An arbitrary size image enhancement method based on frequency aggregation self-attention

Abstract

The application provides an arbitrary size image enhancement method based on frequency aggregation self-attention, comprising: obtaining a first image to be processed; using a trained frequency aggregation self-attention network to process the first image to obtain a second image, the resolution of the second image being higher than that of the first image, the frequency aggregation self-attention network comprising functions of a bilinear space interpolation up-sampling unit, a decoder unit, a frequency utilization unit, a frequency integration unit and an encoder unit. The image features are extracted by using the encoder unit, the frequency information is efficiently extracted by using the frequency integration unit and introduced into the network, the feature map is generated by using the spatial information and the frequency information according to the frequency characteristics by using the frequency utilization unit, the self-attention calculation is performed, finally, the image is reconstructed according to the size to be enhanced by using the decoder and the bilinear space interpolation up-sampling, and excellent performance in the arbitrary size image enhancement task is realized.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to an arbitrary-size image enhancement method based on frequency aggregation self-attention. Background Technology

[0002] In the era of big data, images play a crucial role in many fields such as environmental monitoring, resource exploration, and medical diagnosis. However, limitations in equipment cost, natural environment, and transmission conditions often result in low-resolution, poor-quality, and blurry images. Arbitrary-Scale Image Enhancement (ASIE), on the other hand, can generate high-resolution (HR) images at any magnification from low-resolution (LR) images, overcoming the limitation of traditional image enhancement methods that can only work at a fixed magnification. Therefore, ASIE technology has significant research implications for various fields such as medical imaging, audio-visual entertainment, and security surveillance.

[0003] In recent years, many ASIE methods have been proposed. These include meta-learning reinforcement networks, continuous implicit neural expression networks, and spatial coding-based networks, providing support for image enhancement tasks of arbitrary sizes. However, although existing methods can generate enhanced images at any magnification, the generated images generally suffer from structural artifacts (such as checkerboard and ringing effects) and local blurring, significantly reducing the visual fidelity of the images and their practicality for downstream tasks. Therefore, designing ASIE methods that can achieve higher quality has become an urgent problem to be solved. Summary of the Invention

[0004] In view of the above-mentioned deficiencies of the prior art, the present invention provides an arbitrary-size image enhancement method based on frequency aggregation self-attention to solve the technical problems of blurring and artifacts in high-resolution images obtained by arbitrary-size image enhancement in the prior art.

[0005] To achieve the above and other related objectives, this invention provides an arbitrary-size image enhancement method based on frequency aggregation self-attention, comprising: acquiring a first image to be processed; processing the first image using a trained frequency aggregation self-attention network to obtain a second image, wherein the resolution of the second image is higher than that of the first image, and the expression of the frequency aggregation self-attention network is as follows:

[0006] X HR =H BSI (X LR )+(H D (H FUSAM (H FIM (HE (X LR ))+H E (X LR ))),

[0007] In the formula, X LR and X HR H represents the first image and the second image, respectively. BSI H D H FUSAM H FIM H E These represent functions for the bilinear spatial interpolation upsampling unit, decoder unit, frequency utilization unit, frequency integration unit, and encoder unit, respectively.

[0008] In one embodiment of the present invention, the encoder unit includes a pre-trained dense residual network model.

[0009] In one embodiment of the present invention, the frequency integration unit processes the input feature X through the following steps. E Processing: The input feature X is processed using a Fast Fourier Transform. E Convert to a first complex number; perform convolution processing on the real and imaginary parts of the first complex number, and then recombine them to form a second complex number; combine the second complex number with the input feature X. E The components are fused and then processed using inverse fast Fourier transform and point convolution to obtain the output feature X of the frequency integration unit. FIM .

[0010] In one embodiment of the present invention, the expression for the frequency utilization unit is as follows:

[0011] H FUSAM (X FIM ) = IISA(X FIM )+FCSA(X FIM ),

[0012] In the formula, X FIM and X FUSAM These are the input and output features of the frequency utilization unit, respectively. IISA is a coordinated implicit self-attention block, and FCSA is a frequency-dependent self-attention block. The coordinated implicit self-attention block utilizes the inherent relationship between frequency information and spatial information to perform cross-domain information interaction in order to coordinate frequency information and spatial information. The frequency-dependent self-attention block utilizes the globality of frequency to enhance the model's ability to acquire global information.

[0013] In one embodiment of the present invention, the expression of the coordinated implicit self-attention block is as follows:

[0014]

[0015] In the formula, X and X IISA Let Q and K be the input and output features of the coordinated implicit self-attention block, respectively. The Project operation projects spatial and frequency information into a subspace to perform cross-domain information interaction and generate feature maps Q and K for calculating attention. Conv is a convolution operation used to generate feature map V for calculating attention. It is obtained using the second image coordinate interpolation feature map Q. and The features obtained using the first image coordinate interpolation feature maps K and V are respectively, where γ(X) is a mapping function representing the positional relationship between the first image and the second image, FC represents a fully connected layer, and d x H represents the feature dimension, and H represents the number of attention heads.

[0016] In one embodiment of the present invention, the expression for the frequency-dependent self-attention block is as follows:

[0017] Q1,K1,V1=Chunk(Conv 3*3 (X)),

[0018]

[0019] In the formula, X and X FCSA These represent the input and output features of the frequency-correlation self-attention block, respectively. Conv represents the convolution operation, Chunk represents the uniform segmentation operation, FFT represents the Fast Fourier Transform, and IFFT represents the Inverse Fast Fourier Transform. d x The first image coordinate represents the feature dimension, the second image coordinate represents the linear projection layer, and the third image coordinate represents the interpolation operation using the first image coordinates.

[0020] In one embodiment of the present invention, the decoder unit is composed of multiple cascaded multilayer sensing mechanisms.

[0021] In one embodiment of the present invention, the loss during training of the frequency aggregation self-attention network is calculated using the following formula:

[0022]

[0023] In the formula, The real image corresponding to the input image. The input image is the enhanced result output by the frequency aggregation self-attention network. The superscript i indicates the correspondence between the enhanced result and the real image, and N is the total number of samples in each batch.

[0024] To achieve the above and other related objectives, the present invention also provides an electronic device, including a processor, a memory, and a communication bus; the communication bus is used to connect the processor and the memory; the processor is used to execute a computer program stored in the memory to implement the method provided in any of the above embodiments.

[0025] To achieve the above and other related objectives, the present invention also provides a computer-readable storage medium having a computer program stored thereon, the computer program being used to cause a computer to perform the method provided in any of the above embodiments.

[0026] The beneficial effects of this invention are as follows: This invention proposes an arbitrary-size image enhancement method based on frequency aggregation self-attention. This method uses an encoder unit to extract image features, uses a frequency integration unit to efficiently extract frequency information and introduce it into the network, uses a frequency utilization unit to generate feature maps based on frequency characteristics and spatial and frequency information for self-attention calculation, and finally uses a decoder and bilinear spatial interpolation upsampling to reconstruct the image according to the size to be enhanced, thus achieving excellent performance in arbitrary-size image enhancement tasks. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. The accompanying drawings are incorporated in and constitute a part of this specification, illustrating embodiments consistent with this application, and are used together with the description to explain the principles of this application. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of an image enhancement method provided in an embodiment of the present invention;

[0029] Figure 2 This is an architectural diagram of a frequency aggregation self-attention network provided in an embodiment of the present invention;

[0030] Figure 3 This is an architectural diagram of a frequency integration unit provided in an embodiment of the present invention;

[0031] Figure 4 This is an architectural diagram of a coordinated implicit self-attention block provided in an embodiment of the present invention;

[0032] Figure 5 This is a schematic diagram illustrating the calculation of Q, K, and V in a coordinated implicit self-attention block according to an embodiment of the present invention;

[0033] Figure 6This is an architectural diagram of a frequency-correlation self-attention block provided in an embodiment of the present invention;

[0034] Figure 7 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention.

[0035] Explanation of reference numerals in the attached figures: 101, processor; 102, memory. Detailed Implementation

[0036] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. It should be noted that, unless otherwise specified, the following embodiments and features can be combined with each other. In addition to the specific methods, equipment, and materials used in the embodiments, based on the knowledge of the prior art and the description of the present invention by those skilled in the art, any prior art methods, equipment, and materials similar to or equivalent to the methods, equipment, and materials in the embodiments of the present invention can be used to implement the present invention.

[0037] It should be understood that the terminology used in the embodiments of this invention is for describing specific implementations and not for limiting the scope of protection of this invention. Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art.

[0038] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In some embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0039] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functions, and operations that may be implemented in the methods and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0040] Please see Figure 1 , Figure 1 An embodiment of the present invention provides an arbitrary-size image enhancement method based on frequency aggregation self-attention, comprising: (1) acquiring a first image to be processed; (2) processing the first image using a trained frequency aggregation self-attention network to obtain a second image, wherein the resolution of the second image is higher than that of the first image, and the expression of the frequency aggregation self-attention network is as follows:

[0041] X HR =H BSI (X LR )+(H D (H FUSAM (H FIM (H E (X LR ))+H E (X LR ))),

[0042] In the formula, X LR and X HR These are the first and second images, respectively, H BSI H D H FUSAM H FIM H E These represent the functions of the bilinear spatial interpolation upsampling unit, decoder unit, frequency utilization unit, frequency integration unit, and encoder unit, respectively. The encoder unit performs preprocessing; the frequency integration unit acquires frequency information and integrates it into the network; the frequency utilization unit uses frequency features to coordinate frequency and spatial information and improve the model's ability to acquire global information; and the decoder unit uses this information to enhance the image at any magnification.

[0043] The architecture diagram of frequency aggregation self-attention network is as follows: Figure 2 As shown, before training this frequency aggregation self-attention network, LR-HR image pairs need to be acquired as training samples. These samples are then used to train the constructed frequency aggregation self-attention network, resulting in a trained network. Afterward, simply input the first image to be processed into the trained network to obtain the processed second image. Understandably, the first image needs preprocessing to ensure its size matches that of the frequency aggregation self-attention network.

[0044] In one specific embodiment of the present invention, the encoder unit includes a pre-trained dense residual network model. A dense residual network (RDN) is a deep learning model that combines residual learning and dense connections, primarily used for image super-resolution (SR) and other low-level visual tasks. Its core idea is to enhance the network's feature extraction capabilities through multi-level feature reuse and gradient flow. In this embodiment, a pre-trained dense residual network model is used as the encoder unit, providing a high-quality spatial feature foundation for subsequent frequency processing.

[0045] Please see Figure 3 In a specific embodiment of the present invention, the frequency integration unit processes the input feature X through the following steps. E Processing: (1) Using Fast Fourier Transform (i.e., Figure 3 The FFT in the input features X E (2) Since complex numbers cannot be combined with convolutional layers for information extraction, the real and imaginary parts of the first complex number are convolved separately and then recombined (i.e. Figure 3 (3) In order to introduce frequency information into the network, this step combines the second complex number with the input feature X. E During fusion, the input feature X is used. E This is equivalent to a complex number with an imaginary part of 0, and then using the inverse fast Fourier transform (i.e., Figure 3 The frequency integration unit's output feature X is obtained by processing IFFT and point convolution. FIM The above processing can be expressed by the following formula:

[0046] X FIM =PWConv(IFFT(Conv) 3*3 (FFT(X E ))+X E )).

[0047] Please see Figure 2 In a specific embodiment of the present invention, the expression for the frequency utilization unit is as follows:

[0048] H FUSAM (X FIM ) = IISA(X FIM )+FCSA(X FIM ),

[0049] In the formula, X FIM and XFUSAM These are the input and output features of the frequency utilization unit, respectively. IISA is the coordinated implicit self-attention block, and FCSA is the frequency-dependent self-attention block. The coordinated implicit self-attention block utilizes the inherent relationship between frequency information and spatial information to conduct cross-domain information interaction in order to coordinate frequency information and spatial information. The frequency-dependent self-attention block utilizes the globality of frequency to improve the model's ability to acquire global information.

[0050] Please see Figure 4 In a specific embodiment of the present invention, the expression for coordinating implicit self-attention blocks is as follows:

[0051]

[0052] In the formula, X and X IISA These are the input and output characteristics of the coordinated implicit self-attention block, respectively, where X is the output of the frequency integration unit. FIM The Project operation projects spatial and frequency information into a subspace to perform cross-domain information interaction, generating feature maps Q and K for attention computation. Conv is a convolution operation used to generate feature map V for attention computation. It is obtained using the second image coordinate interpolation feature map Q. and The features obtained using the first image coordinate interpolation feature maps K and V are respectively, where γ(X) is the mapping function representing the positional relationship from the first image to the second image, FC represents the fully connected layer, and d x H represents the feature dimension, and H represents the number of attention heads.

[0053] In this embodiment, firstly, a frequency integration unit is used to further enrich the frequency information. Secondly, spatial and frequency information are projected into a subspace to perform cross-domain information interaction, generating feature maps Q and K for calculating attention. These correspond to... Figure 4 The project in question can be described in detail as follows: First, an independent linear transformation is applied to the output of the frequency ensemble unit to map the input features to a high-dimensional space, preparing for subsequent subspace decomposition. Then, H "heads" are segmented along the channel dimension, each head corresponding to a subspace. Within each subspace, two types of information are processed alternately through a cross-attention mechanism: attention is calculated after frequency transformation of the features in the frequency subspace, and spatial attention is calculated directly based on pixel coordinates in the spatial subspace. Finally, all subspaces are concatenated along the channel dimension, and the dimensions are adjusted through another linear layer to obtain Q and K. The calculation diagram is shown below. Figure 5 As shown.

[0054] Since orthogonal basis vectors in a plane can represent any vector in the plane through linear combination and can be extended to any dimension, and since a vector itself is a mapping from one point to another, the γ(X) orthogonal basis is used to fit this mapping, which facilitates subsequent image reconstruction at any multiple.

[0055] Because the distribution of the normalized exponential function (Softmax) will be related to the feature dimension d x Therefore, the elements in the normalized exponential function are divided by the feature dimension d. x This ensures gradient stability. Then, multiplying this correlation back by the value yields the correlation of each value, i.e., the global dependency of the input sequence. Furthermore, we divide the attention into H attention heads for computation to enable further information interaction.

[0056] Please see Figure 6 In a specific embodiment of the present invention, the expression for the frequency-dependent self-attention block is as follows:

[0057] Q1,K1,V1=Chunk(Conv 3*3 (X)),

[0058]

[0059] In the formula, X and X FCSA These represent the input and output features of the frequency-correlation self-attention block, respectively. `Conv` represents the convolution operation, `Chunk` represents the uniform segmentation operation, `FFT` represents the Fast Fourier Transform, and `IFFT` represents the Inverse Fast Fourier Transform. `d` x The feature dimension is represented by Norm, the linear projection layer is represented by Interpolation, and the interpolation operation is represented by the first image coordinates.

[0060] In this embodiment, for example, input features Perform convolution on it to obtain Then, segment the feature map from the channel to calculate attention. and To leverage the global nature of frequency to enhance the model's ability to acquire global information, we transfer the self-attention's Q1 and K1 to the frequency domain using Fast Fourier Transform (FFT) to calculate frequency correlation. Then, we normalize the obtained frequency correlation using Inverse FFT and a linear layer (Norm) and establish a skip connection with the input to obtain gradient-stable frequency self-attention. Finally, we interpolate the frequency self-attention using the coordinates used for LR interpolation in the coordinated implicit self-attention model to ensure that the coordinated implicit self-attention and the frequency-related self-attention calculate the self-attention for the same region.

[0061] In one specific embodiment of the present invention, the decoder unit is composed of multiple cascaded multilayer perceptrons. The number of multilayer perceptrons can be, for example, five. A multilayer perceptron (MLP) is a classic feedforward neural network composed of multiple fully connected layers stacked together, capable of learning complex nonlinear feature maps.

[0062] In one specific embodiment of the present invention, long skip connections are achieved by upsampling the first image based on bilinear spatial interpolation and adding the result of the decoder unit element by element, thereby maintaining the stability of the gradient and making the network easier to train.

[0063] In a specific embodiment of the present invention, the frequency aggregation self-attention network is trained using an L1 loss function to calculate and measure the enhancement result X. SR Compared with real data X HR The error between the layers is calculated, and the network parameters are optimized using backpropagation to complete the training of the layer-by-layer context information aggregation network. The formula for calculating the L1 loss function is as follows:

[0064]

[0065] In the formula, The real image corresponding to the input image. The input image is the enhanced result output by the frequency aggregation self-attention network. The superscript i indicates the correspondence between the enhanced result and the real image, and N is the total number of samples in each batch.

[0066] It should be noted that the steps of the various methods described above are only for clarity. In practice, they can be combined into one step or some steps can be split into multiple steps. As long as they contain the same logical relationship, they are all within the scope of protection of this application. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, but without changing the core design of the algorithm and process, are also within the scope of protection of this patent.

[0067] In a specific embodiment of the present invention, the DIV2K dataset is used as the training and validation set, and four commonly used benchmark datasets—Set5, Set14, BSD100, and Urban100—are used as the test set to comprehensively test the model performance. After training the frequency aggregation self-attention network, various metrics can be used to evaluate the performance of the trained frequency aggregation self-attention network, such as peak signal-to-noise ratio.

[0068] To verify the effectiveness of this invention, it was compared with several other image enhancement methods on the DIV2K image enhancement task at dimensions of ×2, ×3, ×4, ×6, ×12, ×18, ×24, and ×30. The encoders of all compared image enhancement models at any size were RDNs, and the decoders were five-layer MLPs. The comparison results are shown in Table 1. The best results are indicated in bold, and the second-best results are indicated by underlines.

[0069] Table 1: Comparison of image augmentation tasks of arbitrary size on the DIV2K dataset

[0070]

[0071] As can be seen from the quantitative comparison results in Table 1, the method proposed in this invention achieves the best image enhancement results of arbitrary size in all enhancement dimensions because it uses a more flexible approach to process information of different scales and locations in the image.

[0072] To further verify the performance of this invention, we also compared our proposed frequency-aggregating self-attention network with the aforementioned arbitrary-size image enhancement models at ×4 and ×8 scales, respectively. Performance metrics for all compared models are derived from their respective papers. The comparison results are shown in Table 2.

[0073] Table 2: Comparison of image augmentation tasks of arbitrary size on benchmark datasets

[0074]

[0075] As shown in Table 2, our model achieved the best results on all test sets, demonstrating its excellent performance in image augmentation tasks of arbitrary sizes of natural images.

[0076] In summary, this invention proposes an arbitrary-size image enhancement method based on a multi-scale location self-attention network. It not only solves the problem of large parameter count in existing arbitrary-size image enhancement networks but also enables higher-quality arbitrary-size image enhancement tasks.

[0077] Please see Figure 7 , Figure 7 An electronic device provided in one embodiment of the present invention includes a processor 101, a memory 102, and a communication bus; the communication bus is used to connect the processor 101 and the memory 102; the processor 101 is used to execute a computer program stored in the memory 102 to implement the above-described image enhancement method.

[0078] An embodiment of the present invention also provides a computer-readable storage medium having a computer program stored thereon, the computer program being used to cause a computer to perform the above-described image enhancement method.

[0079] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. An arbitrary size image enhancement method based on frequency aggregation self-attention, characterized in that, The method comprises: acquiring a first image to be processed; processing the first image by using a trained frequency aggregation self-attention network to obtain a second image, the resolution of the second image being higher than that of the first image, and the expression of the frequency aggregation self-attention network being as follows: X HR =H BSI (X LR )+(H D (H FUSAM (H FIM (H E (X LR ))+H E (X LR ))))), wherein X LR and X HR are the first and second images, respectively, H BSI , H D , H FUSAM , H FIM , H E represent functions of a bilinear spatial interpolation up-sampling unit, a decoder unit, a frequency utilization unit, a frequency integration unit, an encoder unit, respectively. The frequency integration unit processes the input feature X E by the following steps: using a fast Fourier transform to convert the input feature X E to a first complex number; convolving the real part and the imaginary part of the first complex number respectively, and then recombining them into a second complex number; The second plurality and the input feature X E The fusion is performed, and the inverse fast Fourier transform and point convolution are used for processing to obtain the output feature X of the frequency integration unit FIM ; the expression of the frequency utilization unit being as follows: H FUSAM (X FIM )=IISA(X FIM )+FCSA(X FIM ), In the formula, X FIM and X FUSAM are input features and output features of the frequency utilization unit respectively, IISA is a coordinated implicit self-attention block, FCSA is a frequency correlation self-attention block, the coordinated implicit self-attention block utilizes the internal relationship between frequency information and spatial information to interact information across domains to coordinate frequency information and spatial information, and the frequency correlation self-attention block utilizes a frequency globality promotion model to obtain global information capability. the expression of the coordination implicit self-attention block being as follows: ， ， ， wherein X and X IISA are input and output features of the coordinated implicit self-attention block respectively, the Project operation is used to project the spatial information and the frequency information into a subspace to generate the feature map Q and K after the information cross-domain interaction, and the Conv is a convolution operation used to generate the feature map V, is obtained by interpolating the feature map Q using the second image coordinates, and are obtained by interpolating the feature map K and V using the first image coordinates respectively, γ(X) is a mapping function representing the positional relationship from the first image to the second image, FC represents a full connection layer, d x is a feature dimension, and H is a number of attention heads.

2. The arbitrary size image enhancement method based on frequency aggregation self-attention according to claim 1, characterized in that, The encoder unit comprises a pre-trained dense residual network model.

3. The arbitrary size image enhancement method based on frequency aggregation self-attention of claim 1, wherein, the expression of the frequency correlation self-attention block being as follows: ， ， wherein X and X FCSA are input and output features of the frequency-dependent self-attention block, respectively, Conv is a convolution operation, Chunk denotes a uniform splitting operation, FFT denotes a fast Fourier transform, IFFT denotes an inverse fast Fourier transform, d x denotes a feature dimension, Norm denotes a linear projection layer, and Interpolation denotes an interpolation operation using the first image coordinates.

4. The arbitrary size image enhancement method based on frequency aggregation self-attention of claim 1, wherein, The decoder unit is composed of a plurality of cascaded multi-layer perception mechanisms.

5. The arbitrary size image enhancement method based on frequency aggregation self-attention of claim 1, wherein, The loss of the frequency aggregation self-attention network during training is calculated by using the following formula: ， In the formula, is a real image corresponding to the input image, is an enhanced result output by the frequency aggregation self-attention network after the input image, the superscript i is used to indicate the correspondence between the enhanced result and the real image, and N is the total number of samples in each batch.

6. An electronic device, comprising: The device comprises a processor, a memory and a communication bus; the communication bus is used to connect the processor and the memory; the processor is used to execute a computer program stored in the memory to realize the method in any one of claims 1-5.

7. A computer readable storage medium characterized in that, A computer program is stored on the device, and the computer program is used to make the computer execute the method in any one of claims 1-5.

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