sensor's neighborhood space. On the other hand, the method introduces a channel-space hybrid attention structure of the Transformer to capture the cross-channel and cross-sensor dependencies in the global range, improving the model's modeling ability under complex interference conditions. At the same time, by encoding the position vector and direction matrix of the sensor and injecting them into the network features in a residual manner, the model has spatial geometric priors under the end-to-end framework of deep learning, which can maintain positioning stability in dynamic scenarios. Compared with traditional analytical modeling, grid search, and simplex optimization algorithms, the method of the application can realize high-precision real-time estimation of the position and attitude of the magnetic capsule while ensuring robustness without complex difference matrix construction or large amounts of search calculations. To achieve the above purpose, the application adopts the following technical solutions:

[0006] Step S1, a multi-channel three-axis magnetic sensor array is laid out in the target area to collect the magnetic field observation signals of the target magnetic dipole at each sensor, and the original data is shaped and input modeling;

[0007] Step S2, residual one-dimensional convolutional networks are used to extract local features from the sensor observation signals, capture the spatial correlation between adjacent sensors, and expand the three-axis signals into high-dimensional feature representations;

[0008] Step S3, the convolution-Transformer bridging module is used to maintain the spatial dimension structure unchanged, and map the convolution domain features to input representations suitable for the Transformer;

[0009] Step S4, the spatial pose information of the sensor is explicitly modeled, the position vector and direction matrix are encoded, and the residual way is injected into the feature matrix to enhance the model's spatial perception ability;

[0010] Step S5, based on the hybrid dimension Transformer coding structure, channel attention modeling is performed first to extract cross-channel dependencies, and then spatial attention modeling is performed to capture the spatial correlation between sensors, thereby obtaining a fused feature matrix;

[0011] Step S6: Perform a global aggregation operation on the fused channel-space feature matrix to integrate the local features into a unified high-dimensional global representation vector, and output the three-dimensional position, attitude parameters and confidence score of the target magnetic source respectively, so as to complete the high-precision estimation of the magnetic source state.

[0012] The present invention also provides an apparatus comprising: a processor and a memory, wherein the memory stores a program, and the program, when executed by the processor, implements the aforementioned method.

[0013] The present invention also provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the aforementioned method.

[0014] The beneficial effects of this invention are as follows:

[0015] In terms of feature extraction, this invention employs a residual one-dimensional convolutional network to process the observation signals from multi-channel magnetic sensors. This fully captures the local spatial correlations between sensor neighborhoods and expands low-dimensional signals into high-dimensional representations, thereby enhancing the model's representational capabilities. Secondly, regarding global dependency modeling, this invention introduces a channel-space hybrid attention mechanism. It first establishes cross-feature global dependencies in the channel dimension and then models the correlations between sensors in the spatial dimension, achieving effective fusion of local features and global patterns. This allows for maintaining high positioning accuracy even in the presence of complex environmental interference and dynamic motion artifacts.

[0016] Regarding the utilization of prior information, this invention encodes the sensor's position vector and orientation matrix in three-dimensional space and injects them into the network features as residuals, enabling the deep learning model to possess spatial geometric prior knowledge. This approach not only enhances the model's ability to perceive the geometric structure of the sensor array but also maintains robust estimation of the capsule magnetic source's position and orientation even when the patient's posture changes or the array as a whole shifts. Simultaneously, the network architecture of this invention employs an end-to-end deep learning framework, avoiding the drawbacks of traditional methods that rely on analytical modeling, global grid search, or complex optimization iterations. This significantly reduces sensitivity to initial values ​​and computational complexity, ensuring both millimeter-level positioning accuracy and real-time performance.

[0017] Experimental verification shows that the method of this invention is superior to existing technologies in terms of positioning accuracy, robustness, real-time performance, and adaptability. It can achieve high-precision real-time pre-positioning of magnetically controlled capsules in dynamic wearable scenarios, providing reliable technical support for accurate detection, path planning, and subsequent minimally invasive treatment of digestive tract lesions. It has significant clinical application prospects and broad promotional value. Attached Figure Description

[0018] Figure 1This is a flowchart of a deep learning pre-positioning method based on a convolutional-transformer hybrid architecture. Detailed Implementation

[0019] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] In the following description, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Clearly, the described embodiments are only a portion of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0021] To address the issues of existing wearable magnetic positioning technologies being susceptible to geomagnetic and environmental interference in dynamic scenarios, prone to getting trapped in local extrema, and highly sensitive to initial values, leading to insufficient pre-positioning accuracy and instability in subsequent magnetic control processes, this invention proposes a deep learning pre-positioning method based on a convolutional-Transformer hybrid architecture. This method achieves collaborative modeling of local features and global dependencies by combining residual convolutional networks and Transformers, and introduces explicit encoding of sensor spatial pose and residual injection strategies, thereby enhancing adaptability to sensor geometric distribution while maintaining model expressiveness. Unlike traditional analytical modeling or global search optimization methods, this invention can simultaneously complete feature extraction and position / pose estimation within an end-to-end learning framework, avoiding complex difference matrix construction or redundant global searches, significantly reducing computational overhead. This method exhibits significant advantages in positioning accuracy, dynamic robustness, and real-time performance, and is particularly suitable for magnetically controlled capsule pre-positioning in wearable magnetic sensor array scenarios. Figure 1 As shown, the specific implementation process includes the following steps:

[0022] Step S1: Use a multi-channel triaxial magnetic sensor array deployed in the target area to collect the magnetic field observation signals of the target magnetic dipole at each sensor, and complete the shaping and input modeling of the raw data.

[0023] Specifically, a sensor array is deployed in the target area to acquire the triaxial magnetic field signal generated by the magnetic dipole in real time. Let the original input data be... ,in This indicates the batch size, and 108 represents the total dimension of the readings from the 36 triaxial sensors. Through a recombination operation, it can be shaped into a three-dimensional tensor:

[0024] ;

[0025] in, Indicates the first In the nth sample The three-axis observations of each sensor. "Batch size" refers to the number of samples fed into the model for training or inference at one time.

[0026] Furthermore, assume that the sensor's position vector in space is Its direction matrix flattened is The spatial pose of the sensor can then be expressed as:

[0027] ;

[0028] in, Used to describe the sensor's position in three-dimensional space. This is used to describe the directional characteristics of the sensor's sensing axis. Therefore, the observation data and the sensor pose together constitute the input model:

[0029] Input modeling refers to the process of processing the raw signals collected by sensors through shaping, normalization, and feature organization to make them conform to the input requirements of a model (such as a deep learning model).

[0030] Step S2: Use a residual one-dimensional convolutional network to extract local features from the sensor observation signals, capture the spatial correlation between adjacent sensors, and expand the triaxial signals into a high-dimensional feature representation.

[0031] Residual one-dimensional convolutional networks are deep networks that perform convolution operations in one dimension. The core idea is to add the result after convolution and activation to the original input at each layer before outputting, thereby avoiding gradient vanishing and enabling the network to deeply extract local spatial features in the sensor sequence.

[0032] Specifically, the input tensor As input to a one-dimensional convolutional neural network, it can capture the local spatial correlation between different sensors and utilize the residual connection structure to achieve deep feature extraction and stable gradient propagation.

[0033] Assume the first The weights of each convolutional kernel are The kernel length is , bias is The output features of the convolution operation can then be expressed as:

[0034] ;

[0035] in, It is the ReLU activation function. Indicates the channel index. This represents the offset of the convolution kernel. By extracting multiple sets of convolution kernels in parallel, combined with residual structure and batch normalization, the model's ability to represent local magnetic field patterns can be significantly enhanced. After stacking multiple layers of convolution-residual blocks, the original 3-channel triaxial signal is gradually expanded into a 256-channel high-dimensional feature representation, forming a feature tensor. Here, 256 represents the number of feature channels extracted after convolution, and 36 represents the number of sensors, maintaining consistency with the input in spatial dimension. This high-dimensional feature provides a richer foundational representation for subsequent Transformer encoding and spatial prior information injection.

[0036] Step S3: By using the convolution-Transformer bridging module to maintain the spatial dimensional structure, the convolutional domain features are mapped to the input representation adapted to the Transformer.

[0037] Specifically, to enable this feature to adapt to the subsequent Transformer encoding structure, a bridging module can be designed to perform morphological mapping and normalization on the convolutional output. This module maps the convolutional domain features to a sequence representation that the Transformer can process, while maintaining the spatial dimension, ensuring the consistency of feature information during cross-domain transmission. Let the bridging operation be denoted by the function... The representation after mapping is:

[0038] ;

[0039] in, With input Maintaining dimensionality consistency—256 channels and 36 spatial dimensions—normalization and scale alignment were performed only in numerical distribution and representation form. This step effectively transforms the local features extracted by the convolutional network into an input tensor adapted to the Transformer, laying the foundation for subsequent introduction of sensor spatial pose encoding and mixed-dimensional attention mechanisms.

[0040] Step S4: Explicitly model the spatial pose information of the sensor, encode the position vector and orientation matrix respectively, and inject them into the feature matrix in the form of residuals to enhance the spatial perception capability of the model.

[0041] In particular, to further enhance the network's ability to model the spatial distribution patterns of sensors, the spatial pose information of the sensors can be explicitly introduced into the model, including the encoding of position vectors and orientation matrices, and fused with the bridged features through residuals.

[0042] The first is obtained through mapping via two layers of perceptron. Position vector encoding of each sensor:

[0043] ;

[0044] in, These are the weight matrices, For bias vectors, Representation layer normalization.

[0045] The first layer is obtained by mapping through two layers of perceptron with the same structure. Orientation matrix encoding of each sensor:

[0046] ;

[0047] in, These are the corresponding weight matrices. This is the corresponding bias vector.

[0048] Position and orientation codes are weighted by learnable weights. Perform linear weighted fusion Then, the fusion features of all sensors Expand it to align it with the convolutional features in the channel dimension (256), forming a matrix. Subsequently, the bridged features are injected using a residual method. ,in These are learnable residual weight coefficients with small initial values, used to control the degree of influence of spatial prior information on the overall features.

[0049] Step S5: Based on the hybrid-dimensional Transformer encoding structure, first perform channel attention modeling to extract cross-channel dependencies, then perform spatial attention modeling to capture spatial correlations between sensors, thereby obtaining the fused feature matrix.

[0050] Among them, the hybrid-dimensional Transformer encoding structure is a two-step encoding method: first, the association between channels is calculated in the channel dimension, and then the dimensional order is reversed to calculate the association between positions in the spatial dimension; through two attention calculations, the network can simultaneously capture the global dependencies between channels and spatial positions.

[0051] Channel attention is a method to measure and emphasize the importance of different channels in a feature: first, channel information at all spatial locations is integrated, then the weight of each channel is calculated, and finally, these weights are used to weight the features of each channel to highlight key channels and suppress redundant channels.

[0052] Cross-channel dependency refers to the fact that each channel is not independent; they may be correlated or complementary. For example, one channel might detect edges, while another detects color; their combination is needed to better represent the target. Cross-channel dependency aims to model the relationships between these channels, rather than looking at each channel in isolation.

[0053] In particular, in order to simultaneously model the inter-channel dependencies and the correlation between sensor spatial locations, a hybrid-dimensional Transformer encoding structure is adopted, which includes two stages: channel attention encoding and spatial attention encoding.

[0054] Spatial attention is a method to measure and emphasize the importance of different spatial locations in a feature: first, information from the same location is integrated across all channels, then the weight of each spatial location is calculated, and finally, these weights are used to weight the features at each location, highlighting key locations and weakening secondary locations.

[0055] First of all Considering it as a sequence of length 256, with each token having an embedding dimension of 36, we get... Under the multi-head self-attention mechanism, let the mapping matrices be respectively Then query matrix Key matrix Value matrix They are respectively:

[0056] , , ;

[0057] in, Then the formula for calculating channel attention is:

[0058] ;

[0059] After multi-head splicing and feedforward network processing, the channel attention encoding result is obtained. Multi-head concatenation is usually the last step in the multi-head attention mechanism in Transformer: concatenating the vectors output by multiple attention heads and then obtaining a unified dimensional representation through a linear mapping.

[0060] Will Transpose the sequence with 36 sensors as the sequence length and 256 as the embedding dimension. Similarly, the spatial attention encoding output is finally obtained. .

[0061] Finally, the spatial attention results are transposed back to the original structure. ,matrix This serves as a deep representation that integrates channel correlation and spatial correlation, for use in subsequent global aggregation and prediction heads.

[0062] Step S6: Perform a global aggregation operation on the fused channel-space feature matrix to integrate the local features into a unified high-dimensional global representation vector, and output the three-dimensional position, attitude parameters and confidence score of the target magnetic source respectively, so as to complete the high-precision estimation of the magnetic source state.

[0063] Specifically, let the global aggregate function be denoted as . Its function is to map the two-dimensional features of the channel-space into a single vector representation. This function can be a weighted average, attention pooling, or differentiable global pooling operator.

[0064] Differentiable global pooling is a learnable function that compresses a two-dimensional feature map into a one-dimensional vector: it assigns an updatable weight to each spatial location, and then performs a weighted summation of all locations according to the weights to obtain a unified global representation, and the entire process can be optimized end-to-end using gradient descent.

[0065] In an embodiment, ,in Here, 512 represents the aggregated feature dimension, which can be expressed as follows if weighted attention pooling is used:

[0066] ;

[0067] in, Attention weights are automatically optimized using learnable parameters.

[0068] Let the prediction function be It consists of a multi-layer sensing mechanism, thus enabling location prediction. Attitude prediction Reliability prediction They are respectively:

[0069] , , .

[0070] This invention discloses a deep learning pre-positioning method based on a convolutional-transformer hybrid architecture. This method achieves high-precision, robust, and real-time initial pose estimation of a magnetically controlled capsule in wearable scenarios through joint modeling of residual convolution and channel-space dual attention mechanisms, combined with a residual injection strategy of sensor spatial pose encoding. The method first shapes and models the multi-channel triaxial magnetic field observation data collected by the sensor array, extracting local spatial correlation features via a residual convolutional network and expanding them into a high-dimensional representation. Then, a convolutional-transformer bridging module maintains structural consistency, introducing explicit encoding of sensor position and orientation and fusing it with feature residuals to enhance the model's adaptability to array geometric priors. Furthermore, a hybrid Transformer encoding combining channel and spatial attention is used to achieve global dependency modeling across channels and sensors. Finally, global aggregation and a multi-task prediction head output the position, orientation, and confidence of the magnetically controlled capsule, thus completing the pre-positioning. Simulation and hardware-in-the-loop experimental results demonstrate that the method of this invention can maintain millimeter-level positioning accuracy even in dynamic scenes and complex interference environments. Compared with traditional analytical modeling, mesh search, or single optimization methods, it has significant advantages in terms of anti-interference capability, computational efficiency, and adaptability. This invention effectively solves the problems of algorithm initialization sensitivity, high computational complexity, and insufficient robustness in wearable magnetic positioning systems, significantly reducing the difficulty of subsequent magnetic navigation and path tracking implementation.

[0071] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A deep learning pre-positioning method based on a convolutional-transformer hybrid architecture, characterized in that, The method includes: Step S1: Use a multi-channel triaxial magnetic sensor array deployed in the target area to collect the magnetic field observation signals of the target magnetic dipole at each sensor, and complete the shaping and input modeling of the raw data; Step S2: Use a residual one-dimensional convolutional network to extract local features from the sensor observation signals, capture the spatial correlation between adjacent sensors, and expand the triaxial signals into a high-dimensional feature representation; Step S3: By using the convolution-transformer bridging module to maintain the spatial dimensional structure, the convolutional domain features are mapped to the input representation adapted to the Transformer. Step S4: Explicitly model the spatial pose information of the sensor, encode the position vector and orientation matrix respectively, and inject them into the feature matrix in the form of residuals to enhance the spatial perception capability of the model. Step S5: Based on the hybrid-dimensional Transformer encoding structure, first perform channel attention modeling to extract cross-channel dependencies, then perform spatial attention modeling to capture spatial correlations between sensors, thereby obtaining the fused feature matrix; Step S6: Perform a global aggregation operation on the fused channel-space feature matrix to integrate the local features into a unified high-dimensional global representation vector, and output the three-dimensional position, attitude parameters and confidence score of the target magnetic source respectively, so as to complete the high-precision estimation of the magnetic source state.

2. The deep learning pre-positioning method based on a convolutional-Transformer hybrid architecture according to claim 1, characterized in that, In step S1, the original input data is ,in The batch size is represented by 108, which indicates the total dimension of the readings from the 36 triaxial sensors. Through a recombination operation, it can be reshaped into a three-dimensional tensor. ； in, Indicates the first In the nth sample Triaxial observations from one sensor; Furthermore, assume that the sensor's position vector in space is Its direction matrix flattened is Then the spatial pose of the sensor can be expressed as: ； Therefore, the observation data and sensor pose together constitute the input model: ,in Represents the entire set of inputs for modeling. Represents observation data, This represents the sensor's pose, where S is the range of values.

3. The deep learning pre-positioning method based on a convolutional-Transformer hybrid architecture according to claim 1, characterized in that, In step S2, it is assumed that the first The weights of each convolutional kernel are The kernel length is , bias is The output features of the convolution operation can then be expressed as: ； in, It is the ReLU activation function. Indicates the channel index. This indicates the offset of the convolution kernel.

4. The deep learning pre-positioning method based on a convolutional-Transformer hybrid architecture according to claim 1, characterized in that, In step S3, the bridging operation is denoted as a function. The representation after mapping is: ； in, With input It maintains consistency in dimensions, with 256 channels and 36 spatial dimensions, and normalization and scale alignment are only performed on the numerical distribution and representation form.

5. The deep learning pre-positioning method based on a convolutional-Transformer hybrid architecture according to claim 1, characterized in that, In step S4, the first layer is obtained through mapping via two layers of perceptrons. Position vector encoding of each sensor: ； in, These are the weight matrices, For bias vectors, Representation layer normalization; The first layer is obtained by mapping through two layers of perceptron with the same structure. Orientation matrix encoding of each sensor: ； in, These are the corresponding weight matrices. This is the corresponding bias vector; Position and orientation codes are weighted by learnable weights. Perform linear weighted fusion Then, the fusion features of all sensors Expand it to align it with the convolutional features in the channel dimension (256), forming a matrix. Subsequently, the bridged features are injected using a residual method. ,in These are learnable residual weight coefficients used to control the degree of influence of spatial prior information on the overall features.

6. The deep learning pre-positioning method based on a convolutional-Transformer hybrid architecture according to claim 1, characterized in that, In step S5, firstly... Considering it as a sequence of length 256, with each token having an embedding dimension of 36, we get... Under the multi-head self-attention mechanism, let the mapping matrices be respectively Then query matrix Key matrix Value matrix They are respectively: ， ， ； in, Then the formula for calculating channel attention is: ； After multi-head splicing and feedforward network processing, the channel attention encoding result is obtained. ; Will Transpose the sequence with 36 sensors as the sequence length and 256 as the embedding dimension. Similarly, the spatial attention encoding output is finally obtained. ; Finally, the spatial attention results are transposed back to the original structure. .

7. The deep learning pre-positioning method based on a convolutional-Transformer hybrid architecture according to claim 1, characterized in that, In step S6, the global aggregation function is denoted as... Its function is to map the two-dimensional features of the channel-space into a single vector representation; this function can be a weighted average, attention pooling, or differentiable global pooling operator; then we have ,in Here, 512 represents the aggregated feature dimension, which, if weighted attention pooling is used, is represented as: ； in, Attention weights are automatically optimized using learnable parameters. Let the prediction function be It consists of a multi-layer sensing mechanism, thus enabling location prediction. Attitude prediction Reliability prediction They are respectively: ， ， 。 8. The deep learning pre-positioning method based on a convolutional-Transformer hybrid architecture according to claim 1, characterized in that, Before global aggregation, regularization is performed on the fused channel space feature matrix to suppress outliers and improve prediction stability.

9. An apparatus, characterized in that, include: A processor and a memory, wherein the memory stores a program that, when executed by the processor, implements the method according to any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to perform the method described in any one of claims 1 to 8.

Images