Analysis method, system and equipment for port image based on random matrix and medium

Abstract

The invention provides a port image analysis method, system and device based on a random matrix, and a medium, and relates to the technical field of port inspection image processing, and the method comprises the steps: obtaining a port inspection image; creating two random matrixes; performing interpolation operation on the two random matrixes by using a bilinear interpolation function; constructing a chaotic system, and adding disturbance parameters to enhance nonlinearity in combination with an interpolation function and a random matrix to obtain a Jacobian matrix; calculating a maximum index value; if the maximum index value is greater than 0, determining that the system is in a chaotic state; drawing a curve of indexes changing along with time, and analyzing sensitive parameters of the system; row and column replacement and bitwise XOR processing are carried out on pixels by using the stable segment of the chaos sequence; performing decryption processing; and outputting the comparison diagram. According to the method, the dynamic key is generated in combination with the random matrix and the sensitive parameters by adopting an encryption mode based on the chaotic sequence, and the image pixels are subjected to multi-stage encryption processing by utilizing the transient state of the chaotic system, so that the security of an encryption algorithm is improved.

Description

Technical Field

[0001] This application relates to the field of port inspection image processing technology, and in particular to a method, system, device and medium for analyzing port images based on a random matrix. Background Technology

[0002] Port inspection images serve as crucial information carriers, containing a wealth of port status data. In-depth analysis of these images allows for the timely detection of issues such as facility malfunctions, abnormal vessel behavior, and potential cargo storage hazards, enabling proactive measures to prevent operational disruptions and safety incidents.

[0003] Current port image analysis methods largely rely on simple image feature extraction and pattern recognition techniques. Feature extraction primarily depends on basic features such as color, texture, and shape. However, port environments are extremely complex, with numerous interfering factors, such as weather changes (rain, fog, strong light, etc.), dynamic changes in ships and equipment, and the stacking of different types of cargo. These factors make target features in port inspection images blurred and variable, making it difficult for traditional basic feature extraction methods to effectively capture the potential features of port facilities in complex environments. Furthermore, current port image encryption technologies suffer from problems such as single keys and simple encryption algorithms. Single keys are easily cracked, and encryption algorithms are not effectively resistant to modern attack methods, leading to the risk of information leakage during the transmission and storage of port inspection images. Finally, the results of port image analysis are often presented in the form of data tables or simple charts, making it difficult for port managers to quickly and intuitively understand the overall status and potential problems of port facilities. Summary of the Invention

[0004] This application provides a method for analyzing port images based on random matrices. It constructs a chaotic system and determines the system state by calculating the maximum Lyapunov exponent, analyzing sensitive parameters. An encryption method based on chaotic sequences is employed, combining the random matrix and sensitive parameters to generate a dynamic key. Multi-stage encryption processing of image pixels is performed using the transient and stable segments of the chaotic system, improving the security of the encryption algorithm. The method outputs Lyapunov heatmaps, encryption / decryption comparison images, and security indicators, providing port managers with intuitive and quantitative analysis results.

[0005] The methods include: Step 101: Acquire port inspection images, convert the port inspection images to RGB format, and then perform normalization processing; Step 102: Create two random matrices that match the size of the port inspection images; Step 103: Use the bilinear interpolation function to interpolate the two random matrices and estimate the value of the point based on the interpolation coefficients at the four nearest neighbors; Step 104: Construct a chaotic system, combine the interpolation function and the random matrix, add perturbation parameters to enhance nonlinearity, and obtain the Jacobian matrix; Step 105: Calculate the maximum Lyapunov exponent value using the eigenvalues ​​of the Jacobian matrix; Step 106: If the maximum Lyapunov exponent value is greater than 0, the system is confirmed to be in a chaotic state; plot the curve of Lyapunov exponent change over time and analyze the sensitive parameters of the system. Step 107: Encrypt the port inspection images and generate a dynamic key based on the random matrix and sensitive parameters; Step 108: Utilize the transient characteristics of chaotic systems to encrypt image pixels using a dynamic key; utilize the stable segments of the chaotic sequence to perform row and column permutations and bitwise XOR operations on the pixels; Step 109: During decryption, the encryption conditions are reused to generate a dynamic key, and the diffusion and scrambling are performed in reverse. Step 110: Output Lyapunov heatmap, encryption / decryption comparison chart, and security indicators.

[0006] It should be further noted that step 101 also includes: separating the illumination component and reflection component in the port inspection image based on adaptive histogram equalization; The CNN model is used to detect key targets in port inspection images and to mark the detected areas. Step 102 also includes: embedding the latitude and longitude grid information of the port map into a random matrix.

[0007] It should be further noted that step 104, in which the chaotic system is constructed, also includes: Configure two 256×256 random integer matrices F and G, with values ​​ranging from 1 to 256; The bilinear interpolation function is used to interpolate the integer matrices F and G, and the values ​​of the new points are estimated based on the function values ​​at the four nearest neighbor points. Construct the interpolation calculation formula: (1) f (F( x , y ))and f (G( x , y )) respectively perform bilinear interpolation on matrices F and G, where x , y The position for interpolation. f ( x , y ) is the interpolation function; When performing bilinear interpolation, two initial iteration values ​​are determined. x and y According to formula (1), the matrices F and G at point ( x , y The interpolation results z1 and z2; The calculated interpolation results z1 and z2 are used to update the iteration value. x and y ; Each iteration is based on a new x and y The interpolation results are recalculated to generate two dynamically changing sequences, ultimately resulting in two sequences.

[0008] It should be further noted that step 103 also includes: defining block bilinear interpolation based on the scale differences of different targets in the port inspection image; Among them, the large-scale blocks of the block bilinear interpolation use low-frequency random perturbation to simulate the blurring effect of ocean waves on the overall image; Small-scale blocks of block bilinear interpolation preserve high-frequency detail parameters.

[0009] It should be further noted that step 105 also includes: Let the state vector of the chaotic system be... Based on random matrices and bilinear interpolation, the recurrence relation is defined as follows:

[0010] Where, x i (t) is the main chaotic component, used to drive the diffusion process of image pixel values; y i (t) represents the auxiliary chaotic component, used to introduce multiphysics coupling perturbations; i is the index variable, representing the row coordinate in the two-dimensional grid; t is the time step, representing the number of iterations of the chaotic system; x i,j (n+1) Let y be the value of the principal chaotic component at grid point (i,j) at time step n+1; i,j (n+1) The value of the auxiliary chaotic component at grid point (i,j) at time step n+1; The local sensitivity index represents the topology of port facilities, characterizing the sensitivity of the grid point to initial conditions; Let n be the value of the principal chaotic component at grid point (i,j) at time step n; Let n be the value of the auxiliary chaotic component at grid point (i,j) at time step n; These are random matrix elements; Taking the partial derivatives with respect to F and G respectively, we obtain the Jacobian matrix J, which is used for subsequent Lyapunov exponent calculation: .

[0011] It should be further noted that the encryption process in step 107 also includes: defining the key K = Ks⊕Kt⊕Kg; Where: Ks is the initial random matrix; Kt is the inspection timestamp; Kg is the location coordinates.

[0012] It should be further noted that in step 107, for chaotic systems, a set of initial data should be randomly generated during the interpolation iteration. x , y Calculate the result after the first interpolation. Xi , Yi ; Formula (2) is used to determine the error range of the result after the first interpolation, and this is used to determine whether the result after each iteration reaches the periodicity. During the iteration process, the number of times a cyclical pattern appears after each iteration is counted and analyzed. The maximum, minimum, and average squared difference and range of each data set are recorded, and the statistical data are compiled into a table. (2).

[0013] This application also provides a system for analyzing port images based on random matrices, the system comprising: The image acquisition module is used to acquire port inspection images, convert the port inspection images to RGB format, and then perform normalization processing. The matrix creation module is used to create two random matrices that match the size of the port inspection image. The interpolation module is used to perform interpolation operations on two random matrices using a bilinear interpolation function, estimating the value of a point based on the interpolation coefficients at the four nearest neighbor points. The chaos building module is used to construct chaotic systems. It combines interpolation functions and random matrices, adds perturbation parameters to enhance nonlinearity, and obtains the Jacobian matrix. The feature calculation module is used to calculate the maximum Lyapunov exponent value using the eigenvalues ​​of the Jacobian matrix; The parameter analysis module is used to confirm that the system is in a chaotic state if the maximum Lyapunov exponent value is greater than 0; to plot the curve of the Lyapunov exponent changing over time and to analyze the sensitive parameters of the system. The encryption processing module is used to perform encryption processing on port inspection images and generate dynamic keys based on random matrices and sensitive parameters; The image processing module is used to encrypt image pixels using a dynamic key by utilizing the transient characteristics of chaotic systems; and to perform row and column permutations and bitwise XOR operations on pixels using the stable segments of the chaotic sequence. The decryption processing module is used to generate a dynamic key by reusing the encryption conditions during decryption, and to reverse-execute diffusion and scrambling. The output module is used to output Lyapunov heatmaps, encryption / decryption comparison charts, and security indicators.

[0014] According to another embodiment of this application, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method for analyzing port images based on a random matrix.

[0015] According to another embodiment of this application, a storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the method for analyzing port images based on a random matrix.

[0016] As can be seen from the above technical solutions, this application has the following advantages: The port image analysis method based on random matrices provided in this application can uncover potential complex features in port inspection images by constructing a chaotic system and combining random matrices with bilinear interpolation. The chaotic system constructed in step 104 incorporates the interpolated random matrix into its recursive relationship, simulating the nonlinear characteristics of port facilities, ships, and other targets under different states, making the analysis more realistic. The state of the chaotic system is determined using the maximum Lyapunov exponent value, and curves of Lyapunov exponent changes over time are plotted, along with the analysis of sensitive parameters. This allows for efficient assessment of the stability of port facilities and their sensitivity to minor disturbances. For example, a large maximum Lyapunov exponent for a certain area can promptly identify potential instability factors in that area, providing strong evidence for facility maintenance and safety monitoring. Encryption processing is applied to port inspection images. A dynamic key is generated based on a random matrix and sensitive parameters. Pixel encryption, permutation, and XOR processing are performed using the transient characteristics and stable segments of chaotic systems, improving image security during transmission and storage. The output includes Lyapunov heatmaps, encryption / decryption comparison charts, and security indicators, providing port managers with intuitive and quantitative analysis results. The Lyapunov heatmaps visually demonstrate the stability of different areas of the port, the encryption / decryption comparison charts verify the effectiveness of the encryption algorithm, and the security indicators quantify the security of the encryption system.

[0017] Furthermore, this application solves the image feature distortion problem caused by uneven lighting and changing viewing angles in port inspections by dynamically matching the random matrix with the spatial resolution of the port image through bilinear interpolation. While preserving image details, it enhances the spatial correlation of random perturbations. Eigenvalue analysis of the Jacobian matrix ensures the sensitive dependence of the chaotic system, solving the predictability problem caused by fixed parameters in traditional encryption methods. Combining row / column permutations and bitwise XOR operations, it realizes the periodic arrangement of targets such as ships and containers in port images. By reusing initial conditions to generate keys, it allows the decryption end to quickly verify key consistency while ensuring encryption efficiency. It is suitable for real-time communication scenarios in multi-terminal collaborative port inspections. Attached Figure Description

[0018] To more clearly illustrate the technical solution of this application, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of a method for analyzing port images based on random matrices. Figure 2 This is a schematic diagram of a bilinear interpolation coordinate system; Figure 3 Peak plots for different interpolation methods; Figure 4 A diagram illustrating interpolation within a matrix; Figure 5 This is a schematic diagram of the iteration process; Figure 6 Plot of the Lyapunov index; Figure 7 For the system phase diagram; Figure 8 A graph showing the difference between iterative sequences; Figure 9 Images showing the encryption and decryption effects; Figure 10 This is a schematic diagram of an electronic device. Detailed Implementation

[0020] In the following sections, various embodiments of the method for analyzing port images based on random matrices will be described more fully. This disclosure may have various embodiments, and adjustments and changes may be made therein. However, it should be understood that there is no intention to limit the various embodiments of this disclosure to the specific embodiments disclosed herein, but rather this disclosure should be understood to cover all adjustments, equivalents, and / or alternatives falling within the spirit and scope of the various embodiments of this disclosure.

[0021] In the method for analyzing port images based on random matrices, the terms "comprising" or "may include," which may be used in various embodiments of this disclosure, indicate the presence of the disclosed functions, operations, or elements, and do not limit the addition of one or more functions, operations, or elements. Furthermore, as used in various embodiments of this disclosure, the terms "comprising," "having," and their cognates are intended only to indicate a specific feature, number, step, operation, element, component, or combination of the foregoing, and should not be construed as primarily excluding the presence of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing, or adding one or more combinations of the foregoing.

[0022] It should be noted that if a description is made of "connecting" one component to another, then the first component can be directly connected to the second component, and a third component can be "connected" between the first and second components. Conversely, when a component is "directly connected" to another component, it can be understood that there is no third component between the first and second components.

[0023] In various embodiments of the method for analyzing port images based on random matrices, the term "user" can refer to a person using an electronic device.

[0024] The terminology used in the various embodiments of this disclosure is for the purpose of describing particular embodiments only and is not intended to limit the various embodiments of this disclosure. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which the various embodiments of this disclosure pertain. Terms (such as those defined in a generally used dictionary) are to be interpreted as having the same meaning as in the context of the relevant technical field and are not to be interpreted as having an idealized or overly formal meaning, unless clearly defined in the various embodiments of this disclosure.

[0025] To make the purpose, features, and advantages of this application more apparent and understandable, specific embodiments and accompanying drawings will be used to clearly and completely describe the technical solution protected by this application. Obviously, the embodiments described below are only some embodiments of this application, and not all embodiments. Based on the embodiments in this patent, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this patent.

[0026] like Figure 1 This is a flowchart of the port image analysis method based on a random matrix provided in this embodiment. The method includes: Step 101: Acquire port inspection images, convert the port inspection images to RGB format, and then perform normalization processing.

[0027] In this embodiment, inspection images are acquired using image acquisition devices such as cameras deployed at the port. Since the color modes of images acquired by different devices may differ, they are converted to RGB format for easier and more uniform processing. The values ​​of each pixel in the port inspection image are defined as R, G, and B in the three RGB channels, respectively. Normalization is performed by mapping the value of each channel to the range [0,1], such as 0-255.

[0028] The port inspection images in this embodiment contain information on various facilities, ships, and personnel. After being converted to RGB format, this information can be displayed in a standard color mode, facilitating the extraction and analysis of image features. Normalization processing makes different images numerically comparable, eliminating the influence of different pixel value ranges caused by differences in equipment. As an example of this application, the illumination component and reflection component in a port inspection image are separated based on adaptive histogram equalization.

[0029] The CNN model is used to detect key targets in port inspection images and to mark the detected areas.

[0030] Key targets in the port can be identified, such as ships, gantry cranes, personnel, and related equipment, allowing for refined processing of the detection area and reducing computational load.

[0031] Step 102: Create two random matrices that match the size of the port inspection images.

[0032] In this embodiment, the port inspection image size is defined as m×n, and two random matrices F and G of the same size m×n are created. The elements in the matrices are generated using a random number generation function, and the random numbers can come from common distributions such as uniform distribution.

[0033] This embodiment also embeds the latitude and longitude grid information of the port map into a random matrix.

[0034] Optionally, matrix element R i,j It can be generated by combining port water depth data, with high-entropy elements corresponding to deep water areas and low-entropy elements to shallow water areas, thereby enhancing the sensitivity of the chaotic system to the port topology.

[0035] If the acquired video stream is a port inspection video stream, then configure a time series weighting factor w(t) and apply progressive perturbations to the random matrix of adjacent frames. Example illustration. It simulates dynamic environmental noise such as tides and waves.

[0036] This embodiment maps two random matrices to the pixels of a port inspection image. By combining these matrices with image pixels or other operations, randomness and uncertainty are introduced for operations such as constructing chaotic systems, in order to uncover potential complex features in the image. This introduces random factors into the entire analysis process, increasing the flexibility of the analysis method and its adaptability to complex port scenarios. The characteristics of random matrices are used to simulate uncertainties and interference factors that may exist in the port environment.

[0037] Step 103: Use a bilinear interpolation function to interpolate the two random matrices, estimating the value of the point based on the interpolation coefficients at the four nearest neighbors.

[0038] This embodiment combines the scale differences of different targets in port inspection images to define block bilinear interpolation.

[0039] In this process, the large-scale blocks of the block bilinear interpolation employ low-frequency random perturbations to simulate the blurring effect of ocean waves on the overall image; while the small-scale blocks of the block bilinear interpolation retain high-frequency detail parameters.

[0040] In this embodiment, each random matrix is ​​further divided into a 4×4 grid, with each grid vertex value being a matrix element.

[0041] For any position coordinate (x) n ,y n Based on the four nearest neighbor vertices Perform interpolation.

[0042] It's important to note that bilinear interpolation is used for image interpolation. This method calculates new pixel values ​​based on the relationships between adjacent pixels. The basic principle of bilinear interpolation is to use the values ​​of four adjacent pixels to calculate a new pixel value.

[0043] Specifically, for a pixel that needs interpolation, bilinear interpolation considers the values ​​of four neighboring pixels and then calculates the new pixel value through interpolation. Because bilinear interpolation considers the pixel values ​​around the current pixel, it can better preserve image details and edges.

[0044] Bilinear interpolation essentially combines linear interpolation in two directions. Although its foundation is linear operation, it can produce nonlinear effects. The following section further explains the calculation method of bilinear interpolation.

[0045] Bilinear interpolation is performed by conducting one linear interpolation operation in each of the two dimensions, involving a total of three linear interpolation operations. For example... Figure 2 As shown, assume there are four known points A. 11 ( x 1, y 1) A 12 (x 1, y 2) A 21 ( x 2, y 1) and A 22 ( x 2, y 2) To estimate the value of a point P( ) within the grid formed by these four points. x , y The value of ).

[0046] In this embodiment, two single-linear interpolations are first performed along the y-axis to obtain two intermediate points R3 and R4, which are located at... x = x 1 and x = x On the cross section of 2. Subsequently, a single linear interpolation is performed in the x-axis direction to obtain the target point P( x , y Similarly, one can choose to first perform two linear interpolations along the x-axis to obtain two intermediate points R1 and R2, and then perform one linear interpolation along the y-axis to obtain the same target point P. x , y Both of these paths ultimately lead to the following formula for bilinear interpolation.

[0047]

[0048] If we place these two points in a matrix, then the element value in the matrix is ​​A. 11 A 12 A 21 With A 22 The value we are looking for is the value of a point in the matrix based on the values ​​of the four elements in the matrix.

[0049] This embodiment compares different interpolation methods on a peak-shaped surface (generated by the peaks function) to demonstrate the characteristics and advantages of each method. Different interpolation methods are suitable for different scenarios; there is no absolute "best," but rather the most suitable method should be selected based on specific needs. Figure 3 In the diagram, (a) is a 3D plot of the Peaks function, (b) is a peak plot of the nearest neighbor interpolation, (c) is a peak plot of the cubic convolution interpolation, and (d) is a peak plot of the bilinear interpolation. The diagrams show the results of nearest neighbor interpolation, bilinear interpolation, and cubic convolution interpolation.

[0050] When interpolating peak-shaped surface data, different methods exhibit their own characteristics and advantages. Nearest neighbor interpolation, due to its simple and direct algorithm implementation, can quickly complete the interpolation task, but the resulting graph often exhibits a noticeable stepped shape and lacks smoothness. Bilinear interpolation improves upon this, not only being computationally efficient but also providing smoother interpolation results by considering the linear relationship between the four neighboring points of the target point.

[0051] It can be seen that bilinear interpolation effectively solves the problem of numerical discontinuity caused by nearest neighbor interpolation while ensuring computational efficiency, and provides satisfactory interpolation results when processing random matrices.

[0052] When performing bilinear interpolation on a specific point in a matrix, the four points to consider are typically that point's direct neighbors (up, down, left, and right). The purpose of bilinear interpolation is to estimate the function values ​​of points within the grid that are not given the function values ​​at the grid points. For example... Figure 4 As shown, the interpolation between points A and B can only be obtained by using the values ​​of the four nearest neighboring elements.

[0053] As can be seen, the pixel distribution in the port inspection images of this embodiment is not always regular. The bilinear interpolation operation is performed on a random matrix, which can simulate the irregular information distribution that may exist in the image. By interpolating the random matrix, a more continuous and variable data foundation is provided for the construction of chaotic systems, which corresponds to the complex scene characteristics of ports. Furthermore, the data characteristics of the random matrix are enhanced, making it more consistent with the irregular and continuous changes that may exist in port inspection images, thus providing more suitable data input for the construction of chaotic systems.

[0054] Step 104: Construct a chaotic system, combine the interpolation function and the random matrix, add perturbation parameters to enhance nonlinearity, and obtain the Jacobian matrix.

[0055] In this embodiment, the chaotic system is constructed in MATLAB by first generating two 256×256 random integer matrices F and G, with values ​​ranging from 1 to 256. Then, a bilinear interpolation function is used to interpolate these two matrices, estimating the value of the new point based on the function values ​​at the four nearest neighbors. The constructed system is shown in equation (1): (1) f (F( x , y ))and f (G( x , y )) respectively perform bilinear interpolation on matrices F and G, where x , y The position for interpolation.f ( x , y ) is the interpolation function.

[0056] When performing bilinear interpolation, it is first necessary to determine two initial iteration values. x and y It lies within the domain of matrices F and G. It should be noted that... x , y At least one of the values ​​must be a decimal; otherwise, it will fall into a periodic iteration loop. According to formula (1), the values ​​of matrices F and G at point ( x , y The interpolation results z1 and z2 are obtained.

[0057] The calculated interpolation results z1 and z2 will be used to update the iteration values. x and y This is done so that the next iteration can proceed. This process is repeated, with each iteration based on a new... x and y The interpolation results are recalculated, generating two dynamically changing sequences. These sequences reflect the trajectories of the interpolation points on matrices F and G as the number of iterations increases. The iterative process is as follows: Figure 5 As shown. Ultimately, we will obtain two sequences, z1 and z2.

[0058] This embodiment incorporates the interpolated random matrix into the construction of a chaotic system, enabling the chaotic system to reflect the complex features in port inspection images. The perturbation parameter simulates uncertainties in the port environment, such as weather changes and minor fluctuations in equipment operating status. The Jacobian matrix is ​​used to describe the local linear approximation of the chaotic system at a certain point, allowing analysis of the dynamic characteristics of the chaotic system, corresponding to the dynamic changes of different regions and elements in the port inspection images. A chaotic system closely correlated with the features of port inspection images is constructed. Perturbation parameters are used to enhance the system's nonlinearity, thus more realistically simulating the complexity of the port environment. The Jacobian matrix provides a foundation for subsequent analysis of the stability, sensitivity, and other properties of the chaotic system, contributing to a deeper understanding of the intrinsic relationship between chaotic systems and port images.

[0059] Step 105: Calculate the maximum Lyapunov exponent value using the eigenvalues ​​of the Jacobian matrix.

[0060] In this embodiment, the state vector of the chaotic system is assumed to be... Based on random matrices and bilinear interpolation, the recurrence relation is defined as follows: .

[0061] Where, x i(t) is the main chaotic component, used to drive the diffusion process of image pixel values; y i (t) is an auxiliary chaotic component used to introduce multi-physics coupling perturbations; i is an index variable representing the row coordinates in the two-dimensional grid; t is the time step, representing the number of iterations of the chaotic system.

[0062] x i,j (n+1) Let y be the value of the principal chaotic component at grid point (i,j) at time step n+1; i,j (n+1) The value of the auxiliary chaotic component at grid point (i,j) at time step n+1; This represents the local sensitivity index of the port facility topology, characterizing the sensitivity of the grid point to initial conditions. The value of the principal chaotic component at grid point (i,j) at time step n is affected by the tidal parameter. Modulation, where A is the tidal amplitude and ω is the tidal period.

[0063] Let n be the value of the auxiliary chaotic component at grid point (i,j) at time step n; Let F be the random matrix element; take the partial derivatives with respect to F and G respectively to obtain the Jacobian matrix J, which is used for subsequent Lyapunov exponent calculation: Chaotic trajectories are generated through nonlinear iteration to provide pseudo-random sequences for encryption. Perturbation parameters break the periodicity, ensuring the system does not fall into loops within a 512×512 range, thus meeting the requirements of large-scale port imaging.

[0064] It should be noted that the Lyapunov exponent involved in this embodiment is an index describing the stability and chaotic properties of a dynamical system, used to measure the impact of small perturbations on the system's behavior. The Jacobian matrix is ​​the coefficient matrix of the first-order Taylor expansion of a dynamical system at a given point, describing the system's locally linearized behavior in the vicinity of that point. For nonlinear dynamical systems, although the overall behavior may be very complex, the system's behavior can be approximated as linear in a small neighborhood, and the Jacobian matrix describes this linearized behavior. For dynamical systems composed of interpolation matrices, the stability of the system over time can be analyzed by iterating and calculating the Jacobian matrix after each iteration.

[0065] By calculating the Jacobian matrix and subsequently obtaining the Lyapunov exponents, we can not only analyze the stability of a system but also identify whether it exhibits chaotic behavior. This embodiment defines a clear iterative rule that describes how each step in the sequence evolves from the previous step. During the iteration process, the Jacobian matrix describes the linearization behavior of the system state, which can then be used to calculate the Lyapunov exponents. The iterative rule is as follows: Figure 5 As shown, Figure 6The Lyapunov exponent plot was used to analyze the evolution of the sequence through 1000 iterations. The Lyapunov exponent was always greater than 0, indicating good chaotic properties. This embodiment also involves a phase diagram of the system, which reveals the trajectory of the system's state variables over time. In a two-dimensional dynamic system, a phase diagram typically refers to the trajectory diagram on a plane formed by two state variables. In this example, an iterative system is defined, with the initial value set to... x 0 = 25.2 and y 0 = 125.5 yields the phase Figure 7 , Figure 7 (a) is a phase diagram. x 0, y 0). The initial value is set to x 1 = 15.2 and y 1 = 15.5 to obtain the phase Figure 7 (b).

[0066] In these two phase diagrams, it can be observed that as the number of iterations increases, the trajectory of the system state variables exhibits a complex and seemingly random distribution. This randomness may be due to the nonlinear characteristics or chaotic behavior of the system itself, which is a typical feature of chaotic systems. However, the points of the system become more densely packed closer to the center, which is related to the fact that during random matrix interpolation, the matrix passes through the center more often, thus making the elements in the middle of the matrix more sensitive.

[0067] To verify the sensitivity to initial conditions, experiments were conducted by changing the initial conditions of the system and observing the differences in the evolution of the system state over time.

[0068] Specifically, first, set the initial conditions. x =2.1 and y =10.5, then perform 200 iterations according to formula (1), and the result after each iteration is... z The value 1 is stored in array A. Then, it is slightly changed... x The value (e.g.) x =2.10000001), repeat the above iterative process, and take the result of each iteration. z The values ​​are stored in array B. By calculating the difference between corresponding elements in arrays A and B, a new sequence C can be obtained, which reflects the results due to the initial conditions. x The difference in system state caused by minute changes in initial values. The same method can also be applied to changes in initial values. y That is, set the initial condition y = 10.50000001, repeat the iteration process, and record the result after each iteration. zThe values ​​are stored in array D. The differences between corresponding elements in arrays A and D are recalculated to obtain a new sequence E, which reflects the changes caused by the initial conditions. y The change in the system state caused by a tiny change.

[0069] Plot the sequences C and E as a line graph, such as Figure 8 As shown. Figure 8 (a) is a difference plot for series C, and (b) is a difference plot for series E.

[0070] It's easy to see how the difference between the two sequences grows with increasing iterations. If the difference between the sequences grows rapidly over time, it indicates that the system is highly sensitive to initial conditions. Such line graphs typically exhibit an exponential growth trend, which is a key characteristic of chaotic systems.

[0071] For the new chaotic system, it is guaranteed that no periodicity will occur in an infinite number of iterations. When conducting the interpolation iteration experiment, a set of initial data is first randomly generated. x , y Then calculate the result after the first interpolation. Xi , Yi Next, a specific formula will be used to... Xi , Yi Perform 512×512 iterations. Due to the limitations of floating-point precision in computer calculations, a perfectly accurate period cannot be obtained. Therefore, a period within the error range is defined as a "period-like period".

[0072] Formula (3) is used to determine this error range, and this range is used to judge whether the result after each iteration reaches the periodicity level. During 512×512 iterations, the number of times the periodicity condition is met is recorded. To improve the accuracy of the experiment, this process is repeated 150 times, each time using different initial data. x , y .

[0073] Finally, the number of times periodic patterns appeared in these 150 data sets after 512×512 iterations was statistically analyzed. The maximum, minimum, squared difference of the mean, and range of each data set were recorded, and these statistics were compiled into a table, as shown in Table 1. In this way, we can understand the frequency of periodic patterns in the iterative sequence within different error ranges, as well as the distribution of these frequencies.

[0074] (3) Table 1 shows the "periodic-like" occurrences of experimental data after iteration within different iteration error ranges.

[0075] Table 1: Periodic Statistics

[0076] The table shows that when the difference between the two numbers in the iteration results is within a certain range, some experimental data exhibit a "periodic" phenomenon. However, as this difference decreases, the number of experimental data exhibiting "periodic" behavior gradually decreases, and the frequency of these "periodic" occurrences also decreases. In particular, when the difference between the two numbers in the iteration results is less than or equal to 0.01, no overlap was observed in the 150 sets of experimental data after 512×512 iterations, indicating that at this error level, the iteration cycle for all initial values ​​exceeds 512×512.

[0077] As can be seen, the maximum Lyapunov exponent in this embodiment reflects the exponential growth of small changes in initial conditions over time in a chaotic system. In port inspection image analysis, it can measure the sensitivity of port facilities, ships, and other targets to small disturbances. For example, if the maximum Lyapunov exponent for a certain area is large, it indicates that the state changes in that area may be very sensitive to small factors, and there may be unstable factors. By determining whether a chaotic system has chaotic characteristics (when λmax > 0, it is in a chaotic state) through the maximum Lyapunov exponent value, the stability and sensitivity of different areas and targets in port inspection images can be analyzed, providing important basis for port facility maintenance and safety monitoring.

[0078] Step 106: If the maximum Lyapunov exponent value is greater than 0, the system is confirmed to be in a chaotic state; plot the curve of Lyapunov exponent change over time and analyze the sensitive parameters of the system.

[0079] This embodiment plots the Lyapunov exponent over time to observe convergence. The Euclidean distance between the trajectory differences is calculated by perturbing the central element of the perturbation matrix. If DD grows rapidly, it indicates that the intermediate element is a sensitive parameter.

[0080] It should be noted that when the Lyapunov exponent value is greater than 0, the chaotic system is considered to be in a chaotic state. To analyze the system's sensitive parameters, other parameters can be fixed, and the parameters in the chaotic system (such as coefficients in the recursive relation, perturbation parameters, etc.) can be changed one by one. The maximum Lyapunov exponent value after each change can be calculated, and its changes can be observed. Plot a curve of the Lyapunov exponent changing with time (number of iterations), with the horizontal axis representing the number of iterations and the vertical axis representing the Lyapunov exponent value.

[0081] In port inspection scenarios, chaos implies complex interactions and uncertainties among various factors in the port environment. The Lyapunov exponent over time can illustrate the changing trends of the state of port facilities and other targets at different times. By analyzing sensitive parameters, it's possible to identify which factors significantly impact the state of port facilities. For example, if a change in a disturbance parameter causes a significant shift in the maximum Lyapunov exponent, then the factor corresponding to that parameter (such as an environmental factor) has a significant impact on the state of the port facilities. Furthermore, analyzing sensitive parameters helps port managers identify key factors affecting the state of port facilities, enabling targeted monitoring and maintenance, and improving the safety and efficiency of port operations.

[0082] Step 107: Encrypt the port inspection images and generate a dynamic key based on the random matrix and sensitive parameters.

[0083] The encryption algorithm in this embodiment can adopt a chaotic sequence-based encryption method. The encryption process also includes defining a key K = Ks⊕Kt⊕Kg; where: Ks is the initial random matrix; Kt is the inspection timestamp; and Kg is the location coordinates.

[0084] The port inspection images in this embodiment contain important information such as the status and layout of port facilities, which requires encryption protection. Generating a dynamic key using a random matrix and sensitive parameters allows the key to be associated with specific characteristics of the port environment. For example, the random matrix reflects certain uncertainties in the port scene, while the sensitive parameters highlight factors that significantly impact the status of port facilities, thus generating a more targeted and secure key.

[0085] In one embodiment of this application, sequence-based encryption is directly applied to image encryption. The code is compiled using MATLAB 2016A on an electronic device equipped with a 2.50GHz Intel(R)_Core(TM)_i5-7300 CPU and 16GB of memory.

[0086] During the image encryption process, taking the images Lena, Cameraman, and Airplane as examples, such as... Figure 9 (a) Figure 9 (d) Figure 9 As shown in (g). The Lena image has a pixel size of 512×512, while the Cameraman and Airplane images are 256×256. The two sets of sequences generated by the system are XORed twice with the plaintext image to obtain the ciphertext image, as shown below. Figure 9 (b) Figure 9 (e) Figure 9 As shown in (h). Performing two XOR operations between the ciphertext image and the two sets of sequences yields the decrypted image, as shown below. Figure 9 (c) Figure 9 (f) Figure 9 As shown in (i).

[0087] Table 2 shows the mean square error, peak signal-to-noise ratio, and structural similarity index of the plaintext and ciphertext images in this embodiment. It can be seen that the encryption algorithm achieves effective encryption without compromising image quality.

[0088] Table 2: Quality Measurement Between Original and Cipher Images

[0089] Step 108: Utilize the transient characteristics of chaotic systems to encrypt image pixels using a dynamic key; utilize the stable segments of the chaotic sequence to perform row and column permutations and bitwise XOR operations on the pixels.

[0090] In this embodiment, a permutation index is generated using the preceding values ​​of the chaotic sequence, and the pixel rows and columns are randomly arranged. Subsequent sequence values ​​are then used to perform a bitwise XOR operation on the scrambled pixels. This is based on the strong randomness of the chaotic sequence during the transient phase of a chaotic system. Let the image pixel matrix be F. A transient segment is extracted from the chaotic sequence and XORed with the image pixels. In the stable segment of the chaotic sequence, the rows and columns of the image pixel matrix are permuted according to the sequence values. For example, the row swapping order is determined based on the values ​​of the chaotic sequence in the stable segment, swapping the i-th row with the j-th row. A similar operation is performed on the columns, and then a bitwise XOR operation is performed to further obfuscate the pixel values.

[0091] The pixel values ​​of the port inspection images in this embodiment contain rich information. By encrypting the pixels using the transient characteristics of chaotic systems and performing permutation and XOR processing on stable segments, the original arrangement and values ​​of the pixels can be scrambled, increasing the difficulty of image decryption. This further enhances the security and complexity of port inspection image encryption. Through the combination of multiple encryption operations, the encrypted image exhibits high randomness and unpredictability at the pixel level, thus better protecting the information security of the port.

[0092] Step 109: During decryption, the encryption conditions are reused to generate a dynamic key, and the diffusion and scrambling are performed in reverse.

[0093] In this embodiment, the decryption process is the reverse of the encryption process. First, based on the initial conditions used during encryption, a chaotic sequence is regenerated to obtain the same keystream as during encryption. Then, the bitwise XOR and row / column permutation operations performed during encryption are executed in reverse. For example, row and column permutations are performed in reverse to restore the pixel arrangement order before encryption to the matrix after permutation, and then the bitwise XOR operation is performed to obtain the original image pixel values.

[0094] At the port receiving end, the encrypted inspection images need to be restored to their original state for analysis and decision-making. Reusing the initial conditions to generate the same keystream ensures consistency between the encryption and decryption processes. Reverse diffusion and scrambling operations restore the encrypted image to its original state, enabling port management personnel to obtain accurate port facility information.

[0095] Step 110: Output Lyapunov heatmap, encryption / decryption comparison chart, and security indicators.

[0096] In this embodiment, the Lyapunov heatmap uses color to represent the maximum Lyapunov index value in different regions. The more vibrant the color (e.g., red), the larger the index value, and the more unstable the corresponding region. The encryption / decryption comparison image shows the original port inspection image, the encrypted image, and the decrypted image, providing a visual comparison of the changes before and after encryption. Security indicators include information entropy, key space size, and histogram uniformity.

[0097] This application also sets the correlation coefficient between adjacent pixels:

[0098] definition By making mandatory requirements This ensures that there is almost no linear correlation between adjacent pixels after encryption, making it impossible for attackers to infer the image content through statistical regularities. By completely destroying the spatial correlation between pixels, the encrypted image can resist correlation-based cryptanalysis. It protects the outline information of critical targets such as ships and containers.

[0099] As can be seen, the method in this embodiment uses Lyapunov heatmaps to help port managers intuitively understand the stability of different areas of the port. For example, red areas may indicate equipment or areas requiring special attention. The encryption / decryption comparison chart verifies the effectiveness of the encryption algorithm, ensuring the correctness of the encryption and decryption processes. It provides port managers with intuitive and quantitative analysis results, enabling users to understand the stability of port facilities, the security of the encryption system, and the accuracy of the encryption / decryption process, so as to take timely measures for facility maintenance and security management.

[0100] The following are embodiments of the port image analysis system based on random matrices provided in this disclosure. This system and the port image analysis method based on random matrices in the above embodiments belong to the same inventive concept. For details not described in detail in the embodiments of the port image analysis system based on random matrices, please refer to the embodiments of the port image analysis method based on random matrices described above.

[0101] The system includes: The image acquisition module is used to acquire port inspection images, convert the port inspection images to RGB format, and then perform normalization processing.

[0102] The matrix creation module is used to create two random matrices that match the size of the port inspection image.

[0103] The interpolation module is used to interpolate two random matrices using a bilinear interpolation function, estimating the value of a point based on the interpolation coefficients at the four nearest neighbors.

[0104] The chaos building module is used to construct chaotic systems. It combines interpolation functions and random matrices, adds perturbation parameters to enhance nonlinearity, and obtains the Jacobian matrix.

[0105] The feature calculation module is used to calculate the maximum Lyapunov exponent value using the eigenvalues ​​of the Jacobian matrix.

[0106] The parameter analysis module is used to confirm that the system is in a chaotic state if the maximum Lyapunov exponent value is greater than 0; it also plots the curve of the Lyapunov exponent changing over time to analyze the system's sensitive parameters.

[0107] The encryption processing module is used to perform encryption processing on port inspection images and generate dynamic keys based on random matrices and sensitive parameters.

[0108] The image processing module is used to encrypt image pixels using a dynamic key by utilizing the transient characteristics of chaotic systems; and to perform row and column permutations and bitwise XOR operations on pixels using stable segments of chaotic sequences.

[0109] The decryption processing module is used to generate a dynamic key by reusing the encryption conditions during decryption, and to reverse-engineer diffusion and scrambling.

[0110] The output module is used to output Lyapunov heatmaps, encryption / decryption comparison charts, and security indicators.

[0111] like Figure 10 As shown, this application also provides an electronic device, including a display module 103, a memory 102, a processor 101, and a computer program stored in the memory and executable on the processor 101. When the processor 101 executes the program, it implements the steps of a method for analyzing port images based on a random matrix.

[0112] In embodiments of the present invention, electronic devices include, but are not limited to, laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the embodiments described and / or claimed herein.

[0113] In this embodiment, processor 101 may be implemented using at least one of an Application-Specific Integrated Circuit (ASIC), a Programmable Logic Device (PLD), a Field-Programmable Gate Array (FPGA), a processor, a controller, a microcontroller, a microprocessor, or an electronic unit designed to perform the functions described herein. In some cases, such implementations may be implemented within a controller. For software implementations, implementations such as processes or functions may be implemented with separate software modules that allow the performance of at least one function or operation. The software code may be implemented by a software application (or program) written in any suitable programming language, and the software code may be stored in memory and executed by the controller.

[0114] The display module 103 is used to display information input by the user or information provided to the user. The display module 103 may include a display panel, which may be configured in the form of a liquid crystal display (LCD), an organic light-emitting diode (OLED), or the like.

[0115] The memory 102 can be used to store software programs and various data. The memory 102 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0116] The system for analyzing port images based on random matrices comprises the units and algorithmic steps of various examples described in conjunction with the embodiments disclosed herein. It can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can implement the described functions using different methods for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0117] This application also provides a storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method for analyzing port images based on a random matrix.

[0118] The storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example,, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of readable storage media include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0119] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for analyzing a port image based on a random matrix, characterized in that, The method comprises: Step 101: Obtain a port inspection image, convert the port inspection image into an RGB format, and then perform normalization processing; Step 102: Create two random matrices matching the size of the port inspection image; Step 103: Perform interpolation operation on the two random matrices using a bilinear interpolation function, and estimate the value of a point based on the interpolation coefficients at the four nearest neighbor points; Step 104: Construct a chaotic system, combine the interpolation function with the random matrix, add a perturbation parameter to enhance nonlinearity, and obtain a Jacobian matrix; Step 105: Calculate the maximum Lyapunov exponent value through the eigenvalues of the Jacobian matrix; Step 106: If the maximum Lyapunov exponent value is greater than 0, it is confirmed that the system is in a chaotic state; Draw a curve of the Lyapunov exponent changing with time, and analyze the sensitive parameters of the system; Step 107: Perform encryption processing on the port inspection image, and generate a dynamic key based on the random matrix and the sensitive parameters; Step 108: Use the transient characteristics of the chaotic system to encrypt the image pixels using the dynamic key; use the stable segment of the chaotic sequence to perform row and column permutation and bitwise XOR processing on the pixels; Step 109: When decrypting, generate a dynamic key under the encryption condition, and perform reverse diffusion and permutation; Step 110: Output the Lyapunov thermodynamic map, the encryption and decryption comparison chart, and the security index.

2. The analysis method of the port image based on the random matrix according to claim 1, wherein Step 101 further comprises separating the illumination component and the reflection component in the port inspection image based on adaptive histogram equalization; Detect the port inspection image based on a CNN model, mark the key targets of the port, and mark the detection area; Step 102 further comprises embedding the latitude and longitude grid information of the port map into the random matrix.

3. The analysis method of the port image based on the random matrix according to claim 1, wherein The step 104 of constructing the chaotic system further comprises: Configuring two random integer matrices F and G of 256x256, with a numerical range from 1 to 256; Performing interpolation operation on the integer matrices F and G using a bilinear interpolation function, and estimating the value of a new point based on the function values at the four nearest neighbor points; Constructing an interpolation calculation formula: （1） f (F( x , y )) and f (G( x , y )) are the bilinear interpolations of the matrix F and the matrix G, respectively, where x , y are the interpolation positions, f ( x , y ) are the interpolation functions; In performing bilinear interpolation, two initial iteration values are determined x and y , and the interpolation results z1 and z2 of the matrices F and G at the point ( x , y ) are calculated according to formula (1); The calculated interpolation results z1 and z2 are used to update the iteration values x and y ; Each iteration process is based on new x and y values to recalculate the interpolation results, thus generating two dynamically changing sequences, resulting in two sequences.

4. The analysis method of the port image based on the random matrix according to claim 1, wherein Step 103 further comprises defining block bilinear interpolation in combination with the scale difference of different targets in the port inspection image; Among them, the large-scale block of the block bilinear interpolation adopts low-frequency random disturbance to simulate the blurring effect of sea waves on the overall picture; The small-scale block of the block bilinear interpolation retains high-frequency detail parameters.

5. The analysis method of the port image based on the random matrix according to claim 1, wherein Step 105 further comprises: Let the state vector of the chaotic system be The recursive relation is defined based on the random matrix and bilinear interpolation as where x i (t) is the main chaotic component, which is used to drive the diffusion process of image pixel values; y i (t) is the auxiliary chaotic component, which is used to introduce multi-physical field coupling disturbance; i is the index variable, representing the row coordinate in the two-dimensional grid; t is the time step, representing the iteration number of the chaotic system; x i,j (n+1) is the value of the main chaotic component at the grid point (i, j) at time step n+1; y i,j (n+1) is the value of the auxiliary chaotic component at the grid point (i, j) at time step n+1; represents the local sensitivity index of the port facility topology, representing the sensitivity of the grid point to the initial conditions; is the value of the main chaotic component at the grid point (i, j) at time step n; is the value of the auxiliary chaotic component at the grid point (i, j) at time step n; is a random matrix element; The partial derivatives of F and G are taken separately to obtain the Jacobian matrix J, which is used in the subsequent Lyapunov exponent solution: .

6. The analysis method of the port image based on the random matrix according to claim 1, wherein The encryption processing in step 107 further comprises defining a key K=Ks⊕Kt⊕Kg; Where: Ks is an initial random matrix; Kt is a time stamp of inspection; Kg is a positioning coordinate.

7. The method of claim 3, wherein, In step 107, for the chaotic system, a set of initial data is randomly generated when interpolation iteration is performed x , y , the result after the first interpolation is calculated Xi , Yi ; The error range of the first interpolation result is determined using formula (2), and it is judged whether the result after each iteration reaches quasi-periodicity; In the iteration process, the number of quasi-periodicity after iteration is counted and analyzed, the maximum value, minimum value, average value, square difference and range of each group of data are recorded, and the statistical data are arranged into a table; （2）。 8. A system for analyzing port images based on random matrices, characterized in that, The system is used to implement the method of claim 1 to 7. The system comprises: An image acquisition module is configured to acquire the port inspection image, convert the port inspection image into an RGB format, and perform normalization processing; A matrix creation module is configured to create two random matrices matching the size of the port inspection image; An interpolation operation module is configured to perform interpolation operation on the two random matrices using a bilinear interpolation function, estimate the value of a point based on the interpolation coefficients at the four nearest neighbor points; A chaos construction module is configured to construct a chaotic system, combine the interpolation function with the random matrix, add a perturbation parameter to enhance nonlinearity, and obtain a Jacobian matrix; A feature calculation module is configured to calculate the maximum Lyapunov exponent value through the eigenvalue of the Jacobian matrix; A parameter analysis module is configured to confirm that the system is in a chaotic state if the maximum Lyapunov exponent value is greater than 0, draw a curve of the Lyapunov exponent changing with time, and analyze the sensitive parameters of the system; An encryption processing module is configured to perform encryption processing on the port inspection image, and generate a dynamic key based on the random matrix and the sensitive parameters; An image processing module is configured to use the transient characteristics of the chaotic system, use the dynamic key to encrypt the image pixels, use the stable segment of the chaotic sequence to perform row and column permutation and bitwise XOR processing on the pixels; A decryption processing module is configured to generate a dynamic key when decryption is performed under the encryption condition, and perform reverse diffusion and permutation. An output module is configured to output the Lyapunov thermodynamic map, the encryption and decryption comparison chart, and the security index.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the steps of the method of claim 1 to 7.

10. A storage medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to implement the steps of the method of claim 1 to 7.

Images