A hyperbolic wave extraction method and system for ground penetrating radar images

Abstract

The application discloses a hyperbolic curve extraction method based on peak point similarity fitting, which comprises the following steps: converting a GPR image into a time sequence for processing, constructing a dynamic window based on a wavelet mean line, and extracting peak points capable of identifying the features of a B-scan image; performing an opening-down peak point clustering operation by using improved DTW correlation between adjacent wave windows; and finally, in combination with the missing or repeated conditions between each type of point cluster, performing a peak point interpolation and curve fitting operation to identify a hyperbolic wave. In a real fuzzy image data set, the application can effectively identify the position and shape of the hyperbolic wave, thereby verifying the accuracy of the method. The application is increasingly widely applied in the fields of military, geological exploration, underground landfill, archaeology and the like, and the result of target identification can be used to determine the conditions of underground targets and achieve breakthrough progress.

Description

Technical Field

[0001] This invention belongs to the field of ground-penetrating radar image processing technology, and particularly relates to a method and system for extracting hyperbolic waves from ground-penetrating radar images. Background Technology

[0002] Ground penetrating radar (GPR) is a non-destructive detection technology that uses antennas to transmit and receive high-frequency electromagnetic waves to detect the distribution of underground media, scan underground objects and soil layers to determine their internal structure or location. Compared with other conventional underground detection technologies, GPR is increasingly widely used in military, geological exploration, underground landfills, archaeology, and other fields, and has achieved breakthrough progress. Extracting hyperbolic waves from GPR images helps analyze the location and internal structure of underground targets, thus enabling efficient detection tasks. However, in practical applications, noise or clutter generated by surface and underground non-target bodies, media inhomogeneity, and inter-wave interactions affects the subsequent extraction of hyperbolic waves from GPR images. Therefore, accurately extracting hyperbolic waves from GPR images is a challenging task.

[0003] Many scholars have devoted considerable research to the problem of hyperbolic wave extraction from ground-penetrating radar (GPR) images. One approach utilizes the HOG feature technique from computer vision to address the detection of landmines and explosives in GPR data. This method provides a stable classifier and pre-screening tool for identifying hyperbolic targets. However, the performance of this algorithm is affected when the processed images contain noise or clutter. When using deep learning for hyperbolic wave extraction, the selection of image samples and the labeling of targets in the training samples are also significant challenges. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a hyperbola extraction method based on peak point similarity fitting. This method involves key point extraction and hyperbola fitting, and has good results.

[0005] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0006] A method for extracting hyperbolic waves from ground-penetrating radar images includes the following steps:

[0007] Acquire ground-penetrating radar images and convert them into a time-series horizontal dataset;

[0008] For each sequence in the aforementioned time series horizontal dataset, multiple sub-sequences are obtained based on a dynamic window, and peak points are extracted.

[0009] Search for multiple peaks located at the top horizontal position of the hyperbola, denoted as flat points. Starting from the flat points, search for peaks in adjacent sequences that satisfy the direction of the downward-opening hyperbola to obtain a set of point clusters.

[0010] Interpolation and curve fitting are performed on the point cluster set to obtain a hyperbolic wave.

[0011] Furthermore, the method for peak extraction is as follows:

[0012] For the wave whose peak is to be extracted, the mean is calculated based on the sampled data of the wave to obtain the mean line;

[0013] The distance between two adjacent intersection points in the depth direction is used as the length of the dynamic window, and the maximum value of the subsequence between the intersection points is taken as the width of the dynamic window, while the dynamic window is kept above the wavelet mean line.

[0014] Peak point extraction is performed based on the dynamic window.

[0015] Furthermore, peak extraction based on the dynamic window includes:

[0016] If there are more than two peaks in a certain dynamic window, the maximum value is taken as the peak of that segment; if all values ​​in a certain dynamic window are equal, the value at the middle position is taken plus the set value.

[0017] Furthermore, the process of obtaining the point cluster set is as follows:

[0018] Search for multiple peaks located at the top horizontal position of the hyperbola, denoted as flat points, and include them in a point cluster set;

[0019] Starting from the flat points in the point cluster set, find the subsequences in the adjacent sequences whose similarity to the subsequences containing these peak points exceeds a set threshold, and add the corresponding peak points to the point cluster set. Repeat this step until there are no peak points that meet the conditions.

[0020] Furthermore, a dynamic time warping method is used to measure the similarity between the two subsequences:

[0021] Find the longest common substring u of the two subsequences s1 and s2;

[0022] The similarity distance PDist(W) between the two subsequences s1 and s2 is:

[0023]

[0024]

[0025] Where σ represents the decay factor and len(s) represents the length of the subsequence.

[0026] Furthermore, the point cluster set is interpolated using a cubic spline function.

[0027] Furthermore, the curve fitting employs a linear regression method.

[0028] One or more embodiments provide a hyperbolic wave extraction system for ground-penetrating radar images, comprising:

[0029] The time series acquisition module is used to acquire ground penetrating radar images and convert the ground penetrating radar images into a time series horizontal dataset.

[0030] The peak extraction module is used to extract peaks for each wave in the time series horizontal dataset based on a dynamic window.

[0031] The similarity clustering module searches for multiple peaks located at the top horizontal position of the hyperbola, denoted as flat points. Starting from these flat points, it searches for peaks in adjacent sequences that satisfy the direction of the downward-opening hyperbola to obtain a set of point clusters.

[0032] The curve fitting module is used to interpolate and fit curves to the point cluster set to obtain a hyperbolic wave.

[0033] One or more embodiments provide an electronic device 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 hyperbolic wave extraction method for ground penetrating radar images.

[0034] One or more embodiments provide a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the described hyperbolic wave extraction method for ground-penetrating radar images.

[0035] The above technical solutions have the following technical effects:

[0036] This invention proposes a hyperbola extraction method based on peak similarity fitting. The method converts GPR images into time series processing, constructs a dynamic window based on the wavelet mean line, and extracts peaks that can identify the features of B-scan images. It uses the improved DTW correlation between adjacent wavelet windows to perform downward-opening peak clustering. Finally, considering the missing or repeated cases among each cluster, peak interpolation and curve fitting operations are performed to identify hyperbolic waves.

[0037] By constructing dynamic windows, each data channel (A-scan) can be dynamically divided into multiple sub-windows. Feature extraction is performed on the dynamic windows of the sequence using a "peak-to-region" approach. Improvements to the dynamic time warping method leverage the high similarity between hyperbolic wave sequences to ensure the algorithm matches more similar sub-sequences, effectively improving the accuracy of clustering results. Furthermore, adding a decay factor during similarity calculation enhances the performance of metric computation. Interpolating the positions of nearby points using cubic spline functions reflects the trend changes of the current point as closely as possible while ensuring smoothness between connection points, avoiding jagged edges during fitting. Attached Figure Description

[0038] Figure 1 This is a flowchart of the hyperbolic wave extraction method for radar ground-penetrating images in one or more embodiments of the present invention;

[0039] Figure 2 These are B-scan images obtained in embodiments of the present invention;

[0040] Figure 3 This is a dynamic window view in the embodiments of the present invention;

[0041] Figure 4 This is a window peak extraction image in an embodiment of the present invention;

[0042] Figure 5 This is a schematic diagram of hyperbolic wave classification in the coordinate system according to an embodiment of the present invention;

[0043] Figure 6(a) is a schematic diagram of the hyperbolic wave clustering search direction in an embodiment of the present invention;

[0044] Figure 6(b) is a schematic diagram of the hyperbolic wave clustering search process in an embodiment of the present invention;

[0045] Figure 7 This is an explanatory diagram of similarity calculation in an embodiment of the present invention;

[0046] Figure 8 This is a peak point clustering result diagram in an embodiment of the present invention;

[0047] Figure 9 This is a schematic diagram of three types of hyperbolic wave crossings in an embodiment of the present invention;

[0048] Figure 10 This is a hyperbolic waveform fitting diagram in an embodiment of the present invention;

[0049] Figure 11 This is a hyperbolic waveform fitting diagram in an embodiment of the present invention;

[0050] Figure 12 This is a hyperbolic waveform fitting diagram in an embodiment of the present invention;

[0051] Figure 13 This is a hyperbolic waveform fitting diagram in an embodiment of the present invention;

[0052] Figure 14 This is a hyperbolic waveform fitting diagram in an embodiment of the present invention;

[0053] Figure 15 This is a hyperbolic waveform fitting diagram from an embodiment of the present invention. Detailed Implementation

[0054] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0055] like Figure 1 As shown, a hyperbolic wave extraction method for radar ground-penetrating images based on peak similarity fitting includes the following steps:

[0056] Step 1: Acquire ground-penetrating radar images and convert them into a time-series horizontal dataset;

[0057] Specifically, the mathematical model for the ground-penetrating radar time series data is described by a finite set of triplets (h, l, v) to represent a B-scan image of size n×m generated by ground-penetrating radar:

[0058]

[0059] Where h represents the temporal variation of A-scan data along the depth direction for a single channel, l represents the temporal variation of A-scan data along the lateral scanning direction, and v represents the detection data recorded under a given depth direction and lateral scanning direction.

[0060] Given a ground-penetrating radar time series lateral dataset P L ={L1,L2,…,L m-1 ,L m}, where L j The pixel value sequence representing the j-th waveform is denoted as L. j ={v 1j ,v 2j ,…,v n-1j ,v nj}, v nj This represents the pixel value corresponding to the j-th waveform with a depth distance of n sampling points.

[0061] Step 2: For each sequence in the time series horizontal dataset, obtain multiple subsequences based on a dynamic window and extract peak points;

[0062] like Figure 2 The image shown is a B-scan image from the experimental test. Figure 3 It is a dynamic window view. Figure 4 This is a peak extraction image. The peak extraction process is as follows:

[0063] Step 2.1: Take the mean of the sampled records of the j-th wave (or sequence) in the horizontal time series dataset. The process involves determining the dynamic window for each wave using the mean line. The specific steps are as follows:

[0064] Step 2.1.1: Take the mean of the sampled records of the j-th wave in the horizontal time series dataset. The processing and calculation methods are as follows:

[0065]

[0066]

[0067] Step 2.1.2: Take the set Q of intersection points between the current j-th waveform and its wavelet mean line. Determine a subsequence s between adjacent intersection points. The total number of windows for the j-th waveform is S, calculated as follows:

[0068]

[0069] Step 2.1.3: Use the distance x between two adjacent intersection points in the depth direction as the length of the dynamic window, and take the maximum value y of the subsequence between the intersection points as the width of the dynamic window.

[0070] Step 2.1.4: Due to the special nature of radar data, only the dynamic window above the wavelet mean line is retained.

[0071] Select a 128×128 B-scan plot, such as... Figure 2 As shown. Wavelet sampling is performed at intervals of 5, and the wavelets identified by the dynamic window are arranged according to the time sequence during the transverse scan, as follows. Figure 3 As shown.

[0072] Step 2.2: Select the peak point that best represents the information of the current subsequence. In this step, representative peak points are obtained using the concept of "representing regions with points".

[0073] The peak set W is defined as:

[0074]

[0075] Where L represents a sequence in the current ground-penetrating radar time series being processed, i represents a window in the current sequence, and r represents the number of peaks in the subsequence of the current window.

[0076] If the Lth jThe positions of more than two peak points in the $i$-th dynamic window of the strip wave Take the maximum value as the peak point of this segment. If the values in the current window are all equal, take the data value at the middle position plus $e$, and the value of $e$ is adjusted according to specific experiments. In this paper, $e = 1$ is used, and the finally determined peak point represents the information of the data in the current dynamic window.

[0077] As Figure 4 shown, intuitively, not only can the region of the hyperbolic wave be clearly distinguished, but also the clutter that does not belong to the hyperbolic wave in the original image can be recognized.

[0078] Step 3: Search for multiple peak points located at the horizontal position of the top of the hyperbola, denoted as flat points. Starting from these peak points, search for the peak points in the adjacent sequence that satisfies the downward-opening hyperbola direction to obtain a point cluster set. Specifically, use the peak points obtained in Step 2 to judge the position of the opening direction, that is, the top of the downward-opening hyperbola. Search according to the opening direction, and perform similarity measurement on the subsequence corresponding to the peak point at the top of the downward-opening hyperbola and the subsequence of the adjacent waveform located within the dynamic window to obtain a subsequence with high similarity, and obtain the corresponding peak points, so as to cluster the peak points with high similarity and obtain the set of hyperbolic wave points to be fitted.

[0079] Establish the hyperbolic wave shape description on the coordinate system, as Figure 5 shown, and define the concepts of point segment, flat point, forward hyperbolic wave and reverse hyperbolic wave.

[0080] Point segment: Given a data set $D$, which contains $n$ subsets $\{d_1, d_2, \ldots, d_n\}$, for any $1 < i \leq n$, if there exist two consecutive subsets $d_i, d_{i + 1}$, then $\{d_i, d_{i + 1}\}$ is called a point segment of $D$. n}, for any $1 < i \leq n$, if there exist two consecutive $d_i, d_{i + 1}$ i , $d_{i + 2}$ i+1 of subsets, then $\{d_i, d_{i + 1}, d_{i + 2}\}$ is called a point segment of $D$. i , $d_{i + 2}$ i+1} is called a point segment of $D$.

[0081] Flat point: Given a data set $D$, which contains $n$ subsets $\{d_1, d_2, \ldots, d_n\}$, for any $1 < i - k \leq \ldots \leq i < n$, if there exist $k$ consecutive equal subsets $\{d_i, \ldots, d_{i + k - 1}\}$, then $\{d_i, d_{i + k}\}$ is called a flat point of $D$. From the peak point extraction result of the B-scan image, it can be seen that the top of the hyperbolic wave is composed of a group of horizontal pixel points in the peak point graph. Therefore, by defining the flat point, the starting position of the hyperbolic wave clustering can be determined. n}, for any $1 < i - k \leq \ldots \leq i < n$, if there exist $k$ consecutive equal $\{d_i, \ldots, d_{i + k - 1}\}$ i-k ... $d_{i + k - 1}$ i} of subsets, then $\{d_i, d_{i + k}\}$ is called a flat point of $D$. i , $d_{i + k}$ i+1} is called a flat point of $D$. Through the peak point extraction result of the B-scan image, it can be seen that the top of the hyperbolic wave is composed of a group of horizontal pixel points in the peak point graph. Therefore, by defining the flat point, the starting position of the hyperbolic wave clustering can be determined.

[0082] Based on the concept of forward and reverse hyperbolic waves defined by coordinate quadrants, and according to the characteristics of hyperbolic waves, the hyperbolic search area is defined in quadrants III and IV with a 15° inclination between adjacent coordinate axes. The α1α2 and β1β2 set in quadrants III and IV can determine the range of downward search, i.e. the α and β regions.

[0083] Forward hyperbolic wave: Given a dataset D, assume there exists E = {d i-k …d i Let} be a k-squared subset of points D. Let LE and RE represent the left and right neighboring point sets of E, respectively. If LE∈β, RE∈α, and α and β refer to the open regions bounded by α1 and α2 in quadrant IV and by β1 and β2 in quadrant III, respectively, then the shape formed by LE, E, and RE is called a positive hyperbolic wave. Figure 5 As shown in Figure (a).

[0084] Inverse hyperbolic wave: Given a dataset D, assume there exists E = {d i-k …d i Let} be a k-squared subset of D, and let LE and RE represent the left and right neighboring point sets of E, respectively. If LE∈θ, RE∈γ, and γ and θ refer to the open regions bounded by γ1 and γ2 in quadrant I and by θ1 and θ2 in quadrant II, respectively, then the shape formed by LE, E, and RE is called an inverse hyperbolic wave. Figure 5 As shown in Figure (b).

[0085] Step 3.1: Search for the peak point located at the horizontal position at the top of the hyperbola, i.e., the flat point, and add it to the point cluster set;

[0086] Step 3.2: Based on the "downward opening" shape characteristic of hyperbolic waves, dynamically select the data of the two subsequences to be used for similarity calculation; specifically, measure the similarity between the subsequence containing the flat point and the subsequences in the adjacent sequence.

[0087] Step 3.3: Similarity measurement based on the improved dynamic time bending method;

[0088] Two time series that need to be compared for similarity may not be of equal length. Euclidean distance can only be used when they are equal, while Dynamic Time Warping (DTW) is a similarity metric that can better match and map two time series by bending the time axis.

[0089] Based on dynamic programming, construct the distance matrix ds[i][j] between subsequences s1 and s2, where ds[i][j] represents the square of the similarity distance between sequences s1[0:i] and s2[0:j], and we have:

[0090]

[0091] Define the similarity distance between two time series as Dist(W), then we have:

[0092]

[0093] Where len(s1) and len(s2) represent the lengths of subsequences s1 and s2, respectively;

[0094] The characteristics of the same reflected wave group on adjacent recording channels of ground penetrating radar remain unchanged. This characteristic is called the similarity of reflected waveforms. According to this characteristic, the values ​​belonging to hyperbolic wave sequences have a high degree of similarity. In order to extract hyperbolic waves more accurately, an improvement based on DTW is made, which is called Public Dynamic Time Warping (PDTW).

[0095] In the common dynamic time warping method, the distance matrix ds[i][j] between subsequences s1 and s2 is constructed based on dynamic programming, and a decay factor σ is determined to improve the performance of the metric calculation. Then, the similarity distance PDist(W) between the two sequences can be expressed as:

[0096]

[0097]

[0098] Here, len(s) represents the length of the subsequence, and u represents the longest common substring between subsequences s1 and s2. When finding the longest common substring, a maximum standard deviation offset tolerance is set to ensure that data within a certain standard deviation can also be considered as part of the common substring.

[0099] The more similar two subsequences are, the longer their common substring will be, and therefore the smaller the value of the attenuation factor σ will be. Changing the attenuation factor ensures the algorithm can match more similar subsequences, effectively improving the accuracy of the clustering results.

[0100] Step 3.4: For subsequences whose similarity exceeds a set threshold, obtain the corresponding peak points and include them in the point cluster set to realize similarity clustering of the peak point set based on shape features;

[0101] Step 3 above is the process of obtaining a set of point clusters belonging to hyperbolic waves by constraining and similaring shape features.

[0102] By searching for peaks in adjacent sequences and checking for segments that satisfy the condition of flat points, the location for determining the direction of the opening can be found. In a positive hyperbola, the set of flat points that opens downwards is called the "top" of the hyperbola, and the "tail" represents the region extending to the left and right from the top. In the ideal case shown in Figure 6(a), when the top of the hyperbola is found, the length range of the flat points [s1, s2] is recorded. k The value is the length of the flat point near the origin. Using the location of the flat point as the cluster center, searches are performed in the α region of quadrant IV and the β region of quadrant III, following the "search and cluster simultaneously" principle to find the nearest subsequence of the time series data. The search process is shown in Figure 6(b). In the cluster search graph, the number of boxes represents the number of windows for similarity calculation of the sequences. The order of the boxes from left to right corresponds to the order of the sequence windows from top to bottom. Dark-marked boxes indicate the obtained window positions.

[0103] By comparing subsequence values ​​from adjacent columns, fast and accurate similarity matching is achieved. Figure 7 In the middle, column L i The subsequence and the subsequence from column L i+1 The subsequence is used for PDTW calculation. In the coordinate system, the peak search range is defined as the α region and the β region, thus obtaining column L. i+1 The subsequence window within this region determines the number of subsequences for correlation calculation. During the search, peaks at the top and bottom that meet the conditions are added to the newly established cluster. Starting from these newly added peaks, the search continues to find the left tail branch in the left subtree or the right tail branch in the right subtree. Peaks are added to the new cluster only when the conditions are met. The search ends when the conditions are no longer met, no data points are found, or the data points deviate from the correct direction. Figure 8 The image shown illustrates the final peak point clustering results for Example 1.

[0104] When an image contains multiple hyperbolic waves, they may intersect. Hyperbolic waves are described using lines, and the intersection points of three types of hyperbolic waves are analyzed using points, such as... Figure 9 As shown. Figure 9 As shown in Figure (a), the λ-type intersection point indicates that the tail of the hyperbola is at the top of another hyperbola. Starting from the flat point, the search for the tail is performed along the left and right sides towards the α and β regions respectively, according to FDTW. When the search reaches the flat point of the next hyperbola, the search conditions are not met, and the search stops. Figure 9 The white box shown in Figure (g) indicates the location where the search stops, and the hyperbolic wave is eventually clustered into two point clusters.

[0105] like Figure 9As shown in Figure (e), the type indicates that at least two branches of the hyperbola intersect. To solve this problem, when a reverse hyperbolic wave is found, a flat point region is marked, and the search proceeds upwards and downwards from this region. When searching downwards, if the characteristics of a forward hyperbolic wave are met, and when searching upwards, the previously marked flat point is found, then the type can be determined to be an x-type hyperbola. Figure 9 As shown in Figure (h), the search begins with the intersection point as the origin of the coordinate system during the clustering process. Points belonging to the β region are clustered into the hyperbola on the right, and points belonging to the α region are clustered into the hyperbola on the left. This step can further verify the intersection position and reduce the error rate of hyperbolic wave recognition.

[0106] like Figure 9 As shown in Figure (c), the V-shape represents the intersection of the tails of two hyperbolas, similar to the X-shape, but without any downward points at the intersection. The search follows the X-shaped hyperbola method, but stops after preserving the pixels within the overlapping white box between the tails at the intersection. Figure 9 As shown in Figure (i).

[0107] Step 4: Use cubic spline interpolation and linear regression for fitting. The specific interpolation steps are shown below. Figure 2 The final experimental fitting results are as follows Figure 10 As shown, in addition Figure 11 , Figure 12 , Figure 13 , Figure 14 , Figure 15 The final fitting results of different ground-penetrating radar images processed using this invention are shown in the figure.

[0108] Shape-based similarity clustering algorithms can eliminate point clusters that do not conform to the positive hyperbolic curve characteristics in the clustering results. However, due to noise in GPR images during environmental detection, peaks identified in the preprocessing may be missed or redundant, leading to fitting bias and overfitting issues when fitting the hyperbola. To solve these problems, it is necessary to further extend the interpolation process based on clustering. The specific steps are as follows:

[0109] Step 4.1: Use the hyperbolic wave values ​​of the clustering results as input;

[0110] Step 4.2: Perform interpolation using a cubic spline function within the known numerical range;

[0111] In step 4.2, the spline function belongs to piecewise smooth interpolation. The basic idea is to approximate each small interval formed by two adjacent nodes with a low-order polynomial, and to ensure smoothness at the connection points of each node. The specific process is as follows:

[0112] The column sets where the peak points are located in the point clusters obtained by clustering are all composed of adjacent waves in the given ground penetrating radar time series horizontal data set P L ={L1, L2, …, L m-1 , L m}. Therefore, for the i-th downward-opening point cluster {d1, d2…d t}, where 3 < t ≤ n, it is used as a data group to be interpolated. F i (d) is a cubic spline interpolation function defined on the interval [1, t]. On any interval d ∈ [d j , d j+1 , j ∈ 1, 2, …, t, all interpolation data are:

[0113] F i,j (d) = a j d 3 + b j d 2 + c j d + e j

[0114] The cubic spline F i,j (d) equation should satisfy:

[0115] (1) On each sub-interval [d j , d j+1 , F i,j (d) is a cubic equation;

[0116] (2) Satisfy the interpolation condition, that is, F i,j (d) = y(d);

[0117] (3) The curve is smooth, that is, F i,j (d), F i,j ′(d), F i,j ″(d) are continuous.

[0118] It can be seen from formula (11) that there are four unknowns [a j , b j , c j , e j in each small interval. There are t small intervals, so there are 4n unknowns. To solve these unknowns, we need 4n equations to solve.

[0119] F i,j (d) = a j (d - d j ) 3 + b j (d - d j ) 2 + c j (d - d j)+e j

[0120] F i,j ′(d)=3a j (dd j ) 2 +2b j (dd j )+c j

[0121] F i,j "(d)=6a j (dd j )+2b j

[0122] By F i,j (d j )=y j It can be seen that e j =y j ; use h j =d j+1 -d j Indicates the step size;

[0123] By F i,j (d j+1 )=y j+1 It can be seen that a j h j 3 +b j h j 2 +c j h j +e j =y j+1

[0124] By F i,j ′(d j+1 ) = F i,j+1 ′(d j+1 It can be seen that 3a j h j 2 +2b j h j +c j =c j+1

[0125] By F i,j "(d j+1 ) = F i,j+1 "(d j+1 It can be seen that 6a j h j +2b j =2b j+1

[0126] Set mi =F i,j+1 "(d j+1 ) = 2b j+1 Formula (17) can be rewritten as 6a j h j +m i =m i+1 have to

[0127] a j ,b j ,e j Substituting into formula (15) yields a j ,b j ,c j ,e j Substituting into formula (16) yields

[0128] Combining the natural boundary conditions, we can obtain that m0=0,m n =0

[0129]

[0130] The coefficient matrix on the left is a strictly diagonal matrix, therefore the system of equations has a unique solution. By solving this system, we can obtain the solution for the i-th downward-opening point cluster {d1, d2…d… t Data based on cubic spline functions in}

[0131] Step 4.3: Using linear regression, the distance between the interpolated data and the top and bottom edges is used as input for the final fitting operation.

[0132] Example 2

[0133] The purpose of this embodiment is to provide a hyperbolic wave extraction system for ground-penetrating radar images, the system comprising:

[0134] The time series acquisition module is used to acquire ground penetrating radar images and convert the ground penetrating radar images into a time series horizontal dataset.

[0135] The peak extraction module is used to extract peaks for each wave in the time series horizontal dataset based on a dynamic window.

[0136] The similarity clustering module searches for multiple peaks located at the top horizontal position of the hyperbola, denoted as flat points. Starting from these flat points, it searches for peaks in adjacent sequences that satisfy the direction of the downward-opening hyperbola to obtain a set of point clusters.

[0137] The curve fitting module is used to interpolate and fit curves to the point cluster set to obtain a hyperbolic wave.

[0138] Example 3

[0139] The purpose of this embodiment is to provide an electronic device.

[0140] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the hyperbolic wave extraction method for ground-penetrating radar images as described in Embodiment 1.

[0141] Example 4

[0142] The purpose of this embodiment is to provide a computer-readable storage medium.

[0143] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the hyperbolic wave extraction method for ground-penetrating radar images as described in Embodiment 1.

[0144] The steps and methods involved in Embodiments 2 to 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0145] This invention discloses a hyperbola extraction method based on peak similarity fitting. The method includes converting a GPR image into a time series, constructing a dynamic window based on the wavelet mean line, and extracting peaks that identify B-scan image features. It calculates the PDTW correlation between adjacent wavelet windows and performs peak clustering of positive hyperbolic waves. Finally, considering missing or repetitive points within each cluster, it performs peak interpolation and curve fitting to identify the hyperbola. This invention effectively identifies the location and morphology of hyperbolic waves in real-world fuzzy image datasets, verifying the accuracy of the method. The application of this invention in military, geological exploration, underground landfills, and archaeology fields is increasingly widespread. The results of target recognition can be used to determine the status of underground targets, achieving breakthrough progress.

[0146] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0147] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for extracting hyperbolic waves from ground-penetrating radar images, characterized in that, Includes the following steps: Acquire ground-penetrating radar images and convert them into a time-series horizontal dataset; For each sequence in the aforementioned time series horizontal dataset, multiple sub-sequences are obtained based on a dynamic window, and peak points are extracted. The method for peak extraction is as follows: For the wave whose peak is to be extracted, the mean is calculated based on the sampled data of the wave to obtain the mean line; The distance between two adjacent intersection points in the depth direction is used as the length of the dynamic window, and the maximum value of the subsequence between the intersection points is taken as the width of the dynamic window, while the dynamic window is kept above the wavelet mean line. Peak point extraction is performed based on the dynamic window; Search for multiple peaks located at the top horizontal position of the hyperbola, denoted as flat points. Starting from these flat points, search for peaks in adjacent sequences that satisfy the direction of the downward-opening hyperbola to obtain a set of point clusters. An improvement based on DTW, denoted as Common Dynamic Time Warping (PDTW), uses variations in the decay factor to ensure the algorithm can match more similar subsequences. The dynamic time warping method is used to measure the similarity between two subsequences. Solve the two subsequences Longest common substring ; The two subsequences The similarity distance PDist(W) is: in, Indicates the attenuation factor. Indicates the length of the subsequence. This represents the longest common substring between subsequences s1 and s2; Interpolation and curve fitting are performed on the point cluster set to obtain a hyperbolic wave.

2. The hyperbolic wave extraction method for ground-penetrating radar images as described in claim 1, characterized in that, Peak extraction based on the dynamic window includes: If there are more than two peaks in a certain dynamic window, the maximum value is taken as the peak of the subsequence; if all values ​​are equal in a certain dynamic window, the value at the middle position is taken plus the set value.

3. The hyperbolic wave extraction method for ground-penetrating radar images as described in claim 1, characterized in that, The process of obtaining the point cluster set is as follows: Search for multiple peaks located at the top horizontal position of the hyperbola, denoted as flat points, and include them in a point cluster set; Starting from the peaks in the point cluster set, find the subsequences in the adjacent sequences whose similarity to the subsequences containing these peaks exceeds a set threshold, and add the corresponding peaks to the point cluster set. Repeat this step until there are no more peaks that meet the conditions.

4. The hyperbolic wave extraction method for ground-penetrating radar images as described in claim 1, characterized in that, The point cluster set is interpolated using a cubic spline function.

5. The hyperbolic wave extraction method for ground-penetrating radar images as described in claim 1, characterized in that, The curve fitting was performed using a linear regression method.

6. A hyperbolic wave extraction system for ground-penetrating radar images, characterized in that, include: The time series acquisition module is used to acquire ground penetrating radar images and convert the ground penetrating radar images into a time series horizontal dataset. The peak extraction module is used to extract peaks for each wave in the time series horizontal dataset based on a dynamic window. The method for peak extraction is as follows: For the wave whose peak is to be extracted, the mean is calculated based on the sampled data of the wave to obtain the mean line; The distance between two adjacent intersection points in the depth direction is used as the length of the dynamic window, and the maximum value of the subsequence between the intersection points is taken as the width of the dynamic window, while the dynamic window is kept above the wavelet mean line. Peak point extraction is performed based on the dynamic window; The similarity clustering module searches for multiple peaks located at the top horizontal position of the hyperbola, denoted as flat points. Starting from these flat points, it searches for peaks in adjacent sequences that satisfy the direction of the downward-opening hyperbola to obtain a set of point clusters. An improvement based on DTW, denoted as Common Dynamic Time Warping (PDTW), uses variations in the decay factor to ensure the algorithm can match more similar subsequences. The dynamic time warping method is used to measure the similarity between two subsequences. Solve the two subsequences Longest common substring ; The two subsequences The similarity distance PDist(W) is: in, Indicates the attenuation factor. Indicates the length of the subsequence. This represents the longest common substring between subsequences s1 and s2; The curve fitting module is used to interpolate and fit curves to the point cluster set to obtain a hyperbolic wave.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the hyperbolic wave extraction method for ground-penetrating radar images as described in any one of claims 1-5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the hyperbolic wave extraction method for ground penetrating radar images as described in any one of claims 1-5.

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